Khac Minh Duc Do; Knyaze , Dmi iy
A icle
The ole o epu a ion in sequel p oduc ion
Games
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MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Khac Minh Duc Do; Knyaze , Dmi iy (2025) : The ole o epu a ion in sequel
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Ci a ion: Do, K. M. D., & Knyaze , D.
(2025). The Role o Repu a ion in
Sequel P oduc ion. Games,16(3), 23.
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A icle
The Role o Repu a ion in Sequel P oduc ion
Khac Minh Duc Do 1and Dmi iy Knyaze 2,*
1TWS Pa ne s, 10117 Be lin, Ge many; [email p o ec ed]
2Depa men o Business Decisions and Analy ics, Uni e si y o Vienna, Oska -Mo gens e n-Pla z 1,
1180 Vienna, Aus ia
*Co espondence: dmi iy[email p o ec ed]; Tel.: +43-1-4277-38164
Abs ac : This pape de elops a simple model o sequel p oduc ion o expe ience goods,
showing how epu a ion shapes a p oduce ’s incen i es. P oduce s di e in p oduc i i y,
which de e mines how much e o hey in es . A sequel is made only i he p e ious
ins allmen exceeds a quali y h eshold, cap u ing he idea ha consume s base u u e
consump ion on pas success. Al hough high-p oduc i i y p oduce s c ea e highe -quali y
o iginals and sequels, he condi ioning on success ul o iginals s ill makes sequels, on a e -
age, wo se han hei p edecesso s. This aligns wi h e idence o sequel unde pe o mance
in media ma ke s.
Keywo ds: sequel; epu a ion; expe ience goods; p oduce incen i es
1. In oduc ion
This pape aims o de elop a simple model o he ole o epu a ion in p oducing
sequels. In pa icula , we show why he e may be incen i es o a p oduce o c ea e
a sequel o lowe quali y. Ou mo i a ion s ems om he e idence ha many mo ie
sequels end o be wo se han hei o iginal coun e pa s. Helme (2011) compa es he
sco es o selec ed o iginal and sequel mo ies ( aken om he e iew agg ega o Ro en
Toma oes) agains each o he . He inds ha he e a e only a ew examples whe e he
sequel ou pe o ms he o iginal, such as S a T ek II o The Da k Knigh , which a e usually
conside ed as he bes mo ies in he espec i e se ies. Bu he as majo i y o sequels
pe o m wo se han he espec i e o iginals. In his pape , we p o ide a model o explain
his ac .
Nelson (1970) in oduced he concep o expe ience goods, which a e goods o which
he consume is no ully in o med abou quali y be o e pu chase o consump ion. Because
i is unclea how much u ili y he consume will de i e be o e making he decision o
acqui e o consume he good, he consume only lea ns his ex pos .
In he li e a u e, goods such as books and mo ies a e o en modeled as expe ience
goods. In heo y, consume “ as es” can di e , leading each consume o de i e di e en
u ili y om he same good. Since consume s do no know ex an e how much u ili y
hey will gain, hey only disco e i ex pos . As a esul , epu a ion may in luence he
consump ion o a sequel, since i p o ides consume s wi h in o ma ion abou he expec ed
u ili y o he p oduc . Among o he ac o s, his epu a ion can be de i ed om he quali y
o ea lie ins allmen s ha he consume has al eady expe ienced.
This pape de elops a simple heo e ical model o explain why sequels o expe ience
goods o en end up wi h lowe quali y han hei p edecesso s despi e being p oduced
by he same i m. We conside a isk-neu al p oduce whose p oduc i i y can be ei he
high o low and is known only o hemsel es. The p oduce ’s e o and an exogenous
Games 2025,16, 23 h ps://doi.o g/10.3390/g16030023
Games 2025,16, 23 2 o 7
shock join ly de e mine a p oduc ’s ealized quali y. C ucially, a sequel is only iable i he
quali y o he o iginal su passes a ce ain h eshold, c ea ing a epu a ion o he p oduce .
I inc eases buye s’ willingness o consume he sequel. Since he p oduce ’s ype is no
known o he consume s and he quali ies o p oduc s a e he only a iables obse able by
consume s, he epu a ion o a p oduce in ou model is ela ed only o he quali y o hei
pas p oduc s.
Ou analysis shows ha high-p oduc i i y p oduce s exe highe e o and hus
deli e highe expec ed quali y o bo h o iginal and sequel p oduc ions (P oposi ion 1).
The highe e o o p oduce s o a highe ype esul s in a highe expec ed quali y o
hei goods (P oposi ion 2). Besides ha , hey p oduce sequels mo e o en (P oposi ion 3).
Howe e , e en hese p oduce s canno ully escape he sequel-quali y d op, because only
su icien ly success ul o iginals mo e on o a sequel. This selec ion e ec implies ha
once a p oduce decides o make a sequel, he condi ioning on he o iginal’s success ul
ou come ende s he expec ed sequel quali y lowe han he expec ed quali y o he o iginal
(P oposi ion 4). These indings align wi h obse ed endencies in he mo ie indus y,
o e ing a o mal explana ion o why many sequels unde pe o m ela i e o hei o iginals
despi e a clea epu a ion-based incen i e o sus ain high quali y.
Ou mo i a ion o adop ing a wo- ype amewo k is o keep he model analy ically
ac able and o clea ly illus a e he co e mechanisms by which epu a ion a ec s sequel
p oduc ion incen i es. The main quali a i e insigh s—such as he epu a ion h eshold
inducing highe e o om high-p oduc i i y p oduce s, he selec ion e ec behind sequel
unde pe o mance, and he pe sis ence o quali y gaps—a e obus o iche se ings. In
pa icula , he compa a i e s a ics and selec ion e ec s would ex end o en i onmen s wi h
a con inuous p oduc i i y dis ibu ion.
The pape is s uc u ed as ollows. In he nex sec ion, we p o ide a e iew o he
ela ed li e a u e. In Sec ion 3, we o mula e he model. Sec ion 4p esen s ou analysis and
he main esul s. Sec ion 5concludes he pape .
2. Rela ed Li e a u e
Building on Nelson’s insigh s, Shapi o (1983) o malized how epu a ional p emiums
eme ge. Fi ms ha con inually p o ide highe quali y can command p ice p emiums
because consume s us hei epu a ion. This epu a ional signaling dynamic unde pins
incen i es o main ain quali y ac oss mul iple “ins allmen s” o p oduc lines.
Ex ending hese ounda ional ideas, Maila h and Samuelson (2001) examined how
epu a ion e ol es in epea ed in e ac ions. They showed ha main aining a good epu a-
ion can yield long- e m bene i s, bu incen i es o de ia e—and p oduce lowe quali y a
imes—may also exis i nea - e m gains ou weigh u u e losses. This ension esona es wi h
he puzzle o sequel quali y: a p oduce migh see sho - un p o i bene i s om lowe ing
p oduc ion cos s, e en i doing so isks ha ming he anchise’s long- e m epu a ion.
Tadelis (2002) s udied a ma ke o epu a ions, p o iding u he insigh in o how
b and names (o “ epu a ion capi al”) can be aded o inhe i ed, po en ially encou aging
o discou aging e o . While his analysis is mo e gene al, i cla i ies how epu a ional
conside a ions migh a y wi h di e en p oduce ypes (e.g., high- s. low-p oduc i i y
i ms) and o e ime.
The e is also li e a u e on how he expe ience o one consume can in luence o he s.
Fo ins ance, Reins ein and Snyde (2005) examine he ole o expe e iews on he con-
sump ion o expe ience goods in he con ex o mo ie eleases. They ind some e idence
ha posi i e e iews co ela e wi h highe ea nings, al hough he e ec ’s signi icance a ies
wi h he scope o elease and mo ie gen e. Gemse e al. (2007) build on hese indings,
compa ing he impac o expe e iews on small- elease a -house mo ies and wide- elease
Games 2025,16, 23 3 o 7
mains eam mo ies. While e iews signi ican ly a ec e enues o smalle eleases, hey
do no ha e he same measu able impac on wide - elease mains eam mo ies, suppo -
ing he indings by Reins ein and Snyde (2005). Mo e i (2011) u he shows ha social
lea ning om non-p o essional opinions also a ec s mo ie e enues.
Rela i ely li le li e a u e add esses he impac o an o iginal on subsequen sequel
consump ion. Fo example, Ka niouchina (2011) p o ides e idence ha being a sequel
can posi i ely a ec a mo ie’s e enues. Simila ly, B. I. Si umeang e al. (2014) show ha
o iginals can in luence sequel consump ion in ideo games, wi h bo h he quali y o pas
edi ions and he a iance in e iews playing a ole.
3. Model
The e is a isk-neu al p oduce who may p o ide a good a pe iod
≥
0 wi h quali y
q
by choosing e o le el
x
. The good p oduced a
=
0 is e e ed o as o iginal and he
good p oduced a any
>
0 as sequel. P oduce is cha ac e ized by ype
θi
, whe e
i
indica es
whe he hey ha e high p oduc i i y
θh
o low p oduc i i y
θl
, such ha
θi∈ {θl
;
θh}
and
θl<θh
. Only he p oduce knows i s own p oduc i i y ype. We u he assume ha
some e o e m
ϵi
a ec s he good’s quali y in addi ion o he p oduce ’s e o . This e o
e m is uni o mly dis ibu ed on he in e al
[−a
,
a]
,
ϵi
∼U[−a
,
a]
, and is independen
and iden ically dis ibu ed o e ime. The quali y o he good p oduced in pe iod
is
q =θix +ϵi
. As a esul o exe ing e o
x
, he p oduce incu s a cos gi en by he
quad a ic cos unc ion cx2
2.
Consume s do no know he quali y ex an e. They canno obse e he p oduce ’s ype
o e o . They only obse e he ealized quali y
q
a e consump ion. We assume ha he
consume s will be willing o consume he sequel only i i s p edecesso is o su icien ly
high quali y. Namely, a sequel a any
>
0 can be p oduced only i he quali y
q −1
in
pe iod
−
1 exceeds a cons an o e ime h eshold
¯
q
. I
q −1≤¯
q
, a sequel a pe iod
canno be p oduced. We assume ha he h eshold
¯
q
is subs an ially low o ensu e a
posi i e op imal le el o e o . In pa icula , we assume:
¯
q<2θl2
c. (1)
We also assume ha he e o e m
ϵi
is su icien ly noisy o ensu e ha he solu ion is well
beha ed, i.e.,
a>2θl2
c−¯
q. (2)
We assume ha he ea nings om selling he good a e p opo ional o i s quali y
q
. Thus,
p oduce ’s p o i Π in pe iod >0 is he ollowing:
Πi
=q −cx2
2.
The p oduce discoun s he u u e alue o
+
1 by a discoun ac o
β
,
β∈[
0, 1
]
. Hence,
he e o chosen in pe iod a ec s po en ial e enue in pe iod +1.
4. Analysis
Fi s , we ob ain he ollowing alue o he p oduce in pe iod :
V =max
x ≥0nEΠ +βV +1P (θix +ϵi
>¯
q)o.
Games 2025,16, 23 4 o 7
The e m
P (θix +ϵ >¯
q)
ep esen s he p obabili y ha a sequel can be p oduced. I his
e en does no occu , i s con ibu ion o he expec ed alue is ze o. Thus, we ob ain he
ollowing Bellman equa ion:
V =max
x ≥0θix −cx2
2+βV +11−¯
q−θix +a
2a. (3)
We sol e o he op imum e o le el by compu ing he i s -o de condi ion:
dV
dx
=θi−cx +βθiV +1
2a=0
⇒x =θi
c+βθiV +1
2ac . (4)
The second-o de condi ion is ul illed because
d2V
dx2
=−c<0,
which indica es ha condi ion (4) indeed de e mines he op imal e o .
No ice ha he p oblem is s a iona y in ime. Hence, o e e y ype
θi
, he alue and
he op imal e o a e cons an o e ime. Deno e
Vi
and
xi
as he alue and he op imal
le el o e o o he p oduce o ype θi. Thus,
xi=θi
c+βθiVi
2ac . (5)
Plugging i back in o Bellman Equa ion (3), we ob ain
Vi=θixi−c(xi)2
2+βVi1−¯
q−θixi+a
2a. (6)
⇔Vi=2aθixi−ac(xi)2
2a−β(a−¯
q+θixi). (7)
Now, we a e eady o p o ide he main esul s o ou analysis. Fi s , we show ha he
p oduce s o highe ype will supply a highe le el o e o .
P oposi ion 1. The op imal le el o e o o he p oduce o a highe ype is highe han he op imal
le el o e o o he p oduce o a lowe ype, i.e.,
xh>xl.
P oo .
We show his by con adic ion. Fi s , assume ha
xl≥xh
. Since
θl<θh
, Equa ion (5)
implies ha o ha e xl≥xhi mus be ha Vl>Vh. De ine unc ion
Φ(x,θ) = 2aθx−ac(x)2
2a−β(a−¯
q+θx).
No ice ha o any i∈ {h,l}
Φ(xi,θi) = Vi.
Since Vl>Vh, i ollows ha
Φ(xl,θl)>Φ(xh,θh).
Games 2025,16, 23 5 o 7
By de ini ion o Vh, i ollows ha
Φ(xh,θh)≥Φ(x,θh)
o any x∈R+. This implies ha
Φ(xh,θh)≥Φ(xl,θh).
Nex , no ice ha unc ion
Φ(x
,
θ)
is inc easing in
θ
because i s nume a o is inc easing, he
denomina o is dec easing in
θ
, and he Assump ions (1) and (2) gua an ee ha bo h he
nume a o and denomina o o
Φ
a e posi i e o he espec i e pa ame e anges. Hence,
Φ(xl,θh)≥Φ(xl,θl).
Finally, combining he las wo inequali ies, we ob ain
Vh=Φ(xh,θh)≥Φ(xl,θh)≥Φ(xl,θl) = Vl.
This is a con adic ion o Vl>Vh.
Nex , we demons a e ha he expec ed quali y o o iginals and sequels is highe o
he p oduce wi h high ype.
P oposi ion 2. The expec ed quali y o good o o iginals and all sequels is highe o he p oduce
o a highe ype han o he p oduce wi h a lowe ype, i.e., o any ≥0
Eqh
>Eql
.
P oo .
We show his by compu ing he expec ed alue and compa ing he esul s o he
op imum e o le els.
Eqi
=θixi+Eϵi
=θixi.
(8)
Since θh>θland om P oposi ion 1 we ha e xh>xl, i ollows ha
θhxh>θlxl.
Besides ha , we can demons a e ha he p oduce o he high ype is mo e likely o
p oduce a sequel han he p oduce o he low ype.
P oposi ion 3. The p oduce o he high ype p oduces sequels mo e o en han he p oduce o he
low ype.
P oo .
The p obabili y o p oducing a sequel o each good p oduced a
is equal o
P (ϵi
>¯
q−θixi
). F om P oposi ion 2, we know ha
θhxh>θlxl.
Hence,
P (ϵh
>¯
q−θhxh)>P (ϵl
>¯
q−θlxl).
Games 2025,16, 23 6 o 7
Ou las esul conce ns he quali y o each sequel compa ed o i s p edecesso .
P oposi ion 4. The expec ed quali y o each good ha ecei es a sequel is highe han he expec ed
quali y o ha sequel.
P oo .
To p o e his esul , we jus need o no e ha i some good p oduced a
ecei es
a sequel, he expec ed quali y o his good is
E[qi
|qi
>¯
q]
. This condi ional expec a ion is
g ea e han he uncondi ional expec a ion, i.e.,
E(qi
|qi
>¯
q)>Eqi
.
Finally, om P oposi ion 2, i ollows ha
Eqi
=θixi=Eqi
+1.
Thus, we ob ain ha
E(qi
|qi
>¯
q)>Eqi
+1.
This esul is consis en wi h he anecdo al e idence p esen ed in he in oduc ion.
In ui i ely, sequels a e usually p oduced o goods o su icien ly high quali y. Thus, e en i
he p oduce applies he same le el o e o o p oducing a sequel, he ac ha he decision
was made o p oduce i means ha he expec ed quali y o he sequel will be lowe han
he expec ed quali y o he o iginal.
5. Conclusions
In his pape , we designed a model in which epu a ion in he o m o he p e ious
pe iod’s quali y in luences he p oduc ion o a sequel. Ou model p edic s ha p oduce s
o highe ypes will apply highe e o , p oduce be e o iginals and sequels, and p oduce
sequels mo e o en han he p oduce s o lowe ypes. Howe e , o bo h ypes o p oduce s,
sequels will ha e a lowe expec ed quali y han hei p edecesso s.
Repu a ion in ou model is ep esen ed by he equali y o he p oduc de eloped in
he p e ious pe iod. The unobse abili y o he p oduce ’s ype o consume s is impo an
because in he model wi h comple e in o ma ion, he consume s should make hei con-
sump ion decisions based on he obse able ype o he p oduce and no on he quali y
o he good in he p e ious p oblem. Gi en he ype o he p oduce , hey would be also
able o sol e he op imiza ion p oblem o he p oduce and compu e he expec ed quali y
o he p oduc . The analysis will be less in e es ing in his case, because any dynamics
would disappea .
Au ho Con ibu ions: Concep ualiza ion, D.K.; Fo mal analysis, K.M.D.D. and D.K. W i ing—
o iginal d a , K.M.D.D.; W i ing— e iew & edi ing, D.K.; Supe ision, D.K. All au ho s ha e ead
and ag eed o he published e sion o he manusc ip .
Funding: This esea ch was unded by he Aus ian Na ional Bank h ough he OeNB Jubiläums onds
g an numbe 19021.
Da a A ailabili y S a emen : No new da a we e c ea ed o analyzed in his s udy.
Con lic s o In e es : Au ho Khac Minh Duc Do was employed by he company TWS Pa ne s.
The emaining au ho s decla e ha he esea ch was conduc ed in he absence o any comme cial o
inancial ela ionships ha could be cons ued as a po en ial con lic o in e es . The unde s had no
ole in he design o he s udy; in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o
he manusc ip ; o in he decision o publish he esul s.
Games 2025,16, 23 7 o 7
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Nelson, P. (1970). In o ma ion and consume beha io . Jou nal o Poli ical Economy,78(2), 311–329.
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mo ie c i ics. Jou nal o Indus ial Economics,53(1), 27–51.
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[C ossRe ]
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Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
