Discrete choice in marketing through the lens of rational inattention

Tu lo, Se gey; Fina, Ma eo; Kasinge , Johannes; Laghaie, A ash; O e , Thomas
A icle — Published Ve sion
Disc e e choice in ma ke ing h ough he lens o a ional
ina en ion
Quan i a i e Ma ke ing and Economics
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Tu lo, Se gey; Fina, Ma eo; Kasinge , Johannes; Laghaie, A ash; O e , Thomas
(2025) : Disc e e choice in ma ke ing h ough he lens o a ional ina en ion, Quan i a i e
Ma ke ing and Economics, ISSN 1573-711X, Sp inge US, New Yo k, NY, Vol. 23, Iss. 1, pp. 45-104,
h ps://doi.o g/10.1007/s11129-025-09292-9
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/323528
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h p://c ea i ecommons.o g/licenses/by/4.0/
Quan i a i e Ma ke ing and Economics (2025) 23:45–104
h ps://doi.o g/10.1007/s11129-025-09292-9
Disc e e choice in ma ke ing h ough he lens o a ional
ina en ion
Se gey Tu lo1·Ma eo Fina1·Johannes Kasinge 2,3 ·A ash Laghaie4·
Thomas O e 1,4
Recei ed: 10 Augus 2023 / Accep ed: 24 Decembe 2024 / Published online: 6 Feb ua y 2025
BSe gey Tu lo
[email p o ec ed]
Ma eo Fina
[email p o ec ed]
Johannes Kasinge
j.kasinge @ ilbu guni e si y.edu
A ash Laghaie
a ash.laghaie@no asbe.p
Thomas O e
[email p o ec ed]
1Johann Wol gang Goe he Uni e si y F ank u , F ank u , Ge many
2Tilbu g School o Economics and Managemen , Tilbu g Uni e si y, Tibu g, Ne he lands
3Leibniz Ins i u e o Financial Resea ch (SAFE), F ank u , Ge many
4No a School o Business and Economics, Ca ca elos, Po ugal
123
© The Au ho (s) 2025
Abs ac
Models de i ed om andom u ili y heo y ep esen he wo kho se me hods o lea n
abou consume p e e ences om disc e e choice da a. Howe e , a la ge body o
li e a u e documen s a ious beha io al pa e ns ha canno be cap u ed by basic an-
dom u ili y models and equi e di e en non-uni ied adjus men s o accommoda e
hese pa e ns. In his a icle, we discuss s a egies how o apply a ional ina en ion
heo y—which explains a la ge a ie y o such depa u es— o he analysis o dis-
c e e choice among mul iple al e na i es desc ibed along mul iple a ibu es. We i s
e iew exis ing applica ions ha make es ic i e belie assump ions o ob ain choice
p obabili ies in closed mul inomial logi o m. We hen p opose a model ha allows
o gene al consume belie s and demons a e i s empi ical iden i ica ion. Fu he , we
illus a e how his model na u ally mo i a es s ylized empi ical esul s ha a e ha d
o econcile om a andom u ili y pe spec i e.
Keywo ds Choice modeling ·Ra ional ina en ion ·Conjoin analysis ·
Disc e e choice expe imen s
JEL Classi ica ion C00 ·C35 ·D83 ·M31
46 S. Tu lo e al.
1 In oduc ion
Disc e e choice models based on a ional ina en ion (RI) heo y a e becoming popu-
la in economics and ma ke ing o s udying consume choices and p e e ences when
in o ma ion p ocessing is limi ed bu adap i e. This a icle demons a es how o apply
hese models in a ious mul i-a ibu e, mul i-al e na i e (MAMA) con ex s. Unlike
he adi ional andom u ili y model (RUM), RI-based choice models p o ide a uni-
ied amewo k o explain phenomena like conside a ion se s, s ake sensi i i y, and
b and-speci ic p ice esponses, which p e iously equi ed ad-hoc adjus men s o he
RUM. This a icle aims o suppo applied esea che s by: i s , aising awa eness o
he po en ial o disc e e choice models unde RI; second, ou lining he s eps o imple-
men ing RI o empi ical esea ch; and hi d, cla i ying he s eng hs and limi a ions
o di e en implemen a ions.
Based on ounda ional ideas om psychology (e.g., Simon & Newell, 1971), a io-
nal ina en ion heo y, in oduced by Sims (2003) in mac oeconomics, sugges s ha
decision-make s (DMs) ace cogni i e limi a ions and, he e o e, do no ake in all
a ailable in o ma ion when making choices. DMs ecognize hei cogni i e limi a ions
and s a egically decide how much and wha ype o cos ly in o ma ion o p ocess in
each decision scena io. RI sugges s ha DMs adjus hei p ocessing e o s based
on p ominen , accessible aspec s o a choice ask, which shape hei p io belie s
abou unknown ac o s a ec ing u ili y. The adap i e and pa ial in o ma ion p ocess-
ing implied by RI mo i a es a ich se o beha io s, e en wi h s anda d addi i ely
sepa able u ili y.
Unde RI, p obabilis ic choice ollows om cos ly and hus impe ec p ocessing
o in o ma ion, i.e., om DMs’ esidual unce ain y abou wha he u ili y maximiz-
ing choice al e na i e is. In con as , he RUM by McFadden (1974) de i es choice
p obabili ies by assuming ha he DM ac s on a la ge in o ma ion se han obse ed
by he analys . Unlike RUMs, RI choice models can explain choices om MAMA se s
wi hou assuming ha only he decision-make obse es ce ain u ili y ac o s. This
aligns wi h ea lie esea ch ha explained andomness in choice h ough cogni i e
p ocesses (e.g., Thu s one, 1927; Quand , 1956; Lou ie e e al., 1999). RI adds o his
li e a u e by o e ing a mic o- ounda ion o p obabilis ic choice based on economic
op imiza ion.
The gene al disc e e choice p oblem unde RI lacks a closed o m solu ion. To
u ilize s anda d es ima ion me hods, cu en empi ical RI disc e e choice models (RI-
DCMs) make pa icula —and po en ially un ealis ic—assump ions abou consume s’
p io belie s, esul ing in choice p obabili ies ha ollow a closed- o m mul inomial
logi (MNL) unc ion o he unde lying u ili y index. While hese models can mo i a e
some de ia ions om he ull in o ma ion RUM, hey ace simila concep ual issues
as logi models, such as un ealis ic subs i u ion pa e s and exogenous conside a ion
se s.
To add ess hese limi a ions, we demons a e how o es ima e a RI-DCM unde
gene al p io belie assump ions, including a ional expec a ions, and consume he -
e ogenei y. In his model, al e na i es’ payo s a e ep esen ed by linea u ili y indices
based on p e e ences and a ibu es, which may be simple o complex. DMs can p ocess
simple a ibu es a no cos , whe eas p ocessing o in eg a ing u ili y om complex
123
Disc e e choice in ma ke ing h ough... 47
a ibu es equi es cos ly e o . DMs ha e p io belie s abou he complex a ibu es,
assuming a ional expec a ions. In choice expe imen s, hese expec a ions a e shaped
by he expe imen al design. We show ha bo h p e e ence pa ame e s and he dis-
inc ion be ween simple and complex a ibu es can be likelihood iden i ied in his
model. The p ima y ad an ages o his model o e exis ing empi ical RI-DCMs a e
ha i) i can explain a b oade ange o phenomena ha de ia e om he RUM-DCM
amewo k and ii) i enables mo e lexible coun e ac ual analysis. The d awback o
his app oach is ha i equi es a nume ical solu ion o he o mal RI p oblem. Table 1
p o ides a compa ison o exis ing me hods o applying RI o MAMA da a.
Using he RI-DCM wi h gene al belie s, we demons a e how di e en phenomena
con adic ing he mic oeconomic ounda ion o RUMs in MAMA se ings endoge-
nously ollow om he op imal deploymen o limi ed cogni i e esou ces. Examples
include b and-speci ic p ice coe icien s (e.g., Ca mone & G een, 1981; Saw oo h
So wa e, 1996; Kal a & Goods ein, 1998), sepa a e coe icien s o di e en aspec s
o p ice such as, e.g., a coe icien o egula p ice and one o a p ice discoun o a
ax (Guadagni & Li le, 1983; Bla be g & Neslin, 1989; Che y e al., 2009), as well
as conside a ion se s and a ibu e non-a endance.
Table 1 Compa ison o di e en empi ical RI-DCMs
S a egy Pape P io belie s Implied choice
p obabili ies
Commen s
RI-DCM wi h
choice in closed
MNL o m
B own and
Jeon (2024)
Belie s o e index o
unknown a ibu es
ollows Ca dell
dis ibu ion
Equi alen o mul ino-
mial logi (addi i e
sepa abili y o e al e -
na i e cha ac e is ics,
ully compensa o y)
Assumed belie dis-
ibu ion has ull sup-
po on he eal line
which may be
un easonable, e.g.,
wi h p ices; does no
ep oduce ce ain RI
ea u es like conside-
a ion se s
Joo (2023) Belie s o e all
u ili y componen s
a e a unc ion o
non-u ili y
componen s,
implici ly de ined
such ha esul ing
choice p obabili ies
a e equi alen o
mul inomial logi
in closed o m
Equi alen o mul ino-
mial logi (addi i e
sepa abili y o e al e -
na i e cha ac e is ics,
ully compensa o y)
App oach mo i a es
he inclusion o non-
u ili y a ibu es in he
logi index; implied
p io dis ibu ion is
no accessible by he
analys ; coun e ac uals
wi h espec o belie s
a e a ailable only in a
es ic ed ashion; does
no ep oduce ce ain
RI ea u es like
conside a ion se s
RI-DCM wi h
gene al belie s
This pape Any p io belie
dis ibu ion o e a
disc e e s a e space,
e.g., a ional expec a-
ions o e choice
asks in a DCE
non-compensa o y,
no addi i ely
sepa able
Resul ing model ep o-
duces all quali a i e
ea u es o disc e e
choice unde RI, e.g.,
conside a ion se s o
a ibu e in e ac ions
123
48 S. Tu lo e al.
In he RI-DCM wi h gene al belie s, p edic ions o , e.g., conside a ion se s and
a ibu e non-a endance become implici unc ions o he composi ion o a choice
se , e lec ing adap a ions o p ominen ea u es o he se . This lexibili y is absen in
cu en empi ical RI-DCMs which in oke e y speci ic assump ions abou consume
belie s (e.g., Joo, 2023; B own & Jeon, 2024). Simila ly, his RI-DCM p edic s e ec s
o a ibu e ange, numbe o a ibu e le els, and he size o choice se s on choice
beha io . RUMs ypically do no accoun o hese common p ope ies o choice da a,
a leas no comp ehensi ely in one uni ied model.
Di e en om ex an models o consume sea ch and lea ning,1RI does no es ic
he s uc u e o in o ma i e signals ha he DM uses. This ea u e makes RI dis inc
and mo e gene ally applicable han models whe e all unce ain y is esol ed upon
sea ch. Fo example, in he con ex o disc e e choice expe imen s (DCEs) all ele-
an pieces o in o ma ion, i.e., a ibu e in o ma ion o all al e na i es, a e eadily
p esen ed o DMs. Thus, he dis inc ion be ween mo e and less p ocessing o he
a ailable in o ma ion is quali a i ely di e en om he dis inc ion be ween knowing
o no knowing ce ain p oduc a ibu e alues as ypical o sea ch models. This idea
esembles he dis inc ion be ween e alua ion cos s and sea ch cos s in Guo (2021)
and Gu and Wang (2022). Consequen ly, RI-DCMs a e pa icula ly impo an and
use ul depa u es om ex an models when e alua ing and in eg a ing in o ma ion o
an upda ed o e all unde s anding o a choice si ua ion is decisi e and e o ul. In
con as , sea ch models a e a guably mo e adequa e when knowing o no knowing a
pa icula a ibu e makes he di e ence.
Finally, sea ch models ha allow o pa ial lea ning abou he alue o a ailable
al e na i es a e mo e closely ela ed o RI (e.g., U su e al., 2020). Howe e , sequen-
ial sea ch/lea ning models applied o MAMA choice likely will be compu a ionally
in ac able wi hou obse ing he sea ch/lea ning sequence. Alas, his sequence ha
in ol es men al ope a ions beyond eading a ibu e in o ma ion may well be unda-
men ally unobse able. In addi ion, he s anda d assump ion o no mally dis ibu ed
p io belie s and signals in hese models does no co espond wi h he empi ical dis-
ibu ion o a ibu es and hei bounded suppo , especially in DCEs.
In his a icle, we p o ide an accessible p esen a ion o he RI heo y o s udying
disc e e choice in MAMA se ings common in economics and ma ke ing. Ou con i-
bu ions a e h ee old. Fi s , we ou line wo gene al s a egies o applying RI o disc e e
choice MAMA da a and discuss hei espec i e ad an ages and disad an ages. The
i s s a egy, ypical o exis ing RI-DCMs, in okes speci ic assump ions abou con-
sume belie s (con inuous wi h ull suppo ollowing a Ca dell dis ibu ion) ha yield
choice p obabili ies in closed MNL o m. The ull suppo assump ion con adic s
obse able dis ibu ions o a ibu es. The second s a egy can accommoda e gene al
consume belie s and equi es a nume ical sol e . A esea che choosing be ween
hese s a egies aces a ade-o be ween concep ual ealism and compu a ional bu -
den. Ou second con ibu ion is ha his a icle is, o ou knowledge, he i s o de ail
he necessa y s eps o implemen ing he second empi ical s a egy (“RI-DCM wi h
gene al p io belie s") while accoun ing o consume he e ogenei y. Thi d, we demon-
s a e ha a RI-DCM wi h gene al belie s can e ec i ely ep oduce a ious beha io al
1Fo a ecen o e iew, see Honka e al. (2019).
123

Disc e e choice in ma ke ing h ough... 49
pa e ns inconsis en wi h s anda d RUM models in MAMA se ings pa simoniously.
In con as , exis ing RI-DCMs ha yield choice p obabili ies in closed MNL o m
imply he same cons ain s as MNL de i ed om RU heo y, such as independence o
i ele an al e na i es and s ic ly posi i e choice p obabili ies o all al e na i es in a
se .2
The emainde o his pape is o ganized as ollows. Sec ion 2de i es disc e e
choice among mul iple al e na i es desc ibed along mul iple a ibu es unde he RI
amewo k. Sec ion 3illus a es es ima ion and empi ical iden i ica ion o he model.
Sec ion 4discusses key ea u es o he RI model and p o ides illus a i e simula ions.
Sec ion 5concludes wi h a discussion and an agenda o u u e esea ch.
2 A a ional ina en ion model o disc e e choice
The basic idea behind RI heo y is ha DMs ace an abundan amoun o in o ma ion
and canno p ocess all o i . Howe e , hey a e awa e o his limi a ion and decide
how o p ocess he a ailable in o ma ion op imally, ading o cos s and bene i s o
being be e in o med. This idea was sugges ed by Sims (2003) o p o ide a uni ying
amewo k o di e en ic ions in mac oeconomics. While he o iginal model was
de eloped o con inuous ac ion spaces, Ma ˇejka and McKay (2015) ex end his heo y
o disc e e choices.
Ou p esen a ion builds on he disc e e choice e sion o he RI model (Ma ˇejka
& McKay, 2015; Caplin e al., 2019) and ailo s i o he ypical MAMA se ing.
In oducing he model, we i s p esen he RI choice p oblem and discuss how i s
a ious componen s ansla e in o he MAMA se ing. Then, we u n o he p oblem’s
solu ion and co e how he a ious p imi i es a ec he esul ing choice beha io . In
pa icula , his will illus a e he impac o he complexi y o a choice ask and o he
incen i es o p ocess in o ma ion.
To ease he exposi ion o he a ious componen s o he RI amewo k, we will
e e as an example o a DCE whe e a DM has o choose be ween a ca and an ou side
op ion. In his example, he inal p ice paid by he DM consis s o wo componen s:
i) a lis p ice ha is easily e alua ed by he DM, and ii) a discoun ha applies only o
speci ic ca s ( hus encou aging he pu chase o such ehicles). While bo h componen s
ha e he same impac on inal u ili y, we assume i is mo e e o ul o ind ou i and
wha discoun applies o a pa icula ca .
This simple example may align well wi h exis ing adi ional sea ch models i
de e mining he eligibili y o a speci ic ca is a simple sea ch ask, e.g., checking
whe he he discoun in mone a y e ms applies o a speci ic ca model. Howe e , we
posi a scena io whe ein he eligibili y o a speci ic ca hinges upon (a combina ion
o ) di e se cha ac e is ics. In such a si ua ion, judging he applicabili y o he discoun
equi es he consume o collec in o ma ion om a ious sou ces and in eg a e i o
2Ma ˇejka and McKay (2015) al eady poin ed ou ha a andom u ili y model canno gene ally cap u e
beha io implied by RI agen s.
123
50 S. Tu lo e al.
de e mine he o e all alue o he discoun . Consequen ly, i is possible ha he DM
p ocesses only some pa s o he in o ma ion and, he e o e, may a i e a a aul y
e alua ion o he inal p ice, which in u n leads o choice e o s.3
2.1 Fo mal p oblem and i s ansla ion in o MAMA se ings
We closely ollow Caplin e al. (2019) in de ining he p oblem aced by he a ionally
ina en i e DM. The e is a ini e numbe o s a es  he DM can lea n abou .4An
ac ion ais a mapping om s a es o u ili ies. Adeno es he se o all possible ac ions.
The mapping u:A×→Rdesc ibes he u ili y om any ac ion in each s a e.
The p oblem aced by he DM is non- i ial because, ypically, di e en ac ions a e
op imal in di e en s a es, and he DM is unce ain abou he ue s a e. Howe e , as
we will explain la e , he DM can cos ly lea n abou he ue s a e.
The gene al na u e o RI heo y p o ides oom o di e en ansla ions o he ame-
wo k in o he ypical MAMA se ing in ma ke ing. We na u ally impose ha ac ions
co espond o di e en al e na i es om which he DM chooses and de ine s a es as
ep esen ing di e en choice se s cha ac e ized by he speci ic a ibu e composi ions
o al e na i es a ailable o he DM. Acco dingly, in his se ing, co esponds o he
se o all a ainable choice se s in a gi en choice en i onmen .
Payo s Simila o he dis inc ion be ween di ec ly obse able a ibu es and a ibu es
ha need o be sea ched in sea ch models (e.g., Honka e al., 2019; Ga de e & Hun e ,
2020) o he dis inc ion be ween a ibu es ha guide conside a ion and a ibu es ha
a e only p ocessed upon conside a ion in wo-s age models o choice (e.g., A iba g e
al., 2018), we assume ha he subjec i e alue o al e na i es is de i ed om a ibu es
ha all in o wo ca ego ies. The i s ca ego y consis s o simple a ibu es xswhose
join alua ion is immedia e o he DM. The second ca ego y comp ises complex
a ibu es xcwhose join alua ion and in eg a ion wi h simple a ibu es equi es
cogni i e e o and ime.5
We assume addi i e sepa abili y such ha he subjec i e u ili y o an al e na i e is
gi en by
u(a,ω)=x
a,s(ω)βs+x
a,c(ω)βc,(1)
3The e a e many mo e hings abou a ca ha a e likely payo ele an o a DM, and i may o may no
be e o ul o e alua e and in eg a e hem in o an o e all e alua ion. Howe e , his minimal example will
help de elop basic p inciples.
4An al e na i e o mula ion wi h a con inuous s a e space is gi en in Ma ˇejka and McKay (2015).
5S udies ha explo e he choice p ocess using eye aces ha e documen ed an “o ien a ion phase” whe e
he DM acqui es pa ial in o ma ion abou he p oduc s, which guide he subsequen in o ma ion acquisi ion
(e.g., Russo & Lecle c, 1994; Musalem e al., 2021). This o ien a ion phase and subsequen beha io in ol es
bo h bo om-up and op-down p ocessing (see Co be a & Shulman, 2002 o a e iew).
123
Disc e e choice in ma ke ing h ough... 51
whe e βsand βca e he espec i e pa -wo hs o simple and complex a ibu es.6
The dependence o xa,sand xa,con ωabo e highligh s ha a ibu es o al e na i es
change om choice se o choice se .7
Be o e lea ning, he DM has some belie s abou he alue o complex a ibu es
xa,c, which become mo e p ecise as he DM p ocesses in o ma ion. No e ha any
unce ain y is due o complex a ibu es. We e e o he po ion o u ili y de i ed om
simple a ibu es as he “simple u ili y componen ” while he po ion de i ed om
complex a ibu es is e med he “complex u ili y componen ”.
In ou example, he lis p ice o a ca is a simple a ibu e, and he discoun is
a complex a ibu e ha equi es ime and cogni i e e o o p ocess and in eg a e
wi h he simple lis p ice o a i e a a inal p ice and an assessmen o u ili y. To
u he illus a e he challenges associa ed wi h in eg a ing in o ma ion, conside he
ollowing examples in ol ing wo p ice componen s: (i) p ices a e gi en in cu ency
uni s and discoun alues in pe cen ages gi en as numbe s, e.g., 9.90 Eu o and a
16% discoun , (ii) discoun alues in cu ency uni s, e.g., 9.90 Eu o and a 1.58 Eu o
discoun , (iii) discoun alues men ioned in some way oge he wi h he inal p ice o ,
in his example, 8.32 Eu o. Cases (i) and (ii) equi e he DM o in eg a e he discoun
in o ma ion wi h he p ice. Howe e , his exe cise a guably is mo e in ol ed in case
(i) han in case (ii) because he DM has o calcula e he discoun alue as pa o
he in eg a ion exe cise. The main poin , howe e , is ha case (ii)—whe e bo h he
p ice and he discoun a e p esen ed in cu ency uni s—is ha de han case (iii), whe e
he inal p ice is displayed. This added di icul y s ems om he need o in eg a e
wo pieces o in o ma ion by sub ac ing he discoun om he p ice o de e mine he
o e all alue.
P io belie s The DM’s p oblem is gi en by a pai (μ, A). He e, μ∈() is he
p io belie o e he s a es o he wo ld, wi h () being he se o dis ibu ions o e
, and A⊂Ais he se o ac ions she can choose om. In ou illus a i e example, a
s a e ωco esponds o a speci ic choice se cha ac e ized by a pa icula combina ion
o a ibu e ealiza ions. Since simple a ibu es a e p ocessed a no cos by he DM,
each combina ion o simple a ibu e ealiza ions xsinduces a di e en p io belie
dis ibu ion μs∈() o e possible choice se s ω∈. In gene al, hese p io belie s,
condi ional on cos less in o ma ion, will di e om he uncondi ional dis ibu ion
o e choice se s. In pa icula , he DM ob ains p io belie s μsby condi ioning he
dis ibu ion o e all choice se s on he simple a ibu e ealiza ions aced in a speci ic
choice se ω. Fo mally, p io belie s a e gi en by
μs(ω) =P ω|{(xa,s(ω))}a∈A
whe e he dis ibu ion o e choice se s, P (ω), is de e mined by he choice en i on-
men .
6Addi i e sepa abili y is by no means a necessa y bu o en a na u al assump ion when, e.g., di e en p ice
componen s add up o a o al p ice.
7Wi h he p esen no a ion, any s a e o choice se is de ined by he con igu a ion o he al e na i es:
ω={(xa,s(ω), xa,c(ω))}a∈A.
123
52 S. Tu lo e al.
Table 2 Se o choice se s wi h espec i e payo s and p io belie s
Choice se ω1ω2ω3ω4
P obabili y o ωiγp(1−γd)γ
pγd(1−γp)(1−γd)(1−γp)γd
Payo s:
Inside al e na i e uIβb−pLβb−pL+Dβb−pHβb−pH+D
Ou side al e na i e uO00 0 0
In o ma ion se p=pL,p=pL,p=pH,p=pH,
d∈{0,D}d∈{0,D}d∈{0,D}d∈{0,D}
P io belie s μs:
P (uI=βb−pL)1−γd1−γd00
P (uI=βb−pL+D)γ
dγd00
P (uI=βb−pH)00 1−γd1−γd
P (uI=βb−pH+D)00 γdγd
Each column ep esen s a di e en choice se ωi. In addi ion o he payo s, he objec i e p obabili y o each
choice se , he in o ma ion se o he DM be o e any lea ning akes place, as well as he esul ing p io belie s
a e displayed. No e ha his ully cha ac e izes he DM’s p io since o all choice se s P (uO=0|ωi)=1
In ui i ely, one can hink o a sequen ially upda ing DM who is awa e o he choice
en i onmen (e.g., an expe imen al design) and he implied dis ibu ion o a ibu es
o e all possible choice se s. Once she obse es he ealized simple a ibu e alues
(xs) in a speci ic choice se , she o ms condi ional p io belie s μs, which in u n
de e mine how she p ocesses complex a ibu es xc.
Re u ning o ou exempla y DCE, suppose he DM chooses only be ween a single
ca b and and an ou side op ion o no buying. The u ili y o he inside al e na i e, i.e.,
he ca , is gi en by uI=βb−p+dwi h βbbeing he b and coe icien , pbeing a simple
p ice, and dbeing a complex discoun . Fo he sake o a minimal example, we assume
ha b and is a simple a ibu e as well and ha wha e e (complex) c i e ia quali y he
ca o he discoun only con ibu e o u ili y h ough he discoun , such ha ca s wi h
and wi hou he discoun ha e he same b and coe icien βb.8We u he assume ha
he DM has o commi o pu chasing he ca a a p ice p, i.e., pay pand only a e is
eimbu sed d, depending on he eligibili y o he ca . The u ili y o he ou side op ion
is no malized o uO=0. Fu he , he expe imen al design is such ha p∈{pL,pH}
wi h P (p=pL)=γpand d∈{0,D},D>0 wi h P (d=D)=γd>0.9In
Table 2, he columns ep esen he possible choice se s o his design. The DM can
ace ou di e en choice se s as he e a e wo a ibu es wi h wo le els each, so
||=4.
The objec i e p obabili ies o each choice se ω(p io o he ealiza ion o he simple
a ibu es) a e displayed in Table 2. Since he e a e only wo possible ealiza ions o
simple a ibu es, cha ac e ized by he wo le els o he simple p ice pLand pH, he e
8In he no a ion o Eq. 1, we ha e he ollowing decomposi ion in o simple and complex con ibu ions o
u ili y: [1,p]s[βb,−1]+dc·1 wi h a sha ed p ice coe icien equal o 1.
9In ou example, he condi ional dis ibu ion o he complex a ibu e equals he ma ginal dis ibu ion due
o he o hogonal design. In designs wi h buil -in co ela ions, e.g., wi h condi ional p icing, he ealized
alues o simple a ibu es will p edic he dis ibu ion o complex a ibu es alues.
123
Disc e e choice in ma ke ing h ough... 59
condi ional on a speci ic choice se o an al e na i e a ead
P(a|ω) =exp{(x
a,s(Cβs+βs)+x
a,cβc)/λ}
bexp{(x
b,s(Cβs+βs)+x
b,cβc)/λ}.
De ining 
βs≡Cβs+βs, one can see how his de i a ion can mo i a e di e en coe -
icien s o , e.g., a simple and a complex componen o p ice. Howe e , he esul ing
model o he wise is indis inguishable om a s anda d logi RUM.
P io belie s consis en wi h RI choice p obabili ies in closed MNL o m In he
applica ion by Joo (2023), each al e na i e a∈Ais cha ac e ized by a se o obse able
conside a ion shi e s da, e.g., ad e ising o shel placing, ha solely a ec p io
belie s bu no consump ion u ili y.15 All p oduc a ibu es a e assumed o be complex
so ha u(a,ω)=x
c,aβc. Gi en p io belie s μ, ha depend solely on he in o ma ional
shi e s {da}a∈A, and in o ma ion cos s λ he DM lea ns and chooses ollowing he RI
amewo k. Joo (2023) shows ha o any combina ion o al e na i e speci ic payo s
{u(a,ω)}a, in o ma ion cos s λ, and s ic ly posi i e uncondi ional choice p obabili ies
P(a), he e a e p io belie s μ ha a e consis en wi h choice beha io o a a ionally
ina en i e DM.
Howe e , he ac ual pa ame e iza ion Joo (2023) b ings o he da a, i.e., a logi
o m wi h an addi i ely sepa able index o al e na i e speci ic a ibu es xc,aand
in o ma ion shi e s da, equi es e y speci ic belie s abou he index om al e na i e
speci ic a ibu es xc,a. These belie s a e no de i ed om he objec i e dis ibu ion o
his index in he ma ke place and a e subs an ially di e en om his dis ibu ion, as
al eady implied by he ull suppo assump ion.16 This limi s he o mula ion p oposed
in Joo (2023) as a model o a ionally ina en i e DMs ha acqui e knowledge abou
he dis ibu ion o al e na i e speci ic a ibu es xc,ain he ma ke place o e longe
ime ho izons.
3.2 RI-DCM wi h gene al p io belie s
The RI-DCM wi h gene al p io belie s does no ha e a closed- o m solu ion, and
we need o sol e o choice p obabili ies nume ically o compu e he likelihood in
his model. Howe e , o e and abo e inco po a ing mo e ealis ic assump ions abou
belie s, his gene aliza ion yields he quali a i ely dis inc i e ea u es o RI disc e e
choice we p e iewed in Sec ion 1and will elabo a e on in Sec ion 4. In applica-
ions, p io belie s can be de e mined, o ins ance, by assuming a ional expec a ions
whe e εaa e iden ically and independen ly T1-EV dis ibu ed. The Ca dell dis ibu ed p io belie s o e
complex u ili y componen s xa,c, oge he wi h εa, ollow he T1-EV dis ibu ion. This ea u e is key o
ob aining uncondi ional choice p obabili ies in closed o m. Fo a de ailed de i a ion, see Supplemen al
Appendix A-1 o B own and Jeon (2024) and Appendices A.1 and A.2 in Be oli e al. (2020).
15 Na an (2021) employs a simila iden i ica ion s a egy. In his pape , howe e , in o ma ion p ocessing
cos s λexplici ly depend on he size o he choice se .
16 While Ca dell belie s esul in addi i e sepa abili y as demons a ed by B own and Jeon (2024), he
model in Joo (2023) is no immedia ely consis en wi h Ca dell belie s because o he assump ion ha he
ou side good payo is known wi h ce ain y.
123

60 S. Tu lo e al.
Fig. 1 Flowcha o he Blahu -A imo o algo i hm o compu e he likelihood in RI-DCM
abou he expe imen al design (in case o DCE da a) o he empi ical dis ibu ion o
a ibu es (wi h obse a ional da a). Howe e , he model could eadily accommoda e
di ec ly elici ed, po en ially he e ogeneous belie s abou he (condi ional) dis ibu ions
o complex a ibu es and implied choice se s.
Likelihood compu a ion Condi ional on βsand βc he u ili y o he DM, u(a,ω),
isgi enbyEq.1.Gi enu(a,ω),μs(ω), and λ, he likelihood can be ob ained by
compu ing he op imal condi ional choice p obabili ies, P(a|ω),inEq.3.AsP(a|ω)
is a unc ion o he endogenous uncondi ional choice p obabili ies Ps(a)in Eq. 3,
we sol e o bo h P(a|ω) and Ps(a)using he Blahu -A imo o algo i hm (Co e and
Thomas, 2006).
The algo i hm s a s by ini ializing he Ps(a)and i e a es be ween upda ing Ps(a|ω)
and Ps(a)un il con e gence. The i s s ep o each i e a ion uses he op imali y
condi ion in Eq. 3 o compu e P +1
s(a|ω) gi en P
s(a)ob ained in he pas i e a ion.
The second s ep compu es P +1
s(a)by in eg a ing P +1
s(a|ω) o e he (condi ional)
p io belie dis ibu ion:
P +1
s(a)=
ω∈
μs(ω)P +1
s(a|ω) =P
s(a)
ω∈
μs(ω) exp{u(a,ω)/λ}
b∈AP
s(b)exp{u(b,ω)/λ}.(5)
We calcula e he dis ance be ween uncondi ional dis ibu ions ob ained in subse-
quen s eps, P +1
sand P
s, ia he Bha acha yya (1946) dis ance D(P +1
s,P
s).The
algo i hm s ops when D(P +1
s,P
s)<ξo when he maximum numbe o i e a ions
i e max is eached. The con e ged condi ional choice p obabili ies gi e us he indi-
idual le el likelihood L(μs(ω), βs,βc,λ)=P∗
s(a|ω).17 No e ha pa ame e s ξand
i e max go e n he p ecision o he nume ical solu ion, and ca e mus be aken in
se ing hei alue. Figu e 1shows he lowcha o he algo i hm. In e ence based on
solu ions om he Blahu -A imo o algo i hm, and speci ically Ma ko Chain Mon e
Ca lo (MCMC) es ima ion, is compu a ionally cos ly as we need solu ions o e e y
unique combina ion o a choice se indexed by simple a ibu e ealiza ions wi h model
pa ame e s isi ed by he MCMC.
To speed up compu a ions, wi hou gi ing up on equi ed p ecision, we employ
wo op imiza ion s a egies. Fi s , we op imize he ini ializa ion o he s a ing al-
ues (Pini (a)in Fig. 1) by le e aging (sa ed) solu ions om he cu en s a e o he
MCMC. A each MCMC d aw ,wese Pini (a)=(1−γ)P∗
s(a)| −1+γ/|A|,
17 Con e gence o he algo i hm has been p o en by Csiszá (1974).
123
Disc e e choice in ma ke ing h ough... 61
whe e P∗
s(a)| −1deno es he con e ged uncondi ional choice p obabili ies om he
las MCMC d aw, γ∈(0,1]is a weigh pa ame e , and |A|is he numbe o al e -
na i es in he choice se .18 Fo =1 we use uni o m choice p obabili ies as ini ial
alues. Second, we implemen a pa allelized e sion o he Blahu -A imo o algo i hm,
which simul aneously compu es likelihoods o mul iple choice obse a ions.
Iden i ica ion As only he a io o cos s and p e e ences can be iden i ied om choice
da a, p e e ences βsand βccan be iden i ied by ixing λand le e aging a ia ions
in simple and complex a ibu es ac oss al e na i es and choice se s p esen ed o he
DM.19 Howe e , he e may be si ua ions wi hou a ia ion in simple a ibu es. Fo
example, one could hink o “b and” as he only simple a ibu e. The RI model is s ill
iden i ied in his case, subjec o a ia ion in a complex a ibu e, e.g., o al p ice, in he
same way as a simple RUM wi h al e na i e speci ic cons an s. Howe e , wi h only
one con igu a ion o simple a ibu es, he e is only one op imal p ocessing s a egy
(see exp ession 2). I his s a egy esul s in a ull conside a ion se , he model is
empi ically indis inguishable om a s anda d RUM. Howe e , no e ha depending on
unobse ed he e ogeneous p e e ences, consume s may ha e di e en conside a ion
se s ha a e endogenous o hei b and p e e ences and p ice sensi i i y. Howe e , i
he en i onmen is such ha no all he b ands a e a ailable all he ime, he e will be
a ia ion in he condi ioning a gumen o he op imal p ocessing s a egy unde RI.
Finally, i is impo an o no e ha poin iden i ica ion o p e e ences may no
be achie ed, since de e minis ic choice is a possible endogenous ou come unde RI.
This occu s, o ins ance, a ex eme alues o λ. In ui i ely, a DM wi h a e y high
in o ma ion acquisi ion cos does no eac o a ia ions in he complex a ibu es,
and one wi h e y low in o ma ion acquisi ion cos s ully p ocesses he complex
a ibu es, leading o de e minis ic choices (see Sec ion 4). Bo h o hese cases esul
in se -iden i ica ion o p e e ence pa ame e s.20 In his con ex , ou Bayesian in e ence
amewo k, illus a ed nex , will be use ul, as he likelihood su ace hen exhibi s la
egions, complica ing maximum likelihood es ima ion.
3.3 Empi ical iden i ica ion wi h DCE da a unde p e e ence he e ogenei y
We now illus a e he Bayesian es ima ion and empi ical iden i ica ion o he RI-
DCM wi h gene al belie s p oposed in Sec ion 3.2, using simula ed da a, in a “small
T, la ge N" se ing, ypical o DCEs in ma ke ing. We use s anda d weakly in o ma i e
subjec i e p io se ings o he pa ame e s indexing hie a chical p io dis ibu ions
(see Appendix A.2 o de ails).
18 The ansi ion ke nel o ou MCMC na u ally esul s in uncondi ional dis ibu ions (implied by a p oposal
o a new pa ame e alue) ha o en a e close o hose a he cu en s a e. The ini ializa ion gua an ees
non-degene a e s a ing alues, i.e., a ec o o p obabili ies wi h all en ies la ge han ze o and smalle
han one. In ou simula ions, we ound γ=0.2 o wo k well.
19 Appendix A.1 illus a es how a di e ence in p ocessing cos s λ can be empi ically iden i ied i a DM
wi h in a ian p e e ences makes decisions in di e en en i onmen s.
20 We illus a e se -iden i ica ion o p e e ences in Appendix A.3.
123
62 S. Tu lo e al.
Table 3 Pos e io means o p e e ence dis ibu ions o di e en model speci ica ions
Model B and P ice Discoun |βp/βd||βp/βb|LMD
Da a gene a ion 2.50 -1.00 ≡−βp1.00 0.40
RI-DCM 2.50 -1.00 ≡−βp1.00 0.40 -2,530.29
(0.05) (0.02)
RU logi sepa a e 27.61 -9.16 4.44 2.06 0.34 -2,620.36
(0.69) (0.22) (0.13)
RU logi join 9.81 -3.95 ≡−βp1.00 0.40 -4,558.35
(0.19) (0.07)
We epo da a gene a ing pa ame e s as well as he es ima ed pos e io means o he RI-DCM and he
benchma k logi models wi h and wi hou he cons ain βp=βd. S anda d e o s a e in pa en heses.
|βp/βd|and |βp/βb|a e he a ios o mean coe icien s
We simula e da a om he ollowing hie a chical se up. A sample o a ionally
ina en i e DMs (N=1,000) ace T=20 choices be ween an inside and an ou side
good each. The u ili y o he inside good o DM jin choice ask is gi en by uj, =
βb,j+βp,j(p −d )whe e βb,jis he b and coe icien , βp,j he p ice coe icien ,
p is he p ice, and d is he discoun . The u ili y o he ou side op ion is no malized
o ze o: uO=0. In ou simula ion, b and and p ice a e simple a ibu es and hus
pe cei ed and p ocessed, i.e., in eg a ed o an o e all u ili y, immedia ely and a no
cos , while he discoun equi es cos ly p ocessing.
We i s illus a e he case wi hou he e ogenei y in p ocessing cos s. He e, all indi-
iduals ha e he same p ocessing cos s o λ=0.25. DMs di e in hei s uc u al
u ili y pa ame e s. P e e ence coe icien s a e gene a ed om he ollowing dis ibu-
ions: βb∼N(2.5,0.25),βp∼N(−1,0.04). P ices pand discoun s da e d awn
uni o mly and independen ly om he ollowing se s: p∈{2.5,3,3.5,4,4.5}and
d∈{0,0.5,1,1.5,2}such ha he esul ing design is o hogonal. Indi iduals know
he alue o he p ice p, and o all p ices and o any discoun le el d he p io belie s
a e gi en by P (d=d|p)=1/5.
Wi h he simula ed da a, we i he RI-DCM and wo RU logi speci ica ions: one
ha allows o sepa a e p ice and discoun coe icien s (“RU logi sepa a e”) and one
wi h only one coe icien measu ing he u ili y o money (“RU logi join ”), as in he
da a-gene a ing p ocess. We ely on Rossi’s bayesm-package o he es ima ion o he
hie a chical RU logi (Rossi e al., 2005). The es ima ion o he hie a chical RI-DCM
employs Me opolis-Has ings s eps o upda e indi idual-le el p e e ence pa ame e s
and elies on s anda d esul s o upda ing pa ame e s indexing he hie a chical p io
dis ibu ions (e.g., Rossi e al., 2005). We ob ain he likelihood by sol ing he p ob-
lem Eq. 2 o gi en pa ame e s nume ically wi h he Blahu -A imo o algo i hm, as
desc ibed in Sec ion 3.2. Wi hou loss o gene ali y, we ix he alue o λ o be equal
o i s ue alue in es ima ion. We will e isi his poin below.
Table 3summa izes pos e io means and Table 4 epo s pos e io a iances. We
see ha he es ima ed RI-DCM nicely eco e s da a-gene a ing pa ame e s. We use
log ma ginal densi y (LMD) es ima es h oughou he pape o compa e model i s
123
Disc e e choice in ma ke ing h ough... 63
Table 4 Pos e io a iances o
p e e ence dis ibu ions o
di e en model speci ica ions
Model B and P ice Discoun
Da a gene a ion 0.25 0.04 ≡Va (βp)
RI-DCM 0.33 0.09 ≡Va (βp)
(0.05) (0.01)
RU logi sepa a e 16.00 1.71 1.93
(4.02) (0.39) (0.31)
RU logi join 4.03 0.71 ≡Va (βp)
(0.71) (0.11)
We epo da a gene a ing pa ame e s as well as he es ima ed pos e io
a iances o he RI-DCM and he benchma k logi models wi h and
wi hou he cons ain βp=βd. S anda d e o s a e in pa en heses
(see Rossi e al., 2005). The in e io i s o he RU logi models, he (s ill) cu en
benchma k, es i y o he empi ical iden i iabili y o he RI-DCM (see he las column
in Table 3). The RU logi wi h sepa a e pa ame e s o p ice and discoun i s he
da a much be e han he RU logi wi h only one p ice coe icien , i.e., sugges ing
ha di e en “sou ces o money” a e alued di e en ly. Howe e , he e he la ge
magni ude o he p ice coe icien , ela i e o he discoun coe icien , simply e lec s
ha a ionally ina en i e DMs eac o he ealized discoun alue adap i ely, bo h as
a unc ion o he ealized (simple) p ice ha a ies ac oss choice se s and as a unc ion
o he e ogeneous p e e ence coe icien s ha a y ac oss DMs.
As a consequence, he RU logi also s uggles wi h measu ing he e ogenei y in
p e e ence pa ame e s. Fo example, he RU logi d ama ically o e es ima es he he -
e ogenei y in he p ice coe icien (and he discoun coe icien , whe e sepa a ely
speci ied). This obse a ion is impo an gi en ha exis ing applica ions o RI o
disc e e choice wi h obse a ional da a p esen ein e p e a ions o RU logi choice
condi ioned on addi i ely sepa able indices.
Finally, Table 5 epo s elas ici ies o all models gi en changes in di e en dis-
coun and p ice le els. Elas ici ies a e calcula ed using pos e io expec ed (changes in)
choice p obabili ies and, he e o e, inco po a e all pos e io unce ain y. The columns
Discoun A and P ice A epo elas ici ies esul ing om a discoun dec ease om
d=1 od=0.5, and a p ice inc ease om p=4 op=4.5, espec i ely. Simila ly,
columns Discoun B and P ice B deno e scena ios whe e discoun s dec ease om
Table 5 Elas ici ies o di e en p ice and discoun le els
Model Discoun A P ice A Discoun B P ice B
RI-DCM 0.28 0.52 0.21 0.52
RU logi sepa a e 0.25 0.53 0.29 0.58
RU logi join 0.38 0.38 0.38 0.38
Columns epo elas ici ies om changes in discoun (Discoun A and Discoun B) and changes in p ice
(P ice A and P ice B). The elas ici ies in he i s wo columns a e calcula ed o an inside good wi h p=4
and d=1 and in he las wo columns o an inside good wi h p=5andd=2
123
64 S. Tu lo e al.
d=2 od=1.5, and p ices ise om p=5 op=5.5. In all ins ances, absolu e
and ela i e changes in o al p ice a e he same.
Unde RI, p ice elas ici ies depend bo h on he sou ce o he p ice a ia ion and on
he composi ion o he inside good. The RI-DCM yields ha he p ice elas ici y is much
smalle (la ge ) when he change in o al p ice comes h ough he complex discoun
( he simple p ice). The RI-DCM also yields ha p ice elas ici y om changing he
discoun u he dec eases a he highe simple p ice (compa e columns Discoun A
and Discoun B in Table 5). The easons a e he in o ma ion ic ion associa ed wi h
p ocessing and in eg a ing he complex discoun and he s onge p io agains he
inside al e na i e when he simple p ice is la ge .
The RU logi sepa a e co ec ly picks up ha p ice changes om he complex
discoun esul in smalle elas ici ies han simple p ice changes. Howe e , his model
w ongly sugges s ha he elas ici y om changing he p ice h ough he discoun
inc eases a he highe simple p ice. Finally, he RU logi ha does no di e en ia e
be ween p ice changes h ough he simple p ice and he complex discoun necessa ily
o e es ima es (unde es ima es) elas ici ies om changing he discoun (changing he
simple p ice).
3.4 He e ogeneous p e e ences, he e ogeneous in o ma ion p ocessing cos s
In gene al, bo h p ocessing cos s and p e e ences likely a y ac oss DMs. Hence,
i may be heo e ically appealing and e icien in a hie a chical model o s uc u e
he e ogenei y in βas esidual he e ogenei y a e conside ing he e ogenei y in λ. Such
a decomposi ion in he con ex o a hie a chical RI-DCM can be iewed as a mic o-
ounded e sion o he idea behind Fiebig e al. (2010)’s gene alized mul inomial logi
model ha , in addi ion o p e e ence he e ogenei y, cap u es he he e ogenei y in he
scale o he e o e m in a hie a chical RU logi .
As al eady men ioned, he objec i e unc ion in he RI amewo k is homogeneous
o deg ee one wi h espec o payo s and cos s, and only hei a io is di ec ly iden i-
iable om choice da a. Howe e , om a s a is ical poin o iew, he combina ion o
con inuous he e ogenei y in p e e ences wi h con inuous he e ogenei y in in o ma ion
Table 6 Pos e io means o p e e ence dis ibu ions o he RI-DCM wi h and wi hou scale mix u e com-
ponen
Model B and P ice Discoun σ2
log(λ) LMD
Da a gene a ion 2.50 -1.00 ≡−βp0.09
RI-DCM 2.40 -0.95 ≡−βp0 -2,984.55
(0.04) (0.02)
RI-DCM scale mix u e 2.48 -0.99 ≡−βp0.08 -2,884.90
(0.06) (0.02) (0.01)
We epo da a gene a ing pa ame e s as well as he es ima ed pos e io means o he RI-DCM wi h homoge-
nous and he e ogeneous in o ma ion p ocessing cos s. S anda d e o s a e in pa en heses. σ2
log(λ) is he
a iance o log in o ma ion p ocessing cos s in he popula ion
123

Disc e e choice in ma ke ing h ough... 65
Table 7 Pos e io a iances o
p e e ence dis ibu ions o he
RI-DCM wi h and wi hou scale
mix u e componen
Model B and P ice Discoun
Da a gene a ion 0.25 0.04 ≡Va (βp)
RI-DCM 0.41 0.07 ≡Va (βp)
(0.05) (0.01)
RI-DCM scale mix u e 0.31 0.05 ≡Va (βp)
(0.06) (0.01)
We epo da a gene a ing pa ame e s as well as he es ima ed pos e-
io a iances o he RI-DCM wi h homogenous and he e ogeneous
in o ma ion p ocessing cos s. S anda d e o s a e in pa en heses
cos s gi es ise o a scale mix u e dis ibu ion. Fo a well-known example, he S uden
-dis ibu ion can be de i ed as a scale mix u e o no mal dis ibu ions.
Because scale mix u es can be iden i ied and dis inguished om hei non-mixed
coun e pa s (see, e.g., Choy & Smi h, 1997), one can iden i y he e ogenei y in he uni
in o ma ion cos s and p e e ences, as long as one is willing o assume a con inuous
dis ibu ion o p e e ences ha is no a scale mix u e. Fo example, popula semi-
pa ame ic dis ibu ions such as a mix u e o no mals a e s ic ly con inuous and
no scale mix u es. Howe e , again because he objec i e unc ion de ining he RI
p oblem is homogeneous o deg ee one, he join dis ibu ion o p e e ences and uni
in o ma ion cos s is only iden i ied up o he i s momen o he la e dis ibu ion.
Fo illus a ion, we ex end he simula ion om Sec ion 3.3 o include he e ogenei y
in in o ma ion p ocessing cos s wi h log(λj)∼N(μlog(λ) =−1.4,σ2
log(λ) =0.09)in
he da a gene a ing mechanism. As no ed p e iously, he mean o his dis ibu ion is no
join ly iden i ied wi h he mean o he dis ibu ion o p e e ence pa ame e s. Hence, we
ix μlog(λ) o he da a gene a ing alue in es ima ion and wi hou loss o gene ali y.21
Tables 6and 7documen ha we eco e he join dis ibu ion o p e e ence pa ame e s
and in o ma ion cos s subjec o ixing he i s momen o he la e . Mo eo e , we
see ha by no accoun ing o he e ogenei y in in o ma ion p ocessing cos s, one
o e es ima es he p e e ence he e ogenei y, he e e lec ed in b and and p ice a iance
es ima es in he RI-DCM wi h homogeneous in o ma ion cos s.
Complemen ing he illus a i e simula ions he e, we conduc a simula ion s udy ha
a ies he numbe o inside goods (one e sus wo), simula es da a wi h and wi hou
he e ogenei y in p ocessing cos s (in addi ion o p e e ences he e ogenei y), and adds
a wo-s age choice model wi h conside a ion se s om sc eening on p ice (see, e.g.,
Gilb ide & Allenby, 2004; Pachali e al., 2023) o he model compa ison. We simula e
50 da a se s in he ou da a-gene a ing se ings. The benchma k models a e es ima ed
once wi h a single p ice pa ame e and once wi h sepa a e pa ame e s o he (simple)
p ice and he (complex) discoun s. We summa ize esul s in Tables 15,16,17, and 18
and discuss addi ional de ails in Appendix A.2.
No su p isingly, we ind ha only he RI-DCM eco e s da a-gene a ing pa ame-
e s. We also ind ha (i) we can eliably dis inguish he da a gene a ing RI-DCMs om
he benchma k models, (ii) he benchma k models a e ela i ely much wo se in he
21 No maliza ion o he in o ma ion p ocessing cos s is analogous o ha o he e o a iance in RU logi
models in ha i does no a ec ma ke sha e o wel a e compu a ions.
123
66 S. Tu lo e al.
la ge choice se because o he co esponding inc ease in numbe o op imal RI in o -
ma ion s a egies, and (iii), sligh ly wo se when p ocessing cos s a e he e ogeneous
(in addi ion o p e e ences he e ogenei y).
3.5 On he dis inc ion be ween simple and complex aspec s o a choice ask
Di e en om ex an sea ch models, RI mo i a es in o ma ion ic ions e en in si ua-
ions in which all a ibu e in o ma ion is essen ially equally accessible, and he DM’s
challengeisno o esol e alueso unknowna ibu es bu oin eg a e accessible in o -
ma ion o o e all u ili y. Hence, ano he p ac ical challenge o he p oposed amewo k
is he iden i ica ion o simple and complex a ibu es. In some cases, p io knowledge
may be su icien o classi y a ibu es, possibly as a unc ion o he speci ics o a
p oduc ca ego y unde s udy o he expe imen al design. In o he cases, we en ision
ha he dis inc ion be ween simple and complex a ibu es mus be empi ical.
This dis inc ion is g ea ly acili a ed whene e heo y cons ains coe icien s in he
u ili y unc ion o be equal, such as in he example o di e en p ice componen s. In
his case, desc ip i e models, o e en jus ma ginal summa ies o he da a, can e eal
ha choice p obabili ies eac mo e s ongly o changes, say, in p ice componen A
han in p ice componen B. I ollows ha p ice componen A is simple ela i e o
p ice componen B, and p ice componen B is complex ela i e o componen A (e.g.,
B own & Jeon, 2024).
Ob iously, his a gumen ails when heo y allows o di e en u ili y coe icien s
o di e en a ibu es. Nex , we illus a e by simula ion ha he dis inc ion be ween
simple and complex a ibu es is likelihood iden i ied, e en in his case. Whe eas
heo e ical esul s imply ha any combina ion o a ionally ina en i e beha io and
in o ma ion p ocessing cos s can be a ionalized wi h some s a e-con ingen payo s
(Lipnowski and Ra id, 2022), we illus a e ha addi i e linea sepa abili y in u il-
i y con ibu ions can su ice o dis inguish be ween simple and complex a ibu es
empi ically, gi en Shannon cos s and a non-degene a e dis ibu ion o e s a es.22
One inside good We simula e 2,000 choice asks, each in ol ing a DM choosing
be ween an inside and an ou side good. The inside good is cha ac e ized by wo linea
a ibu es, xsand xc, ha addi i ely combine in o o e all u ili y. A ibu e xsis simple,
and he a ibu e xcis complex. Each o he wo linea a ibu es is ep esen ed by h ee
le els in he expe imen al design: xs∈{2,2.25,5}and xc∈{1,1.5,3}. P e e ences
a e gi en by βs=−βc=−1 and in o ma ion p ocessing cos is se o λ=0.5.
In his design, he gene a ed da a comp ises p obabilis ic and de e minis ic choices.
A ibu e combina ions de ining inside goods a e d awn om independen uni o m
dis ibu ions o e he disc e e a ibu e suppo . Wi h he simula ed da a, we es ima e
di e en s uc u al RI-DCMs.
In he i s speci ica ion, he dis inc ion be ween simple and complex a ibu es ol-
lows ha o he da a-gene a ing p ocess. In he second model, we ( alsely) e e se wha
22 In he con ex o sea ch, Abaluck e al. (2022) p opose how o iden i y limi ed in o ma ion abou an
a ibu e unde he assump ions ha ano he a ibu e is known o be ully p ocessed and all-o -no hing
lea ning.
123
Disc e e choice in ma ke ing h ough... 67
Table 8 Iden i ica ion o simple and complex a ibu es in a design wi h one inside al e na i e and one
ou side al e na i e
Model min 25% 50% 75% max ML
Co ec - Linea -380.52 -371.39 -370.68 -370.25 -369.94 -369.93
Misspeci ied - Linea -1076.47 -1067.22 -1066.28 -1065.71 -1065.11 -1039.15
Misspeci ied - Linea Ou -417.41 -412.02 -411.30 -410.95 -410.78 -410.70
Misspeci ied - Ca ego ical -382.63 -375.21 -374.04 -373.13 -370.54 -369.23
Qua iles as well as he minimum and he maximum o he log-likelihood MCMC d aws a e epo ed o
he co ec linea , he misspeci ied linea , he misspeci ied linea wi h an addi ional ou side pa ame e , and
he misspeci ied ca ego ical model, espec i ely. The las column epo s he maximum o he likelihood
(ML) unde an imp ope p io , i.e., he “ equen is maximum”
is simple and complex in es ima ion. The hi d model adds a coe icien o he ou side
good (equal o ze o in he da a-gene a ing p ocess). This model isola es he linea i y
o u ili y di e ences be ween inside goods in a ibu es as a sou ce o iden i ica ion.
Finally, we es ima e a model wi h comple ely lexible u ili y wi hin a ibu es by cod-
ing he wo a ibu es as ca ego ical while misspeci ying which a ibu e is simple and
which is complex in es ima ion. As subjec i e p io dis ibu ion o p e e ence pa am-
e e s we use β∼N(0,100I). We also epo he maximum o he log-likelihood
unde an imp ope p io , o sa egua d agains an undue in luence o his subjec i e
p io se ing.
Table 8p esen s quan iles o he log-likelihoods om Ma ko -Chain-Mon e-Ca lo
(MCMC) es ima ion and he nume ical maxima o he likelihoods implied by he
di e en models. We ind ha , subjec o cons ain s on he u ili y unc ion, he e
is scope o empi ical iden i ica ion o wha is simple and complex in a choice ask
(compa ing he i s h ee lines o Table 8). Howe e , once we gi e up on linea i y in
a ibu es (see he las line in Table 8), we can no longe dis inguish be ween simple
and complex in his minimal example.23
Two inside goods A basic cons ain om u ili y heo y, namely ha o no c oss-
e ec s be ween al e na i es in a model o pe ec subs i u ion, does no come in o play
when he e is only one ou side good. To showcase iden i ica ion om his cons ain ,
we ex end he simula ion desc ibed abo e and include a second inside al e na i e.
The DM chooses be ween wo inside goods and an ou side good. The inside goods
ha e wo a ibu es, one simple and one complex wi h h ee le els each. The majo
di e ence o he one inside good case is ha simple a ibu e ealiza ions o wo inside
goods now e ec i ely in e ac in de e mining he op imal p ocessing s a egy. Fo
example, pa icula ealiza ions o simple a ibu es may lead o conside ing bo h,
23 In Appendix A.3, we addi ionally show ha we can no longe dis inguish be ween simple and complex
a ibu es based on model i once p ocessing cos s a e ei he small enough o la ge enough such ha (essen-
ially) de e minis ic choices ensue. When λbecomes su icien ly small, all in o ma ion is ully p ocessed,
and he concep ual and empi ical dis inc ion be ween simple and complex anishes. When λbecomes
su icien ly la ge, he in o ma ion in complex a ibu es is ne e in eg a ed in o he o e all e alua ion o
al e na i es, and a model wi h ex eme coe icien s o he simple a ibu e (misspeci ied as complex) will
app oach a pe ec i o he da a.
123
68 S. Tu lo e al.
Table 9 Iden i ica ion o simple and complex a ibu es in a design wi h wo inside and one ou side al e -
na i e
Model min 25% 50% 75% max ML
Co ec - Linea -715.7 -709.2 -708.6 -707.6 -707.3 -707.1
Misspeci ied - Ca ego ical -1589 -1585 -1583 -1582 -1581 -1580.3
Qua iles as well as he minimum and he maximum o he log-likelihood MCMC d aws a e epo ed o he
co ec linea and he misspeci ied ca ego ical model, espec i ely. The las column epo s he maximum
o he likelihood (ML) unde an imp ope p io , i.e., he “ equen is maximum”
only one, o none o he wo inside al e na i es. Misspeci ying he simple a ibu e
ha d i es he DM’s choice o in o ma ion s a egy as complex ails o cap u e hese
possibili ies,e eni we d op he linea i y cons ain and code all a ibu esca ego ically
(see Table 9).
4 Fea u es o disc e e choice in MAMA con ex s unde RI
In his sec ion, we illus a e he implica ions o RI heo y o disc e e choice in MAMA
se ings, as common in ma ke ing. We use he RI-DCM wi h gene al belie s and
show h ough simula ions how se e al well-documen ed phenomena in he disc e e
choice li e a u e ha a e di icul o jus i y in a RU amewo k na u ally ollow om
RI. We u he demons a e ha es ima ing a s anda d RU logi can yield misleading
conclusions abou he beha io o RI agen s. This app oach ollows a common esea ch
s a egy in ha li e a u e. O en, a ious logi models a e es ima ed and compa ed in
di e en con ex s, e.g., wi h a ying numbe s o inside al e na i es. This compa ison
hen allows us o iden i y he mode a ing e ec o con ex , he eby e ealing de ia ions
om he s anda d RU logi model.
While ce ain implica ions ha e been discussed in p io ( heo e ical) RI li e a u e,
we add o his body o wo k by explo ing addi ional implica ions due o he MAMA
s uc u e. In gene al, he p esen ed implica ions a ise om how RI agen s ansla e
he MAMA choice en i onmen in o he uncondi ional choice p obabili ies ou lined
abo e. Exis ing RI-DCMs impose simpli ying assump ions on his e y p ocess o
acili a e es ima ion a he expense o no cap u ing he ea u es p esen ed he e. In ou
illus a ions, we dis inguish be ween i) endogenous ea u es o RI (Sec ion 4.1) and
ii) con ex e ec s (Sec ion 4.2).
Endogenous ea u es a ise as a esul o he op imal alloca ion o limi ed cogni i e
esou ces in he RI-DCM. These ea u es can explain empi ical phenomena in MAMA
se ings ha canno be cap u ed by basic RUMs. P e iously, esea che s ha e applied
di e se, non-uni ied adjus men s o RUMs o add ess hese phenomena. Table 10 ou -
lines impo an endogenous ea u es o RI and includes examples om s udies ha
ha e made non-uni ied modi ica ions o RUMs o accommoda e he ela ed phenom-
ena. In Sec ion 4.1, we discuss he ollowing endogenous ea u es o disc e e choice
unde RI:
123
Disc e e choice in ma ke ing h ough... 75
Fig. 3 Iso-choice-p obabili y se s o he RI-DCM and he RU logi . This Figu e displays se s o p ice-
discoun combina ions o he inside good ha esul in he same condi ional choice p obabili ies o he
RI-DCM (le panel) and he RU logi ( igh panel). The hin solid line is he 45◦line. Unde he RU logi ,
he iso-choice p obabili y se s a e linea and indi idual se s a e pa allel o each o he . In con as , unde he
RI-DCM, he subs i u ion a e a ies depending on he composi ion o he inside good so ha i is non-linea
and he indi idual se s a e no pa allel. The do s in he le panel indica e ac ual a ibu e combina ions o
he inside good
RI, i ma e s whe he he sou ce o u ili y is a simple o a complex a ibu e. As
shown in he le panel o Fig. 3, he a io o changes in he discoun and p ice ha
keep choice p obabili ies cons an is smalle han one, i.e., an inc ease o he discoun
by one uni o se s an inc ease in he p ice ha is s ic ly smalle han one unde RI
e en hough bo h p ice and discoun ha e he same impac on u ili y. This is explained
by he in o ma ion ic ion p esen in he RI-DCM, which makes choice p obabili ies
a unc ion no only o an al e na i e’s u ili y alue bu also o he sou ce o ha u ili y.
Unde he RI-DCM, he e will be p ices ha a e su icien ly low (high) so ha he
DM chooses de e minis ically (gi en a simple p ice) in he limi . Consequen ly, wi h
a ixed discoun dis ibu ion, he iso-choice se s become lowe (uppe ) con ou se s
wi h a bounda y ha is la in he discoun . In con as , unde he RU logi , he e a e no
combina ions o ini e discoun s and p ices so ha he DM chooses de e minis ically.
Fo a inal illus a ion, Fig. 4displays he condi ional choice p obabili y o he
inside good o di e en combina ions o he p ice and he discoun o a ixed u ili y.
All poin s displayed a e associa ed wi h he same ne u ili y equal o one, uI=1
whe e uI=βb−βpp+βddwi h βb=6 and βp=−βd=−1. Howe e , going
om le o igh , we inc ease he discoun and he p ice simul aneously by he same
amoun so ha p−5=dwi hin he same expe imen al design. Unde he RU logi , he
choice p obabili y o he inside good emains cons an . In con as , choice p obabili ies
dec ease weakly as he p ice inc eases unde he RI-DCM. E en hough he discoun is
jus a nega i e p ice in u ili y e ms, he dis inc ion ma e s unde RI i p ice is simple
and he discoun is mo e complex o p ocess and in eg a e.
123

76 S. Tu lo e al.
Fig. 4 Condi ional choice p obabili ies o di e en composi ions o he inside al e na i e unde RI-
DCM and RU logi . This Figu e depic s he condi ional choice p obabili y o he inside good in he
discoun unde he cons ain ha he p ice inc ease equals he discoun inc ease wi h p−5=dso ha
he ne u ili y o he inside good is cons an . While choice p obabili y is cons an unde he RU logi , i
is weakly dec easing when bo h he p ice and he discoun a e inc easing in he conside ed a ia ion o
he inside good composi ion. The do s a e he condi ional choice p obabili ies o he speci ic inside good
composi ions
4.1.3 Ina en ion o al e na i es
A cen al ea u e o disc e e choice unde RI is ha conside a ion se s o m endoge-
nously. These se s include only he al e na i es ha ha e a s ic ly posi i e p obabili y
o being chosen. Conside a ion se s a ise as a esul o he DM’s op imal in o ma-
ion s a egy. He e, we demons a e how a ibu es—speci ically he con igu a ion o
simple a ibu es—de e mine which al e na i es a e conside ed.26
Figu e 5depic s choice p obabili ies in a choice se wi h ou inside al e na i es
i=1, ..., 4 ha p o ide u ili ies o ui=βb,i−pi+diwi h βb,i∈{2,1.75,1.5,1},
pi=2 and a discoun diwi h P (di=0)=P (di=2)=0.5. The speci ic
alues o βb,ia e chosen o illus a ion pu poses. While βb,4 ep esen s he leas
p e e ed b and al e na i e, we demons a e how he DM eac s quali a i ely di e en ly
o his b and as he composi ion o he choice se changes. The op-le panel o Fig. 5
26 Fo ela ed illus a i e examples o endogenous conside a ion se o ma ion ha do no di e en ia e
be ween a ibu es, see Caplin e al. (2019).
123
Disc e e choice in ma ke ing h ough... 77
Fig. 5 Conside a ion se o ma ion. The abo e panels p esen choice p obabili ies o a a ionally ina en-
i e DM acing up o ou al e na i es {a1,a2,a3,a4}o de ed om highes o lowes simple b and βb,i
wi h iden ical p ices piand iden ically dis ibu ed complex discoun s di. The op-le panel shows he
uncondi ional choice p obabili ies. The op- igh depic s condi ional choice p obabili ies gi en a choice se
whe e al e na i e a4p o ides he highes u ili y. Due o in o ma ion ic ions, e en in such a case, al e na-
i e a4is ne e chosen. The bo om-le panel exhibi s he upda ed uncondi ional choice p obabili ies in a
educed choice se ha d ops al e na i e a1. Finally, he bo om- igh panel shows ha , as a consequence
o upda ing uncondi ional choice p obabili ies o he smalle se , al e na i e a4has he highes condi ional
choice p obabili y in he s a e whe e i deli e s he highes payo
illus a es uncondi ional choice p obabili ies ha ep esen he DM’s belie s abou
how she will choose be o e any p ocessing o he complex discoun has aken place.
The op- igh panel shows he choice p obabili ies condi ioned on a speci ic choice
se , i.e., ealized alues o he complex discoun ( om he analys ’s pe spec i e, as
he DM will no necessa ily lea n he exac choice se because o p ocessing cos s).
The complex discoun s in he speci ic choice se a e d1=d2=d3=0 and d4=2,
implying ha a4p o ides he highes u ili y in he speci ic choice se (u4=1>uj
o j= 4). Ye , as appa en om he igu es, he DM does no conside a4because
excluding a4 om he endogenous conside a ion se was (a p io i) op imal o he DM
gi en he p ocessing cos s and he small p io p obabili y ha a4is, in ac , op imal.
Howe e , in con as o ex an wo-s age models (e.g., Gilb ide & Allenby 2004;
Goe ee, 2008; Te ui e al., 2011), RI p edic s ha a4will be conside ed once a1is no
longe a ailable o he DM (see he uncondi ional choice p obabili ies in he bo om-
le panel o Fig. 5). Due o upda ing uncondi ional choice p obabili ies o he smalle
123
78 S. Tu lo e al.
se , al e na i e a4has he highes condi ional choice p obabili y in he s a e whe e i
deli e s he highes pay-o (bo om- igh panel).
Acco dingly, RI implies de e minis ic conside a ion se s condi ional on λ,p io
belie s μsand a u ili y unc ion, while choice condi ional on such a conside a ion
se is s ochas ic. Howe e , because p io belie s μsa e a unc ion o ealized simple
a ibu e alues, conside a ion se s will gene ally change om choice se o choice
se in ways ha canno be cap u ed by an al e na i e speci ic index o decision ule.
I he simple in o ma ion in a choice se does no a y, RI s ill implies conside a ion
se s ha a e endogenous o consume s’ p e e ences, p io s o e complex a ibu es,
and in o ma ion p ocessing cos s. An a ac i e ea u e o cha ac e izing conside a ion
se s his way is ha he exclusion o , e.g., a b and om conside a ion in a pa icula
choice se , does no ha e o be mo i a ed by pe sis en ex eme as es o sc eening
ules. The la e may no gene alize o changes in he se o a ailable b ands o he
p io s o e complex a ibu es.
4.2 E ec s o choice en i onmen a ia ions unde RI
4.2.1 Impac o in o ma ion p ocessing cos s and incen i es
A la ge body o expe imen al e idence documen s ha he complexi y o choice asks
and incen i es a ec choice beha io (e.g., Swai & Adamowicz, 2001; Ding e al.,
2005). In RI, bo h aspec s in luence a en ion alloca ion and, hus, obse able choice.
Recall ha he cos s o in o ma ion p ocessing in RI a e he p oduc o mu ual
in o ma ion and he s ic ly posi i e uni in o ma ion cos λ>0, see exp ession Eq. 2.
S uc u ally, cha ac e is ics o he (expec ed) choice ask as well as cha ac e is ics o
he DM ela e o λ(e.g., Regie e al., 2014). To con inue wi h ou example o a complex
discoun , p ocessing he eligibili y equi emen s will be a ec ed by he numbe o
c i e ia ha mus be checked, o e en he on size used o desc ibe he discoun .
In ui i ely, mo e c i e ia ha need checking o a smalle on size will inc ease λ.
Simila ly, a less cons ained DM, o mo e expe ience wi h he p oduc o he eligibili y
c i e ia, will be e lec ed in a ela i ely smalle λ.
Finally, i is possible o cas λas a unc ion o he incen i es o e ed in a DCE.27
Fo example, i an incen i ized DCE ins uc s pa icipan s acing Nchoice asks ha
one o he Nchoices will become an ac ual ansac ion, he ealiza ion p obabili y o
a speci ic choice is ρ=1/N. Wi h p obabili y 1 −ρ he DM’s choice is hypo he ical,
i.e., she does no ac ually ob ain he chosen al e na i e.28 F om he pe spec i e o he
27 The implici assump ion he e is ha a change in incen i es does no a ec he payo unc ion o he
(subjec i e) p io dis ibu ion o e s a es ω.
28 Recall ha in an incen i e-aligned DCE, he DM is endowed wi h a budge . When he DM chooses he
ou side op ion, she e ains he endowed budge .
123
Disc e e choice in ma ke ing h ough... 79
DM, he esul ing RI objec i e unc ion o each choice ask is gi en by
ρ
ω∈
μs(ω) 
a∈A
P(a|ω)u(a,ω)
−λ
ρ
ω∈
μs(ω) 
a∈A
P(a|ω) ln P(a|ω)
−
a∈A
P(a)ln P(a).
This o mula ion e eals ha a highe ealiza ion p obabili y has he same impac
on choice beha io as a dec ease in he in o ma ion p ocessing cos s. Fo example, a
1% inc ease in in o ma ion p ocessing cos s λwill be o se by a 1% inc ease in he
ealiza ion p obabili y ρ. Thus, one way o in e p e ing he pa e ns we illus a e nex
is h ough he lens o changing incen i es in a DCE.
Conside he case when he DM chooses be ween an inside al e na i e, cha ac e ized
by a simple b and alued a βb=1.2 a a simple p ice p=2 and a complex discoun
dwi h P (d=0)=P (d=2)=0.5. Based on expec ed u ili y, he DM hus
p e e s he inside good. Figu e 6illus a es how λa ec s a en ion and choice in his
example. The op le panel shows ha when λinc eases, he p ocessing o complex
a ibu es dec eases un il he DM lea ns no hing beyond he known dis ibu ion o he
complex discoun a ibu e (a λ=λ), i.e., condi ional choice p obabili ies equal
he uncondi ional choice p obabili ies. A λ≥λ, he DM de e minis ically chooses
he inside op ion based on p io expec a ions (bo om le and igh panel), which o
cou se implies ha choice p obabili ies no longe change as a unc ion o he complex
discoun ( op igh panel). A λ=λ=0, he DM pe ec ly lea ns he complex
discoun and de e minis ically chooses he al e na i e wi h he highes u ili y, and
hence maximally eac s o changes in he complex discoun alue.
No e ha changes in λcan impac wha is e ealed abou he DM’s p e e ences.
The bo om-le panel o Fig. 6shows ha as λinc eases, he e is a choice e e sal as
he DM swi ches om choosing he ou side good (based on lea ning ha he complex
discoun does no apply) o choosing he inside good (based on p io expec a ions and
wi hou lea ning he ue choice se ω). Finally, he bo om- igh panel o Fig. 6shows
ha choice p obabili ies, and he e speci ically he p obabili y o making a choice
e o ( om he poin o iew o he analys who has all in o ma ion abou al e na i e
speci ic payo s), can be non-mono onic in he amoun o cogni i e p ocessing ( op-
le panel). The non-mono onic ela ionship he e de i es om he p io poin ing o he
payo maximizing choice in he absence o p ocessing complex in o ma ion.
To showcase wha an analys aking a RU pe spec i e when analyzing RI choice
da a may ind in his example, we i logi models o RI choices condi ional on di e en
alues o λ. Figu e 7summa izes poin es ima es o logi coe icien s o b and, p ice,
and discoun , ac oss di e en simula ed RI choice da a se s wi h a ying λ.
We see ha absolu e alues o he b and and p ice coe icien s, i.e., he coe i-
cien s associa ed wi h he simple a ibu es, i s dec ease and hen inc ease, while ha
o he complex discoun dec eases in λ. The la e e ec is immedia e, since highe
123
80 S. Tu lo e al.
Fig. 6 Impac o in o ma ion p ocessing cos s on a en ion, discoun e ec , and choice. The uppe le
panel shows mu ual in o ma ion as a unc ion o in o ma ion cos s. The uppe igh panel displays he impac
o a ixed inc ease o he complex discoun ( om 0 o 2) on condi ional choice p obabili y o di e en
le els o λ. The panels in he bo om ow show condi ional choice p obabili ies o he inside al e na i e
in choice se s whe e he discoun is 0 (le ) and 2 ( igh ). Thus, he inside good p o ides a lowe (highe )
payo in he le ( igh ) panel han he ou side op ion. No e ha choice is de e minis ic o in o ma ion
cos s λequal o ze o and la ge han λ
p ocessing cos s dampen he e ec o he discoun , as discussed p e iously. The a io-
nale o he o me pa e n is ha a small alues o λ, he DM p ocesses in mos
choice se s all a ailable in o ma ion, and choice becomes nea ly de e minis ic. Fo
in e media e le els o λ, some choice se s (cha ac e ized by di e en simple p ices)
will mo i a e mo e, and some less in o ma ion p ocessing, causing a highe le el o
o e all s ochas ici y in he da a ha is e lec ed in absolu ely smalle b and and p ice
coe icien s ( om he iewpoin o a RU logi ).
Fig. 7 Logi app oxima ion o di e en le els o in o ma ion p ocessing cos s. Each panel shows logi
es ima es o he espec i e coe icien s o a ying le els o in o ma ion p ocessing cos s λ. No e ha each
poin is he esul o an es ima ion om simula ed da a wi h T=1,000 choice asks each. The da a
gene a ing pa ame e s a e βp=−βd=−1, βb=2, pis uni o mly d awn om [2,4],anddis dis ibu ed
wi h P (d=0)=P (d=2)=0.5
123

Disc e e choice in ma ke ing h ough... 81
Fig. 8 Choice consis ency is non-mono onic in he in o ma ion p ocessing cos s λ. Choice consis ency
is measu ed by McFadden’s pseudo R-squa ed. Fo de ails, see Domencich and McFadden (1975)
E en ually, as λinc eases, ealized discoun alues a e igno ed, as i becomes oo
cos ly o p ocess he co esponding complex eligibili y equi emen s and he discoun
coe icien app oaches ze o in he logi i . Howe e , as he amoun o p ocessing o
complex in o ma ion dec eases beyond some le el, so does he le el o s ochas ici y
in he da a. E en ually, RI choices a e based on p io in o ma ion only, condi ioned
on he simple a ibu es b and and p ice he e, and de e minis ic. This is e lec ed
in absolu ely inc easing b and and p ice coe icien s in he logi i s, summa ized in
Fig. 7. I is common in he choice modeling li e a u e o epo he es ima ed e o e m
a iance as a measu e o choice consis ency (e.g., DeShazo & Fe mo, 2002. Figu e 8
plo s McFadden’s pseudo R-squa ed in ela ion o λ. I illus a es ha RI choices a e
mo e de e minis ic a e y low and e y high alues o λ, and less de e minis ic a
in e media e alues.
Figu e 9ex ends he illus a ion o RI choice as a unc ion o λ o he case o h ee
al e na i es.29 Al e na i e ai,i=1, ..., 3, yields u ili y ui=βb,i−pi+diwi h βb,1=
3.5, βb,2=3.25, βb,3=3, pi=4, and dia e independen ly dis ibu ed acco ding
o P (di=0)=P (di=2)=0.5. Based on p io in o ma ion, al e na i e a1is
he bes and a2is he second bes . Figu e 9displays condi ional choice p obabili ies
o a choice se ωwhe e al e na i e a3p o ides he highes payo based on ealized
alues o he complex discoun a ibu e, illus a ing how in o ma ion cos s λimpac
he o ma ion o conside a ion se s.
As λinc eases, he numbe o al e na i es chosen wi h s ic ly posi i e uncondi-
ional p obabili y i s dec eases om h ee o wo (a λ), and e en ually esul s in
de e minis ic choice o a1based on p io conside a ions only ( o he igh o λ). As
he in o ma ion cos s inc ease, he cos s o esol ing unce ain y abou a p io i less
a ac i e al e na i es ou weigh he (expec ed) bene i s. As a consequence, i becomes
op imal o igno e such al e na i es e en i he e exis choice se s ωin which he igno ed
29 Fo ease o exposi ion and wi hou loss o gene ali y, he e is no ou side op ion in his example.
123
82 S. Tu lo e al.
Fig. 9 Impac o in o ma ion cos s on conside a ion se size. Condi ional choice p obabili ies o h ee
al e na i es a e displayed as a unc ion o in o ma ion p ocessing cos s λin he choice se whe e a3is
he bes al e na i e. As in o ma ion cos s inc ease, he DM a ionally chooses o igno e al e na i es in he
choice se . λ,λ,andλ indica e h eshold alues o which he conside a ion se size changes. Fo cos s
λ=0 choice is de e minis ic, and he bes al e na i e a3is always chosen, howe e , a e conside ing all
al e na i es. Fo cos s la ge han λ, choice becomes de e minis ic again, howe e now because he DM
igno es al e na i es a2and a3, ega dless o ealized complex discoun le els
al e na i es p o ide he highes payo (as depic ed in Fig. 9).30 Toge he , he illus a-
ions in his sec ion sugges ha RI p o ides a use ul basis o b idging ac oss choices
unde di e en incen i e o di icul y le els.
4.2.2 A ibu e ange/dispe sion and le els e ec s
Nex , we show how he a ibu e ange, ypically measu ed as he di e ence be ween
he highes and he lowes le el o an a ibu e, o mo e gene ally, he dispe sion
o complex a ibu es, mode a es he impac o a one-uni inc ease in ha a ibu e
on choice. The unde lying mechanism is ha as he ange o he complex a ibu e
inc eases, he expec ed gain om iden i ying i s ealized alue also inc eases, making
p ocessing in o ma ion mo e aluable. This ul ima ely inc eases he impac o he
complex a ibu e on choice and in con as o wha one would expec when aking a
RU pe spec i e.
Figu e 10 illus a es his mechanism in ou leading ca example. We se βb=6
and ecall ha βp=−βd=−1. He e, we s udy he impac o an inc ease in he
discoun om 2 o 3 on condi ional choice p obabili ies o di e en discoun anges.
Bo h lines in Fig. 10 depic how condi ional choice p obabili ies change when he
complex discoun inc eases by one uni o di e en alues o he simple p ice. The
dashed blue line ep esen s he case whe e he complex discoun is d awn om he
se {1,2,3,4}, while in he second case (solid ed line) he discoun akes alues in
30 This way, RI can mo i a e a posi i e p obabili y o choosing an al e na i e ha is domina ed a pos e io i,
i.e., a e p ocessing (some) complex in o ma ion (c . Ruan e al., 2008 who p opose a sequen ial sampling
model o model dominance as a o m o simila i y).
123
Disc e e choice in ma ke ing h ough... 83
Fig. 10 Range e ec s o complex a ibu es. This Figu e displays condi ional choice p obabili y di e -
ences o he inside al e na i e in eac ion o an inc ease o he discoun om 2 o 3 gi en a la ge ange (solid
ed) and a small ange (dashed blue) o he complex discoun as a unc ion o he simple p ice. Speci ically,
complex a ibu e le els a e {1,2,3,4}when he ange is small, and hey a e {0,2,3,5}when he ange is
la ge
{0,2,3,5}. In bo h cases, he DM’s belie s a e uni o m o e he espec i e suppo .
Figu e 10 shows ha as he ange o he complex discoun a ibu e inc eases, he
impac o a one-uni inc ease o he discoun also inc eases. Technically, an inc ease
in he a ibu e ange sp eads he ange o possible payo s om choosing he inside
good u he , mo i a ing la ge (cos ly) depa u es o condi ional choice p obabili ies
om hei uncondi ional coun e pa s as a esul o he op imal p ocessing s a egy.
To showcase wha an analys aking a RU pe spec i e when analyzing RI choice
da a may ind in his example, we i logi models o simula ed RI choices condi ional
on di e en anges o he complex discoun in he expe imen al design. We gene a e
da a se s as ollows: βb=5, βp=−βd=−1, p∈[8,10], and dis d awn wi h equal
p obabili y om he bina y se {4−x,4+x}wi h x∈[0.25,4]. Figu es 11 and 12
summa ize he logi es ima es as well as McFadden’s pseudo R-squa ed alues as a
unc ion o he ange o he complex discoun in a pa icula expe imen al design. When
he ange o he complex discoun is small, he es ima ed b and and p ice coe icien s
a e absolu ely la ge, and he discoun coe icien is, ela i ely, much smalle . As he
ange inc eases, b and and p ice coe icien s become smalle in absolu e alue, and
he in e ed discoun coe icien s end o inc ease.
123
84 S. Tu lo e al.
Fig. 11 Logi es ima es o di e en le els o he discoun ange. This Figu e displays es ima ed coe i-
cien s o b and, p ice, and discoun o di e en anges o he complex a ibu e. Each poin is he esul o
i ing a logi model wi h simula ed da a om T=1,000 choices wi h da a gene a ing pa ame e s λ=0.5,
βb=5, βp=−βd=−1, and pbeing uni o mly d awn om [8,10]. The discoun ange, gi en as he
di e ence be ween he wo discoun le els, is a ied om 0.5 o8
Figu e 12 exhibi s a U-shaped ela ionship be ween choice consis ency and he
ange o he complex discoun . When he ange is e y small, he DM makes less cos ly
mis akes when choosing based on p io belie s, condi ioned on he simple a ibu es
b and and p ice in his example. As a consequence, he DM pays li le a en ion o he
ealized discoun le els and chooses a he consis en ly based on simple a ibu es as
well as he expec ed discoun le el only. As he ange inc eases, he mis akes when
choosing based on p io belie s can become a he cos ly. Howe e , he e s ill a e
p ices a which lea ning he ealized complex discoun in addi ion does no add much
alue. In he RU logi app oxima ion, he ela i e impo ance o he discoun inc eases,
howe e , choice consis ency dec eases.
Finally,when hediscoun angebecomessola ge ha ewe and ewe simple p ices
wi hin he suppo o he design ansla e in o a good enough choice (in expec a ion)
wi hou knowing he ealized discoun le el, he DM will p ocess he complex discoun
consis en ly. This again esul s in less s ochas ic da a.
Fig. 12 Non-mono onic e ec o he discoun ange on choice consis ency. Choice consis ency is mea-
su ed as McFadden’s pseudo R-squa ed. Fo de ails, see Domencich and McFadden (1975)
123
Disc e e choice in ma ke ing h ough... 91
key ques ion is hus how o assess and simula e (likely) belie s in he ma ke se ing.
Choosing belie dis ibu ions based on ac abili y in a closed- o m logi amewo k
wi h addi i ely sepa able indices, as cu en ly s anda d in empi ical applica ions (see
Sec ion 3.1), does no seem o be a sa is ac o y solu ion.
In ligh o a g owing empi ical RI li e a u e ha elies on belie assump ions mo i-
a ed by analy ical con enience, we eel ha esea ch in o he sensi i i y wi h espec
o di e en assump ions abou belie s will be use ul, as well as an in eg a ion o
me hods o s udy po en ially he e ogeneous ma ke belie s empi ically. The cha ac-
e iza ion o an RI-DCM ha allows o gene al p io belie s in his pape pa es he
way o his line o esea ch. O he amewo ks modeling limi ed in o ma ion, such
as consume sea ch models o lea ning models, ace a simila challenge o dealing
wi h ypically unobse able (consume ) belie s as a key building block o empi ical
analysis and coun e ac ual compu a ions and a e o en qui e sensi i e wi h espec o
assump ions abou belie s (Chin agun a & Nai , 2011).
No ably, some o hese con ibu ions ha e explo ed he added bene i o elici ing
belie s h ough auxilia y in o ma ion a he han elying on pu ely heo e ical assump-
ions, such as a ional expec a ions. Success ul app oaches ha ha e been employed
in o he a eas o lea n abou belie s use su ey-based belie elici a ion me hods (e.g.,
Ca allo e al., 2017; Coibion e al., 2018; A mona e al., 2019) o obse a ional da a
such as clicks eam da a (e.g., Hu e al., 2019), o eye- acking da a (e.g., U su e
al., 2024). Fo a ecen o e iew in ma ke ing, see he li e a u e sec ion in Jindal and
A iba g (2021).
5.5 Al e na i e in o ma ion cos unc ions
The e is an ongoing discussion in he economics li e a u e on he ques ion o which
a en ion cos unc ion is app op ia e o which choice ci cums ances. Mos o he
expe imen al s udies, ei he explici ly o implici ly, es ima e he cos unc ion, which
is hen used in subsequen analyses. Consequen ly, much o he expe imen al li e a u e
dealing wi h RI (implici ly) es s he applicabili y o di e en cos unc ions in a a ie y
o s ylized se ings. As in he p esen pape , many esul s in RI heo y ha e been de i ed
unde he assump ion o cos s ha a e linea in Shannon mu ual in o ma ion.35
Fo ins ance, expe imen al e idence sugges s ha non-linea i ies o in o ma ion
cos s exis , whe e subjec s pay oo li le a en ion o high ewa ds compa ed o low
ewa ds (Caplin & Dean, 2013; Dean & Neligh, 2019). Pe haps mo e impo an o
analyzing MAMA choice, a linea Shannon en opy cos unc ion p ecludes he con-
cep o pe cep ual dis ance, whe e some s a es a e ha de o dis inguish han o he s
(Dean & Neligh, 2019; Hébe & Wood o d, 2021). As a esul o his c i ique, some
pape s gene alize he linea Shannon cos unc ion o apply di e en cos unc ions.
Fo ins ance, Hébe and Wood o d (2021) in oduce a neighbo hood cos unc ion o
35 Ma´ckowiak e al. (2023) discuss wha ea u es o RI a e obus wi h espec o he unc ional o m o
in o ma ion p ocessing cos s.
123

92 S. Tu lo e al.
add ess he p oblem ha some s a es a e ha de o dis inguish han o he s.36 A de ailed
discussion o his mos ly heo e ical li e a u e is beyond he scope o his pape .37
We belie e ha he choice o cos unc ion could become impo an o he appli-
ca ions en isioned in his pape as well. Fo ins ance, he model o mula ion based on
Shannon cos s implies ha any wo possible choice se s (s a es ω) wi hin an expe -
imen al design a e equally ha d o dis inguish. Howe e , i is no unlikely ha he
dis inc ion be ween wo choice se s ha pose many complex ade-o s may be ha de
han ha be ween wo choice se s ha pose ewe ade-o s each. We hus conjec u e
ha neighbo hood-based cos s ha allow o impose ha ce ain se s o choice se s
a e ha de o dis inguish han o he s may e en ually become use ul. We no e ha his
is ela ed o a ine dis inc ion o le els o p ocessing di icul y han he dis inc ion
be ween simple and complex a ibu es p oposed in his pape .
5.6 Concep ualiza ion o ee in o ma ion
The his o y o esea ch on choice in ma ke ing, economics, and psychology is ich in
empi ical and heo e ical esul s abou wha may be simple and mo e complex abou
a pa icula choice ask o se o such asks. Fo example, i may be wo hwhile o
econside he li e a u e on heu is ics in choice as in o ma ion ( o he analys ) abou
simple aspec s o choice asks ha , in he con ex o a RI-DCM, may gi e ise o
p io belie s ha guide he amoun o p ocessing o mo e complex aspec s o a choice
ask.38
In ou sugges ed speci ica ion o he RI-DCM, some a ibu es a e conside ed simple
so ha p ocessing hem does no equi e (signi ican ) cogni i e e o . Thus, i is hese
a ibu es xs ha de e mine (condi ional) p io belie s μs, which hen o m a key
ing edien o how much p ocessing o complex a ibu es should occu (see Sec ion 2).
This o mula ion imposes a speci ic mapping om choice se s in o p io belie s ha is
no gi en by RI heo y bu assumed by he analys (e en i , as we showed, an empi ical
dis inc ion be ween simple and complex a ibu es is possible, in gene al).
In p inciple, any aspec o a choice se and he a ibu e con igu a ion p esen ed
he ein could be simple in o ma ion and hus de e mine p io belie s. Conside , o
example, a DCE design whe e he discoun has alues d∈{50, ..., 90,100}.ADM
may easily ecognize ha he discoun equals 100 due o he subs an ially di e en
isual s imulus ( wo s. h ee digi s). In his case, he DM may assign a posi i e belie
o all choice se s whe e d=100 and ze o o all o he .
This aises he concep ual ques ion o which pieces o in o ma ion in any choice
ask can be conside ed ee and, consequen ly, how o map choice se s in o (condi-
ional) p io belie s. Ou discussion ega ding he empi ical iden i ica ion o simple
s. complex a ibu es in Sec ion 3.5 should be iewed as a special case o his b oade
36 A ela ed gene aliza ion o Shannon cos s ha allows o al e na i es o ha e di e en in o ma ion cos s
is sugges ed by Hue ne e al. (2019).
37 Fo an o e iew o di e en in o ma ion cos unc ions applied in he beha io al ina en ion li e a u e,
see Gabaix (2019); o a mo e de ailed discussion on en opy-based cos unc ions, see Dean and Neligh
(2019) as well as Ma´ckowiak e al. (2023).
38 See also Ma´ckowiak e al. (2023) who p opose he idea ha RI p o ides a model o he o ma ion o
heu is ics.
123
Disc e e choice in ma ke ing h ough... 93
conside a ion. Due o he high dimensionali y o his ques ion, i will ypically no be
iable o gi e pu ely empi ical answe s, and an appeal o heo y and p e ious empi ical
esul s is equi ed.
While his is beyond he scope o his pape , i sugges s ha he RI amewo k
may be able o ui ully in eg a e conjec u ed and empi ically demons a ed choice
simpli ica ion s a egies wi h ully a ional beha io ha is guided by p io s o med
on he basis o wha e e a DM may easily and immedia ely p ocess abou a choice
ask. Wi h an eye owa ds indus y-g ade applica ions wi h many a ibu es and many
al e na i es, his is an impo an pa o u u e esea ch.
A Appendix
A.1 Iden i ica ion o 1 ac oss decision en i onmen s unde s able p e e ences
Nex , we p esen es ima ion esul s o show ha a ela i e change in in o ma ion
p ocessing cos s unde s able p e e ences can be iden i ied (see Table 14). We sim-
ula e 2,000 choices o one indi idual, wi h one inside and one ou side op ion. The
i s hal o he 2,000 choices a e made in an “easy” en i onmen wi h lowe in o -
ma ion p ocessing cos s λlow, and he second hal in a mo e di icul en i onmen
subjec o highe in o ma ion p ocessing cos s λhigh. The inside good consis s o h ee
a ibu es: wo simple and one complex. One simple a ibu e is a b and in e cep , and
he emaining a ibu es ha e he ollowing le els: simple p ice p∈{2.5,3,3.5,4,4.5}
and complex discoun d∈{0,0.5,1,1.5,2}. The p e e ence ec o is gi en by
β=(βb,βp,β
d)=(2.5,−1,1)and in o ma ion p ocessing cos s a e λlow=0.1
and λhigh =0.3. In es ima ion, we ix λhigh o he da a gene a ing alue and join ly
es ima e λlowand β. The hi d ow in Table 14 shows ha we can eco e he da a-
gene a ing pa ame e s, and he i h ow illus a es he bias om igno ing he di e ence
in p ocessing cos s, as well as he poo e i om doing so.
A.2 Simula ion s udy
The simula ion s udy builds on he se -up used o illus a i e simula ions in Sec-
ion 3.3 o he pape . We a y he numbe o inside goods (one e sus wo), simula e
Table 14 Pos e io means o p e e ences and in o ma ion p ocessing cos s
Model B and P ice Discoun λlowλhigh LMD
Da a gene a ion 2.50 -1.00 ≡−βp0.10 0.30
RI-DCM 2.59 -1.03 ≡−βp0.10 0.30 -253.38
(0.10) (0.04) (0.01)
RI-DCM wi h ixed λ2.28 -0.91 ≡−βp0.20 0.20 -298.98
(0.11) (0.04)
In he i s model, λhigh is ixed o da a gene a ing alue in es ima ion. Fo he second model, he in o ma ion
p ocessing cos s a e ixed o 0.2
123
94 S. Tu lo e al.
Table 15 Means o pos e io means and a iances o p e e ence dis ibu ions o di e en model speci-
ica ions using 50 simula ions wi h one inside and one ou side good each and homogenous in o ma ion
p ocessing cos s
Pos e io Means Model Fi s
Model B and P ice Discoun LMD LMD
Da a gene a ion 2.50 -1.00 ≡−βp
RI-DCM 2.51 -1.00 ≡−βp-2,465.49
(0.02) (0.01) (63.88)
RU logi sepa a e 26.41 -8.71 4.41 -2,630.29 162.17
(0.84) (0.32) (0.19) (75.46) (26.47)
RU logi join 9.94 -4.01 ≡−βp-4,602.05 2018.19
(0.14) (0.09) (236.44) (50.34)
BC sepa a e 27.43 -9.08 4.51 -2,608.36 136.66
(0.89) (0.51) (0.25) (73.41) (25.72)
BC join 11.48 -4.13 ≡−βp-3,160.25 685.37
(0.99) (0.16) (82.37) (49.87)
Pos e io Va iances
Model B and P ice Discoun
Da a gene a ion 0.25 0.04 ≡Va (βp)
RI-DCM 0.29 0.05 ≡Va (βp)
(0.04) (0.01)
RU logi sepa a e 14.01 1.82 1.12
(0.84) (0.32) (0.19)
RU logi join 5.31 0.70 ≡Va (βp)
(1.01) (0.30)
BC sepa a e 20.11 1.73 1.57
(1.06) (0.57) (0.45)
BC join 9.73 0.44 ≡Va (βp)
(0.83) (0.20)
S anda d de ia ions a e in pa en heses. Fo he BC sepa a e and BC join model, he means o pos e io
means o he p ice h eshold a e 10.91 and 4.67 wi h s anda d de ia ions o 5.02 and 0.81, espec i ely.
The means o he pos e io a iances o he p ice sc eening h esholds a e 8.41 o he BC sepa a e and
1.01 o he BC join model
da a wi h and wi hou he e ogenei y in p ocessing cos s (in addi ion o p e e ences he -
e ogenei y), and add a wo-s age choice model wi h conside a ion se s om sc eening
on p ice (see e.g., Gilb ide & Allenby, 2004; Pachali e al., 2023) o he model compa -
ison. We use he ollowing (s anda d) weakly in o ma i e subjec i e p io pa ame e
se ings o he one and he wo-inside good cases, espec i ely: {¯
β∼N(0,100I),
Vβ∼IW(4,1.5I)}and {¯
β∼N(0,100I),Vβ∼IW(5,2I)}. The sligh ly mo e
in o ma i e subjec i e p io o he hie a chical p io a iance o {βi},Vβis owed
o he inc eased dimensionali y o he es ima ion p oblem. When we es ima e he
hie a chical p io a iance o {log(λi)},weuseσ2
log(λ) ∼IG(3,1).
123
Disc e e choice in ma ke ing h ough... 95
We simula e 50 da a se s in he ou da a-gene a ing se ings and es ima e i e mod-
els o each: he RI-DCM, wo RU logi models, and wo models wi h p ice-based
conside a ion se s (BC sepa a e and BC join ). The benchma k models a e es ima ed
once wi h a single p ice pa ame e and once wi h sepa a e pa ame e s o he (sim-
ple) p ice and he (complex) discoun . Each da a eplica ion in his simula ion s udy
esamples N×Tchoice se s om he design base de ined by p ices pand discoun s d,
d awn uni o mly and independen ly om he ollowing se s: p∈{2.5,3,3.5,4,4.5}
and d∈{0,0.5,1,1.5,2}and e-samples p e e ences (and p ocessing cos s when
Table 16 Means o pos e io means and a iances o p e e ence dis ibu ions o di e en model speci ica-
ions o e 50 simula ions wi h wo inside goods and one ou side good each and homogenous in o ma ion
p ocessing cos s
Pos e io Means Model Fi s
Model B and 1 B and 2 P ice Discoun LMD LMD
Da a gene a ion 2.50 2.50 -1.00 ≡−βp
RI-DCM 2.54 2.53 -1.03 ≡−βp-3,807.55
(0.05) (0.05) (0.03) (56.43)
RU logi sepa a e 24.89 24.55 -8.06 4.33 -4,160.46 272.48
(0.76) (0.69) (0.31) (0.19) (102.34) (54.03)
RU logi join 10.01 9.97 -3.99 ≡−βp-6,838.41 2940.38
(0.25) (0.24) (0.05) (107.61) (60.37)
BC sepa a e 25.19 24.91 -8.41 4.44 -4,196.47 228.54
(0.69) (0.62) (0.33) (0.10) (94.31) (48.01)
BC join 11.15 11.67 -4.01 ≡−βp-5,431.81 1549.33
(0.29) (0.37) (0.09) (81.69) (50.67)
Pos e io Va iances
Model B and 1 B and 2 P ice Discoun
Da a gene a ion 0.25 0.25 0.04 ≡Va (βp)
RI-DCM 0.28 0.30 0.05 ≡Va (βp)
(0.05) (0.06) (0.01)
RU logi sepa a e 12.01 11.19 1.97 1.22
(0.84) (0.72) (0.21) (0.11)
RU logi join 6.31 6.23 0.60 ≡Va (βp)
(0.41) (0.44) (0.17)
BC sepa a e 17.41 16.33 1.70 1.27
(3.16) (3.55) (0.39) (0.21)
BC join 8.73 8.56 1.04 ≡Va (βp)
(0.83) (0.81) (0.20)
S anda d de ia ions a e in pa en heses. Fo he BC sepa a e and BC join model, he means o pos e io
means o he p ice h eshold a e 12.01 and 4.26 wi h s anda d de ia ions 5.04 and 0.71, espec i ely. The
means o he pos e io a iances o he p ice sc eening h esholds a e 10.39 o he BC sepa a e and 0.91
o he BC join model
123
96 S. Tu lo e al.
Table 17 Means o pos e io means and a iances o p e e ence dis ibu ions o di e en model speci-
ica ions o e 50 simula ions wi h one inside and one ou side good each and he e ogeneous in o ma ion
p ocessing cos s
Pos e io Means Model Fi s
Model B and P ice Discoun LMD LMD
Da a gene a ion 2.50 -1.00 ≡−βp
RI-DCM scale mix u e 2.51 -1.01 ≡−βp-2,444.54
(0.04) (0.03) (53.41)
RU logi sepa a e 26.97 -8.92 4.43 -2,616.04 185.58
(1.51) (0.47) (0.10) (62.66) (17.39)
RU logi join 10.07 -4.02 ≡−βp-4,530.19 2083.55
(0.69) (0.21) (95.38) (61.37)
BC sepa a e 27.50 -8.84 4.23 -2,603.48 156.47
(2.31) (1.04) (0.68) (74.31) (21.71)
BC join 11.31 -4.40 ≡−βp-3,171.05 663.49
(1.62) (0.60) (67.46) (82.94)
Pos e io Va iances
Model B and P ice Discoun σ2
log(λ)
Da a gene a ion 0.25 0.04 ≡Va (βp)0.09
RI-DCM scale mix u e 0.30 0.05 ≡Va (βp)0.08
(0.05) (0.01) (0.02)
RU logi sepa a e 15.11 1.62 1.73
(0.94) (0.32) (0.29)
RU logi join 6.21 0.73 ≡Va (βp)
(1.54) (0.14)
BC sepa a e 14.41 1.84 1.90
(2.13) (0.41) (0.45)
BC join 10.15 0.39 ≡Va (βp)
(1.23) (0.13)
S anda d de ia ions a e in pa en heses. Fo he BC sepa a e and BC join model, he means o pos e io
means o he p ice h eshold a e 10.38 and 4.13 wi h s anda d de ia ions 5.26 and 0.80 espec i ely. The
means o he pos e io a iances o he p ice sc eening h esholds a e 13.94 o he BC sepa a e and 0.89
o he BC join model. σ2
log(λ) is he a iance o log in o ma ion p ocessing cos s in he popula ion
he e ogeneous) om popula ion pa ame e s. In each eplica ion, a ( esh) sample o
a ionally ina en i e DMs (N=1,000) ace T=20 choices se s.
The u ili y o inside good i o DM jin choice ask is gi en by uj,i, =βb,j,i+
βp,j(pj,i, −dj,i, )whe eβb,j,iis he b and coe icien , βp,j hep ice coe icien , pj,i,
is he p ice, and dj,i, is he discoun . The u ili y o he ou side op ion is no malized
o ze o: uO=0. As in he illus a i e simula ions in Sec ion 3.3, b and and p ice a e
simple a ibu es, while he discoun equi es cos ly p ocessing. When p ocessing cos s
a e homogenous, hey a e se o λ=0.25. When he e ogeneous, hey a e gene a ed
om log(λj)∼N(−1.4,0.09). P e e ence coe icien s a e independen ly gene a ed
123

Disc e e choice in ma ke ing h ough... 97
Table 18 Means o pos e io means o p e e ence dis ibu ions o di e en model speci ica ions o e 50
simula ions wi h wo inside goods and one ou side good each and he e ogeneous in o ma ion p ocessing
cos s
Pos e io Means Model Fi s
Model B and 1 B and 2 P ice Discoun LMD LMD
Da a gene a ion 2.50 2.50 -1.00 ≡−βp
RI-DCM scale mix u e 2.52 2.52 -1.02 ≡−βp-3,800.39
(0.04) (0.04) (0.02) (56.51)
RU logi sepa a e 27.33 27.19 -7.34 4.71 -4,172.86 363.87
(4.56) (5.31) (0.97) (0.53) (75.37) (44.63)
RU logi join 10.94 10.88 -5.63 ≡−βp-6,873.34 3,014.79
(1.34) (1.57) (0.81) (79.31) (84.28)
BC sepa a e 26.39 26.01 -8.11 5.01 -4,114.34 305.67
(5.11) (4.89) (1.02) (0.64) (69.37) (50.31)
BC join 10.70 10.17 -5.21 ≡−βp-5,404.29 1,603.48
(1.31) (1.29) (0.93) (79.14) (85.34)
Pos e io Va iances
Model B and 1 B and 2 P ice Discoun σ2
log λ
Da a gene a ion 0.25 0.25 0.04 ≡Va (βp)0.09
RI-DCM scale mix u e 0.29 0.28 0.05 ≡Va (βp)0.09
(0.06) (0.06) (0.01) (0.01)
RU logi sepa a e 13.11 9.59 1.62 1.17
(0.83) (0.68) (0.25) (0.12)
RU logi join 6.95 6.77 0.68 ≡Va (βp)
(0.48) (0.48) (0.19)
BC sepa a e 16.44 15.98 1.65 1.31
(3.50) (3.31) (0.40) (0.25)
BC join 9.02 8.74 0.64 ≡Va (βp)
(0.88) (0.80) (0.23)
S anda d de ia ions a e in pa en heses. Fo he BC sepa a e and BC join model, he means o pos e io
means o he p ice h eshold a e 13.31 and 4.43 wi h s anda d de ia ions 6.84 and 0.83 espec i ely. The
means o he pos e io a iances o he p ice sc eening h esholds a e 16.73 o he BC sepa a e and 0.96
o he BC join model. σ2
log(λ) is he a iance o log in o ma ion p ocessing cos s in he popula ion
om he ollowing dis ibu ions: βb,j,i∼N(2.5,0.25)and βp,j∼N(−1,0.04),
i.e., he wo b ands a e symme ic in he popula ion in he case o wo inside b ands.
Tables 15,16,17, and 18 epo dis ibu ions o p e e ence es ima es and model
i ac oss da a eplica ions in ou ou da a gene a ing se ings o each o he i e
models i . The las column in he uppe ables, LMD, shows log-ma ginal densi y
di e ences ela i e o he RI-DCM ac oss simula ions. Posi i e alues indica e ha
he RI-DCM achie es be e model i .
No su p isingly, we ind ha only he RI-DCM eco e s da a-gene a ing pa ame-
e s. We also ind ha (i) we can eliably dis inguish he da a gene a ing RI-DCMs om
all he benchma k models (see columns LMD and LMD in he espec i e ables), (ii)
123
98 S. Tu lo e al.
Table 19 Qua iles as well as he minimum and he maximum o he log-likelihood MCMC d aws o
di e en λle els o he co ec and w ong speci ica ion espec i ely
Model min 25% 50% 75% max
λ=0.01
Co ec - Linea -1.42 0.00 0.00 0.00 0.00
Misspeci ied - Linea -1.86 0.00 0.00 0.00 0.00
λ=5
Co ec - Linea -4.85 -3.83×10−7-9.82×10−9-1.71×10−10 0.00
W ong - Linea -1.45 -3.73×10−7-1.07×10−8-2.36×10−10 0.00
he app oxima ing benchma k models a e ela i ely much wo se in he la ge choice
se because o he co esponding inc ease in he numbe o op imal RI in o ma ion
s a egies39 (compa ing LMD in Tables 15 and 17 o ha in Tables 16 and 18, espec-
i ely), and (iii), sligh ly wo se when p ocessing cos s a e he e ogeneous, in addi ion
o p e e ences he e ogenei y (compa ing LMD in Tables 15 and 16 o ha in Table
17 and 18, espec i ely).
Finally, we can see ha benchma k models subs an ially bene i om including
sepa a e coe icien s o p ice and discoun and ha modeling sc eening based on
p ice u he imp o es he i o benchma k models. Howe e , e en he combina ion
o sepa a e coe icien s o p ice and discoun wi h p ice sc eening i s eliably wo se
han he RI-DCM. In he case o one inside good only, wha is missing om his
app oxima ion is he complex in e ac ion be ween p ice and discoun implied by op i-
mal p ocessing unde RI. In he case o wo inside goods, conside a ion o one inside
good also depends on simple ea u es o he o he inside good. Simila ly, he p ocessed
con ibu ion o one b and’s discoun depends on he simple a ibu es o his b and
and ha o he o he b and.
A.3 Iden i ica ion in he case o ex eme in o ma ion p ocessing cos s
Dis inc ion o simple and complex u ili y aspec s o a choice ask Table 19 illus a es
ha he dis inc ion be ween simple and complex a ibu es becomes mu e once he da a
become (essen ially) de e minis ic a e y low o e y high p ocessing cos s λ.We
again simula e 2,000 choice asks wi h he same design as ou lined in Sec ion 3.5
bu now wi h in o ma ion p ocessing cos s λ=0.01, making p ocessing complex
in o ma ion essen ially ee, and λ=5, making in o ma ion p ocessing in easible.
When λis su icien ly small, all in o ma ion is ully p ocessed, and he concep ual and
39 Recall om exp ession Eq. 2 ha op imal in o ma ion s a egies a e condi ional on ealized le els o
simple a ibu es. Wi h one inside b and and i e le els o simple p ice, he e a e i e di e en op imal
p ocessing s a egies, depending on he ealized simple p ice in a choice se . Wi h wo inside b ands and
i e le els o simple p ice, he e al eady a e 52=25 di e en con igu a ions o simple a ibu es, gi ing
ise o di e en op imal p ocessing s a egies.
123
Disc e e choice in ma ke ing h ough... 99
Fig. 15 His og am o MCMC d aws o he complex a ibu e pa ame e unde di e en in o ma-
ion p ocessing cos s λ. This Figu e shows his og ams o he pos e io dis ibu ion o complex a ibu e
coe icien based on 100,000 d aws om he implied ma ginal pos e io o co ec ly speci ied simple and
complex a ibu es. The solid e ical line indica es he da a-gene a ing alue
empi ical dis inc ion be ween simple and complex anishes. When λis su icien ly
la ge, he in o ma ion in complex a ibu es is no in eg a ed in o he o e all e alua ion
o al e na i es. I , in his case, he analys alsely speci ies complex a ibu es as simple
and simple a ibu es as complex, he es ima o will in e ex eme u ili y pa ame e s
o he la e ela i e o he o me such ha de e minis ic choice based on simple
a ibu es ( alsely assumed o be complex) ensues.
Se iden i ica ion o p e e ences Figu e 15 illus a es ha u ili y coe icien s a e
only se -iden i ied once choices become (essen ially) de e minis ic, using he example
o he complex a ibu e coe icien in he co ec ly speci ied model.
Acknowledgemen s We hank Ana Ma ino ici, Dan Ba els, Xiaolin Li, Tame Boyaci, Robe Zei ham-
me , Daniel Acke be g, Jean-Pie e Dubé, Je emy Fox, Wes Ha mann, Gün e Hi sch, Ca l Mela, and
S ephan Seile o help ul commen s and sugges ions. We also bene i ed om he commen s o semi-
na pa icipan s a he 17 h Annual Bass FORMS Con e ence in Dallas, EMAC 2022 in Budapes , he
INFORMS Ma ke ing Science Con e ence 2022, as well as he Kleinwalse al Semina s in 2020-2022. We
g a e ully acknowledge inancial suppo by he Ge man Resea ch Founda ion (DFG G an ID: OT 447/2-
1). A ash Laghaie acknowledges unding by Fundação pa a a CiênciaeaTecnologia(UIDB/00124/2020,
UIDP/00124/2020, UID/00124, No a School o Business and Economics and Social Sciences Da aLab -
PINFRA/22209/2016), POR Lisboa and POR No e (Social Sciences Da aLab, PINFRA/22209/2016).
123
100 S. Tu lo e al.
Funding Open Access unding enabled and o ganized by P ojek DEAL.
Da a A ailabili y Code o es ima ion and eplica ion o ables and igu es in he pape a e a ailable a :
h ps://gi on .io/ /use -3843061/Sq bQZ5sX bH/Ra ional-Ina en ion-Disc e e-Choice/
Decla a ions
Con lic s o In e es This wo k was suppo ed by he Ge man Resea ch Founda ion (G an ID: OT 447/2-1).
The au ho s ha e no u he compe ing in e es s o decla e ha a e ele an o he con en o his a icle.
123
Open Access This a icle is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License, which
pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long as you gi e
app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons licence,
and indica e i changes we e made. The images o o he hi d pa y ma e ial in his a icle a e included
in he a icle’s C ea i e Commons licence, unless indica ed o he wise in a c edi line o he ma e ial. I
ma e ial is no included in he a icle’s C ea i e Commons licence and you in ended use is no pe mi ed
by s a u o y egula ion o exceeds he pe mi ed use, you will need o ob ain pe mission di ec ly om he
copy igh holde . To iew a copy o his licence, isi h p://c ea i ecommons.o g/licenses/by/4.0/.
Re e ences
Abaluck, J., Compiani, G., & Zhang, F. (2022). A me hod o es ima e disc e e choice models ha is obus
o consume sea ch. Unpublished manusc ip , Yale School o Managemen , Uni e si y o Chicago,
and Uni e si y o Cali o nia.
Ande son, N. H. (1981). Founda ions o In o ma ion In eg a ion Theo y. Academic P ess.
Ande son, N. H. (1982). Me hods o In o ma ion In eg a ion Theo y. Academic P ess.
And ews, R. L., & S ini asan, T. (1995). S udying conside a ion e ec s in empi ical choice models using
scanne panel da a. Jou nal o Ma ke ing Resea ch, 32(1), 30–41.
A iba g, A., O e , T., Zan edeschi, D., Allenby, G. M., Ben ley, T., Cu y, D. J., Do son, M., Hende son,
T., Honka, E., Kohli, R., e al. (2018). Ad ancing non-compensa o y choice models in ma ke ing.
Cus ome Needs and Solu ions, 5(1), 82–92.
A men e , R., Mülle -I en, M., & S angebye, Z. R. (2024). Geome ic me hods o ini e a ional ina en ion.
Quan i a i e Economics, 15(1), 115–144.
A mona, L., Fus e , A., & Za a , B. (2019). Home p ice expec a ions and beha iou : E idence om a
andomized in o ma ion expe imen . The Re iew o Economic S udies, 86(4), 1371–1410.
Be oli, S., Mo aga, J.F.-H., & Guicha d, L. (2020). Ra ional ina en ion and mig a ion decisions. Jou nal
o In e na ional Economics, 126,
Bes a d, A. B., & Fon , A. R. (2021). A ibu e ange e ec s: P e e ence anomaly o unexplained a iance?
Jou nal o Choice Modelling, 41, 100321.
Bha acha yya, A. (1946). On a measu e o di e gence be ween wo mul inomial popula ions. Sankhy¯a:
The Indian Jou nal o S a is ics, pp. 401–406.
Bla be g, R. C., B iesch, R., & Fox, E. J. (1995). How p omo ions wo k. Ma ke ing Science, 14(3), G122–
G132.
Bla be g, R., & Neslin, S. (1989). Sales p omo ion: The long and he sho o i . Ma ke ing Le e s, 1,
81–97.
Boyacı, T., & Akçay, Y. (2017). P icing when cus ome s ha e limi ed a en ion. Managemen Science, 64(7),
2995–3014.
B onnenbe g, B. J., & Vanhonacke , W. R. (1996). Limi ed choice se s, local p ice esponse and implied
measu es o p ice compe i ion. Jou nal o Ma ke ing Resea ch, pp. 163–173.
B own, Z. Y., & Jeon, J. (2024). Endogenous in o ma ion and simpli ying insu ance choice. Econome ica,
92(3), 881–911.
Cao, X., & Zhang, J. (2021). P e e ence lea ning and demand o ecas . Ma ke ing Science, 40(1), 62–79.
Caplin, A., & Dean, M. (2013). Ra ional ina en ion and s a e dependen s ochas ic choice. Unpublished
manusc ip , New Yo k Uni e si y.