Nji u, Ru h Dionisia Gicuku; Dong, Changxing; Appel, F anziska; Balmann, Al ons
A icle — Published Ve sion
S a egic bidding beha iou in ag icul u al land en al
ma ke s: Rein o cemen lea ning in an agen -based model
In e na ional Food and Ag ibusiness Managemen Re iew
P o ided in Coope a ion wi h:
Leibniz Ins i u e o Ag icul u al De elopmen in T ansi ion Economies (IAMO), Halle (Saale)
Sugges ed Ci a ion: Nji u, Ru h Dionisia Gicuku; Dong, Changxing; Appel, F anziska; Balmann, Al ons
(2025) : S a egic bidding beha iou in ag icul u al land en al ma ke s: Rein o cemen lea ning in
an agen -based model, In e na ional Food and Ag ibusiness Managemen Re iew, ISSN 1559-2448,
B ill, Leiden, Vol. 28, Iss. 2, pp. 392-422,
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S a egic bidding beha iou in ag icul u al land en al ma ke s:
ein o cemen lea ning in an agen -based model
RESEARCH ARTICLE
Ru h Dionisia Gicuku Nji uai, Changxing Dongb, F anziska Appelb, Al ons Balmannc
aDoc o al Resea che , bDoc o , cP o esso , Depa men o S uc u al Change, Leibniz Ins i u e o Ag icul u al
De elopmen in T ansi ion Economies (IAMO), Theodo -Liese -S . 2, 06120 Halle (Saale), Ge many
Abs ac
Ag icul u al land ma ke s a e c ucial o e icien land alloca ion, ye hey ace complexi ies a ising om
land cha ac e is ics and he he e ogeneous na u e o ma ke pa icipan s. This s udy explo es how o
add ess he e ogenei y in he modelling p ocess o land ma ke s models by in eg a ing Deep Rein o cemen
Lea ning (DRL) in o he agen -based model Ag iPoliS, o model s a egic bidding beha iou . The simula ions
demons a es ha a DRL agen adap s i s bidding s a egies based on long- e m g ow h objec i es, expe ience,
compe i i e in e ac ions and adap i e decision-making leading o inc eased land en al and a m g ow h
compa ed o a s anda d agen using a ixed bidding s a egy. The esul s e eal how s a egic beha iou no
only imp o e indi idual a m pe o mance bu also a ec neighbou ing a ms, emphasizing he dynamic
in e ac ions wi hin land ma ke s. By cap u ing he agen ’s s a egic beha iou , his wo k con ibu es owa ds
mo e ealis ic modelling o ag icul u al land ma ke dynamics and o e s insigh s in o he implica ions o
po en ial land ma ke egula ions. Fu u e esea ch will explo e mul i-agen amewo ks o u he e ine
hese in e ac ions and add ess he limi a ions o s a ic bidding s a egies.
Keywo ds: Ag iPoliS, agen -based modelling, bidding s a egy, deep ein o cemen lea ning, a m g ow h,
s a egic in e ac ions
JEL codes: C63, D21, Q18
iCo esponding au ho : [email p o ec ed]
In e na ional Food and Ag ibusiness Managemen Re iew
Volume 28, Issue 2, 2025; DOI: 10.22434/IFAMR.1126
Recei ed: 1 May 2024 / Accep ed: 7 Feb ua y 2025
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In e na ional Food and Ag ibusiness Managemen Re iew
1. In oduc ion
The p ima y unc ion o ag icul u al land ma ke s is o acili a e land owne ship, u iliza ion, and access, he eby
e icien ly alloca ing he sca ce esou ce o land and enabling in es men and de elopmen o a ms (De
Jan y e al., 2001). Howe e , land ma ke s a e highly complex due o he unique cha ac e is ics o land such
as immobili y, non- enewabili y and he e ogeneous quali ies (soil quali y, p oduc i i y, loca ion). He e ogenei y
o he ac o s in e ms o a m size, esou ces, mo i a ion, access o in o ma ion and decision-making p ocesses
u he adds o he complexi y (Ma ga ian, 2014).
Because o hese complexi ies, he e is deba e abou how well land ma ke s unc ion, esul ing in inc eased
calls o land ma ke egula ions by ma ke pa icipan s and policy make s. In Ge many, o example,
se e al ede al s a es ha e o mula ed p oposals aimed a limi ing land concen a ion pe owne o a m and
con olling sale and en al p ices (Deu sche Bundes ag, 2018; Land ag on Sachsen-Anhal , 2020; MLUK,
2023a; NASG, 2017). These policy ini ia i es, which ha e no ye come in o o ce, aim o add ess issues
such as he le el o land p ices, he alloca ion and dis ibu ion o land – including in a- and in e -sec o al
dis ibu ion – and s uc u al p oblems wi hin a ms, which include medium- and long- e m e ec s on he
e iciency o he sec o , he dis ibu ion o en s and he exploi a ion o ma ke powe in land ansac ions.
In addi ion o he ins i u ional amewo k, he po en ial impac o hese o simila egula ions depends
hea ily on he s uc u e and dynamics o compe i ion on he land ma ke s and on he indi idual beha iou
and objec i es o ma ke pa icipan s. Bu he e a e s ill linge ing ques ions such as whe he hese measu es
a e e ec i e o wo k as in ended? And how can we analyse hem?
These mul i ace ed complexi ies make empi ical analysis o land ma ke s challenging as add essed by
Balmann e al. (2021), who discusses di e en models ha deal wi h di e en aspec s o he land ma ke :
Spa ial compe i ion models, o example, conside he immobili y o land and concen a e on he geog aphical
dis ibu ion o supply and demand, accoun ing o ac o s such as anspo a ion cos s and loca ion p e e ences.
Sea ch and ma ching models ac o in he e ogenei y o land quali y and he ansac ion cos s o cos ly sea ch
and nego ia ion p ocesses. Auc ion heo y conside s po en ial ma ke powe , which a ises e en wi hou an
explici nego ia ion p ocess due o he ypically low numbe o po en ial bidde s. Howe e , Balmann e al.
(2021) emphasize he challenges associa ed wi h modelling he unc ion o land ma ke s. Cap u ing all spa ial,
empo al, and especially beha iou al aspec s o land ma ke in e ac ions is inhe en ly complex. One aspec
ha is pa icula ly di icul o depic in such models a e he a ious ac o s and he e ec s o hei pe cep ions
and ac ions. Me hods ha accoun o he impac o di e en ac o s and hei pe cep ions and beha iou , a e
mos ly limi ed o expe imen al insigh s. Buchholz e al. (2022) highligh s ha he e ogenei y among a me s
a ec s hei decision making in ag icul u al land ma ke s and hei esponse o land ma ke changes. Appel
and Balmann (2023), o example, hin owa ds a s ong in luence o speci ic ac o s on he land ma ke s. This
unde sco es he need o be e accoun o he he e ogenei y o ac o s in models o analysing land ma ke s
and he assessmen o policy p oposals aiming a a s onge egula ion o land ma ke s.
In his espec , p io success ul applica ions show ha agen -based models (ABMs) like Ag iPoliS (Ag icul u al
Policy Simula o ; Happe e al., 2006) can p o ide impo an insigh s o policy assessmen s. Agen -based
models explici ly ocus on modelling he in e ac ions among a ms (e.g. ia land ma ke s) o s udy eme gen
p ope ies on he sys em le el. While Hein ich e al. (2019) use Ag iPoliS o speci ically analyse a ious
ypes o land ma ke egula ions. O he applica ions o Ag iPoliS such as Happe e al. (2008), U hes e al.
(2011) and Appel e al. (2016) implici ly add ess land ma ke implica ions o policy e o ms, as hey assess
he e ec s o di e en policy measu es o changes on ag icul u al s uc u es, which a e undamen ally linked
o land ma ke in e ac ions.
Agen -based models a e lexible ega ding modelling o agen beha iou . Examples o beha iou al app oaches
ange om simple ules o compu a ional in elligence, including lea ning. Howe e , agen -based models o
he ag icul u al sec o o en assume ha a m beha iou is d i en by p o i - o u ili y-maximizing p inciples,
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po aying a me s as pe ec ly a ional p ice- ake s (Ag iPoliS, c . Happe e al. (2006); MP-MAS, c . Be ge
and Sch einemache s (2006); Sch einemache s and Be ge (2011); SWISSLand, c . Möh ing e al. (2016)).
These app oaches o en also o e look he complexi ies o decision-making in eal-wo ld scena ios. Common
weaknesses include he sensi i i y o op imiza ion esul s o unce ain expec a ions, neglec o s a egic
conside a ions, and he assump ion o pe ec a ionali y among agen s.
Wi h his pape , we ocus on how inco po a ing he beha iou o s a egically o ien ed agen s – who make hei
bidding decisions based on long- e m g ow h objec i es, pas expe ience, cu en a m condi ions, compe i i e
in e ac ions, and adap i e decision making – can imp o e he modelling o land ma ke dynamics. To ha
end, we explo e how he in eg a ion o Deep Rein o cemen Lea ning (DRL) in o he decision-making o
he agen s in he exis ing agen -based model, Ag iPoliS, enables s a egic decision making in land ma ke s.
Such an app oach is o iginal o he analysis o ag icul u al land ma ke s and ela ed policies. To he bes
o ou knowledge, he e is no agen -based model in he ag icul u al sec o using DRL (c (G oene eld e al.
(2017); Hube e al. (2018); K emmydas e al. (2018); S o m e al. (2020)).
The pape is s uc u ed as ollows: Sec ion 2 ocuses on selec ed concep s ela ed o ABM and DRL.
Sec ion 3 illus a es Ag iPoliS and he expe imen al se -up o in eg a ing DRL in Ag iPoliS. In Sec ion 4,
he esul s o he simula ion a e p esen ed and he ea e discussed in Sec ion 5. In Sec ion 6, a conclusion
o he pape is p esen ed.
2. S a e o he a
2.1 Agen -based models and hei beha iou al app oaches
ABM is a bo om-up app oach o simula ing complex and dynamic sys ems h ough modelling he beha iou
and in e ac ions o en i ies e e ed o as agen s (C ooks and Heppens all, 2012). The agen s could ep esen
indi idual o collec i e agen s in pu sui o a speci ic objec i e(s). The agen s a e au onomous, he e ogeneous,
ac i e and in e ac wi h each o he and hei en i onmen . Th ough he indi idual beha iou and in e ac ions,
eme gen phenomena and sys em dynamics a e obse ed (Bonabeau, 2002; Railsback and G imm, 2019).
ABMs usually employ beha iou al app oaches ha a e p e alen in ag icul u al policy analyses, such as
myopic op imiza ion using mixed-in ege p og amming. K emmydas e al. (2018) disco e ed in a li e a u e
e iew ha app oxima ely 45% o modelling amewo ks explici ly employ ma hema ical p og amming
op imiza ion, including al e na i e me hods like posi i e ma hema ical p og amming. Mo eo e , app oxima ely
30% o models ely on simple ules, while 25% a e based on beha iou al heu is ics. Simila indings by
G oene eld e al. (2017) o agen -based land-use models indica e widesp ead use o op imiza ion, heu is ics,
and s ochas ic decision-making componen s. Fu he , An (2012) o e s a speci ic me hodological classi ica ion
o beha iou al models o ABMs, examining coupled human and na u al sys ems. This classi ica ion includes
mic oeconomic models, space heo y-based models, psychosocial and cogni i e models, ins i u ion-based
models, expe ience- o p e e ence-based decision models, pa icipa o y ABM, empi ical o heu is ic ules,
as well as e olu iona y p og amming and assump ions, and calib a ion-based models. Howe e , hese
beha iou al app oaches, especially hose used in models o he ag icul u al sec o , do no conside he
indi idual s a egic beha iou o a ms.
An explo a i e s udy by Appel and Balmann (2023) emphasizes he e ec s o indi idual beha iou on land
ma ke s. They analyse he spa ial in luences o di e en beha iou al clus e s o a m manage s. As a u he
aspec , Appel and Balmann (2023) conclude ha he de elopmen and ac ions o a a m a e no only in luenced
by o he ac o s on he local land ma ke , bu also by he i e e sibili y o decisions and in e ac ions. Thei
indings also align wi h he indings om Shang e al. (2021) whe e echnology adop ion and di usion is
in luenced by he a me ’s beha iou , ma ke condi ions, ins i u ional amewo ks and social ne wo ks.
Cap u ing hese spa ial, beha iou al and empo al aspec s o land ma ke in e ac ions is inhe en ly complex.
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Machine lea ning me hods (ML) ha e shown a lo o p omises in modelling complex beha iou and ha e
he po en ial o be used o cap u e land ma ke in e ac ions.
2.2 Machine lea ning and a i icial in elligence used in ag icul u e
S o m e al. (2020) o e an o e iew o machine lea ning (ML) app oaches in ag icul u al and applied
economics, emphasizing quan i a i e analysis. They also discuss he use o ML o su oga e models, which
app oxima e he mapping be ween inpu s and ou pu s o complex unde lying models, such as lea ning o
eplica e beha iou al cha ac e is ics o agen -based models (Shang e al., 2024). Simila ly, an de Hoog
(2017) explo es he u iliza ion o a i icial neu al ne wo ks as su oga e models o me a-modelling app oaches
in ABMs o educe complexi y and compu a ional demands. Addi ionally, bo h S o m e al. (2020) and an
de Hoog (2019) men ion he po en ial applica ion o ML and ein o cemen lea ning (RL) in simula ion
models, enabling agen s o lea n op imal beha iou in dynamic, eac i e en i onmen s.
In ecen yea s, deep lea ning app oaches based on complex mul i-laye a i icial neu al ne wo ks, known as
deep neu al ne wo ks (DNNs), ha e been combined wi h RL. Such DRL app oaches ha e p o en excep ionally
success ul in mas e ing complex s a egic games like Go and Chess. P ominen examples include AlphaGo,
AlphaGoZe o and AlphaZe o (Sil e e al., 2018; Sil e e al., 2017).
S udies show ha DRL can imp o e he p ecision o beha iou al modelling in ABMs by allowing he
agen s o modi y hei beha iou h ough in e ac i e lea ning and in e ac ion wi h hei en i onmen hus
gene a ing mo e lexible and adap i e agen s who in e ac wi h hei en i onmen in such a way ha esul s
in op imal beha iou and hus op imiza ion agen s (Dehko di e al., 2023; Osoba e al., 2020; Tu gu and
Bozdag, 2023; Zhang e al., 2023). Fo ins ance, Va gas-Pé ez e al. (2023) demons a ed ha DRL agen s
ou pe o med s a ic agen s as an aid in building a decision suppo sys em o he bes media ad e ising
in es men s a egy. Olmez e al. (2022) show ha DRL p o es use ul in c ea ing agen s ha display
in elligen and adap i e beha iou h ough ime and space in a p eda o and p ey ABM. Li e al. (2019)
applies an ex ended Ro h-E e RL algo i hm (Ro h and E e , 1995), o indi idual agen decision-making
p ocess in a esiden ial land g ow h ABM which signi ican ly imp o ed he agen s’ adap i e beha iou and
imp o ed he models’ simula ion powe . Liang e al. (2020) adop ed a DRL algo i hm o bidding s a egies
in elec ici y gene a ing companies while accoun ing o incomple e in o ma ion and in high dimensional
con inuous s a e and ac ion spaces.
RL enables agen s o lea n which ac ions (such as bids on he land ma ke ) lead o g ea e long- e m ewa ds
(such as inc eased equi y capi al) h ough epea ed in e ac ion wi hin he en i onmen . Such a RL amewo k
is desc ibed by Su on and Ba o (2018): I is based on s a es, ac ions, ansi ions and ewa ds. In a simpli ied
RL se up, he algo i hm is exp essed as a Ma ko decision p ocess (MDP), ep esen ed by a uple (S, A, T,
R, π, γ), as elabo a ed below:
• S a es (S), whe e S = s1, s2, s3, …, sn, is a ini e se o all possible si ua ions ha he agen s may ind
hemsel es in wi hin hei en i onmen .
•
Ac ion a1, a2, a3, …, an, is a se o all possible ac ions ha he agen s may ake wi hin hei en i onmen
based in hei cu en s a e (s) a e e y possible ime s ep ( ).
•
T ansi ion (T ) is he ansi ion unc ion be ween s a es. The e o e, when an agen akes an ac ion (a )
a a gi en imes ep ( ), i ansi ions om he old s a e (s ) o a new s a e (s +1) in he en i onmen .
• Rewa d (R) is he ewa d esul an in he agen ’s ac ion (a ) and ansi ioning o a new s a e (s +1).
I is usually ep esen ed as a scala ewa d and can be ei he nega i e o posi i e. The ewa d can
be gi en a he end o e e y ime s ep o can be gi en a e he end o se e al s eps. The goal o he
agen is o maximize he cumula i e ewa d which is he summa ion o all he ewa ds ecei ed un il
he e minal ime s ep.
•
RL policy unc ion π de ines how he agen chooses he ac ion o ake in i s cu en s a e o maximize
i s cumula i e ewa d i.e. maps ha s a es in o ac ion. Discoun ac o γ is a ac o be ween 0 and 1
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ha discoun s u u e ewa ds ha helps he agen balance be ween sho - e m and long- e m ewa ds.
Values close o 0 indica e ac ions ha lead o long- e m ewa ds. And o a policy π, we can es ima e
a alue unc ion Vπ, which is he alue o he accumula ed ewa d.
In a simpli ied way, as depic ed in Figu e 1, he agen obse es he cu en s a e o i s en i onmen and uses
his in o ma ion o decide which ac ion o ake. The agen hen ecei es new in o ma ion and he ewa d
because o he ac ion. Based on he new obse a ion, he agen decides whe he o ake new ac ion o epea
he ac ion. The cycle con inues un il he e minal s a e. The goal o he agen is o lea n he op imal RL policy
om i s en i onmen . One c i ical aspec o RL is ha he agen s lea n om explo ing i s en i onmen bu
a he same ime exploi ing good ac ions ha ha e been aken be o e i.e. ade-o be ween explo a ion and
exploi a ion. In he nex sec ion we del e a bi deepe on he model Ag iPoliS and he p oposed amewo k
o he in eg a ion o DRL in Ag iPoliS.
3. Me hodology and expe imen al se -up
3.1 Ag iPoliS
Ag iPoliS (Ag icul u al Policy Simula o ) is an ABM used o simula e e ec o di e se policies and egula ions
on ag icul u al s uc u al change o e ime (Balmann, 1997; Happe e al., 2006). The Ag iPoliS en i onmen
is a i ual landscape wi h spa ially loca ed ag icul u al a ms which a e ep esen ed as a m agen s. The a m
agen s a e closely simila o ypical a ms in he egion, he e ogenous, ha e di e en ac o endowmen s,
di e en manage ial skills, di e en a m ages, pu sue a de ined goal e.g. income maximiza ion and exhibi
myopic beha iou (Appel e al., 2016; Balmann, 1997; Happe e al., 2006; Sah bache e al., 2012). The
a ms a e de ined p io o ini ialized based on eal a m da a, Eu opean Union’s Fa m Accoun ancy Da a
Ne wo k (FADN), handbook da a on a ming p ac ices (e.g., o Ge many, Associa ion o Technology and
Cons uc ion in Ag icul u e (KTBL)), a m s uc u al su ey (FSS) and/o expe knowledge (Nji u e al.,
2024; Sah bache and Happe, 2008).
The land ma ke is a he cen e o Ag iPoliS whe e en al plo s become a ailable upon expi a ion/ e mina ion o
exis ing en al con ac s, a ms downsizing o a m closu es. Fa ms can solely g ow h ough en ing addi ional
land h ough he land en al auc ion ma ke . The en al ma ke also o ms he basis o in e ac ion among he
agen s h ough hei compe i ion o addi ional land. The en al ma ke akes place a he beginning o he
p oduc ion pe iod. The en al plo s a e spa ially dis ibu ed and he a m agen incu s anspo cos s be ween
hei own a m plo s and he plo s a ailable (Happe, 2004; Kelle mann e al., 2008). The a ms p esen bids
o he land en al ma ke . The agen wi h he highes bid ecei es he plo . The auc ion is held in an i e a i e
manne un il all he plo s a e alloca ed. The bids (equa ion 1) e lec he shadow p ice, q (addi ional bene i
Figu e 1. Simpli ied ein o cemen lea ning amewo k. Adap ed om Su on and Ba o (2018).
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o en ing he land), he spa ial loca ion o he plo (calcula ed by he anspo cos be ween he a m plo s
and he plo s a ailable o en ), TC, and a ixed land en al coe icien , β, which de e mines he sha e o he
shadow p ice ha is passed on o he landowne (Happe, 2004). The emaining sha e 1-β emains wi h he
a me o co e u he cos s (including axes, adminis a i e expenses, ees) and he isk. Fo β he ollowing
applies: 0< β <1. In a pe ec ly compe i i e ma ke , one would expec β o be 1.0. Howe e , a heo e ical
s udy by G aubne (2018) emphasizes he po en ial o spa ial p ice disc imina ion in he ag icul u al land
ma ke . Acco dingly, in egions whe e space plays a signi ican ole, such as hose wi h la ge a ms, one
would assume he sha e ans e ed o en al p ices ends o be lowe . In he p esen s udy, Ag iPoliS simula es
a egion wi h a limi ed numbe o a he la ge a ms. The e o e, β is assumed o be 0.5 o all a ms o he
espec i e model egion.
bid = [q − TC] * β (1)
Th ough use o mixed in ege p og amming (MIP), ac o endowmen s (land, labou ( amily labou , hi ed
labou ), ixed asse s), key p oduc ion ac i i ies (li es ock, c ops), in es men op ions (machine y, li es ock
housing), inancing op ions (sho - e m and long- e m c edi , liquidi y) and o he ac i i ies speci ic o he
egion (e.g. manu e disposal, li es ock densi y es ic ions) a e ep esen ed simul aneously while conside ing
esou ce cons ain s inhe en in ag icul u e. In each pe iod, he a m agen s ollow a sequen ial p ocess
i.e. pa icipa es in he land en al auc ion ma ke , makes in es men , decides on wha o p oduce, does he
ac ual p oduc ion, does he annual a m accoun ancy, decides on whe he o con inue o exi a ming and
he p ocess es a s. A ypical simula ion un in Ag iPoliS is done o e 25 i e a ions/ ime pe iods.
As he agen s a e myopic, hey only conside decisions one pe iod ahead. This poses signi ican isks o he
a m agen s such as jeopa dising he a ms’ inancial s abili y, inc eased ulne abili y o economic shocks
and educed esilience o challenges such as changing ma ke condi ions. This necessi a ed he ex ension o
he Ag iPoliS model owa ds s a egic beha iou h ough s a egic bidding decisions ha ac o in long- e m
planning while le e aging on pas expe iences (e.g. p e ious en al a es), cu en a m si ua ion (e.g.
Liquidi y), conside a ion o compe i i e in e ac ions (e.g. numbe o a ms) and adap i e decision-making.
In ou no el app oach, he a m agen would come up wi h a s a egic bidding DRL policy based on s a e
a iables e lec ing a m and sec o condi ions, bid in e dependence, and long- e m planning. The ewa d
mechanism is based on cumula i e sum o equi y capi al a he end o all he i e a ions. In he nex sec ions,
de ails on he me hodological and expe imen a ion se up o in eg a ing DRL in Ag iPoliS a e explained.
3.2 The amewo k o in eg a ing DRL in Ag iPoliS
In his new amewo k, one agen is equipped wi h DRL while he o he agen s used he Ag iPoliS beha iou .
The DRL agen o mula es a bid i.e. ac ion based on he cu en s a e o he en i onmen which is ansmi ed
o he land ma ke and subsequen ly ecei es eedback i.e. new s a es and uses his in o ma ion o o mula e
a new bid. The i e a i e p ocess con inues un il he end o he simula ion un, a which poin he cumula i e
sum o equi y capi al is calcula ed. The echnical de ails a e discussed in he ollowing sec ions while access
o he ODD+D p o ocol, da ase s and code a e a ailable on he Ag iPoliS websi e.
3.2.1 The objec i e
In Ag iPoliS, e e y a m agen makes decisions independen ly and in e ac s wi h o he agen s h ough di e en
ma ke s, o which he land ma ke is he mos impo an . As he decisions a e made by op imizing he p o i
only o he cu en yea , hey a e myopic and migh no be op imal o he agen ’s long- e m de elopmen .
The objec i e is o ind a bidding s a egy in he land ma ke ha maximizes a single a m agen ’s long- e m
equi y capi al by enhancing he agen wi h ein o cemen lea ning abili y and he e o e making s a egic
bidding decisions in he land en al ma ke s ha maximizes he agen s’ long- e m g ow h.
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3.2.2 The en i onmen
As his wo k se es mainly as p oo o concep , he in es iga ed egion is delibe a ely made small. I consis s
o se en ypical a ms om he ag icul u al egion, Al ma k in Ge many. One o he a ms is designa ed as
he DRL agen while he o he 6 a ms a e s anda d Ag iPoliS a ms. The amewo k consis s o h ee logical
componen s as shown in Figu e 2. The i s componen is he machine lea ning uni (MLU), h ough which
he bidding s a egy can be lea n . The second componen is he adap ed Ag iPoliS en i onmen whe e he
simula ion ake place, hence o h e e ed o as he APS-ENV. The hi d componen is a message queue
sys em ha allows eliable communica ion be ween he MLU and he APS-ENV bo h locally and emo ely
and is e e ed o as he COM-MQ.
This modula amewo k design allows he independen de elopmen o he MLU wi h espec o no only
he di e en aining algo i hms and pa ame e s bu also he p og amming languages and compu e ope a ing
sys ems.
An agen in Ag iPoliS hence o h e e ed o as he DRL agen is ained wi h he MLU o o mula e s a egic
bids also known as ac ions which a e hen ansmi ed in o he APS-ENV ia COM-MQ. The esul an
da a i.e. s a es and ewa ds a e ansmi ed back o he MLU h ough he COM-MQ. Essen ially, in his
amewo k, he ac ions go om MLU h ough COM-MQ o APS-ENV while he s a es and ewa ds low
in he opposi e di ec ion.
3.2.3 The s a e space
The s a e space e lec s he cu en s a e o he a m and egion, he in e dependence o bids on o he a m
le el decisions (e.g. how highe /lowe bids a ec he in es men s) and long- e m planning e ec . The
selec ed a iables o ep esen a DRL agen ’s s a e a e shown in Table 1. The e a e wo di e en soil ypes
(a able and g azing) and 47 di e en in es men op ions. A s a e has 67 a iables because some a iables a e
di e en ia ed be ween he soil ypes. The agen ecei es s a e s
and uses he in o ma ion o p epa e he bid.
3.2.4 The ac ion
In he s anda d Ag iPoliS Model, he β is ixed a 0.5 ep esen ing 50% o he alua ion while o his new
amewo k he DRL agen ’s β is de e mined by a neu al-ne wo k-based DRL a chi ec u e. The ac ion space
is hus a con inuous a iable.
3.2.5 The ewa d
Since he goal is o lea n a bidding s a egy ha maximizes he agen ’s long- e m ewa d, he DRL agen only
ge s a ewa d a he e minal s a e. A s a e is e minal, i i is he s a e a he end o an Ag iPoliS simula ion
Figu e 2. Rein o cemen lea ning amewo k wi hin Ag iPoliS.
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Table 1. Va iables ep esen ing DRL agen s a es.
Name Type Numbe o
a iables
Le el No es
Te mina ing
plo s
Lis o
in ege s
10 Fa m Dis ibu ion o plo numbe s o e es con ac leng h
(1 o 5 yea s). This is di e en ia ed be ween a able
land and g assland
Liquidi y Real 1Fa m Abili y o o he a m o mee sho e m liabili ies
Fa m age In ege 1Fa m Age o he a m
In es men s Lis o
eal
47 Fa m Remaining li e o he in es men s
P e ious
en al a e
Real 2Fa m The la es amoun o en paid by he agen s. This is
di e en ia ed be ween a able land and g assland
Managemen
coe icien
Real 1Fa m This is e lec ing he a ms’ manage ial abili y by
manipula ing he a iable cos s.
F ee plo s In ege 2Region Numbe o a ailable ( emaining) ee plo s in he
egion. This is di e en ia ed be ween a able land and
g assland
Numbe o
a ms
In ege 1Region Numbe o compe ing a ms
A e age en
p ice
Real 2Region The a e age en al a e in he egion o he p e ious
yea . This is di e en ia ed be ween a able land and
g assland.
un. Fo he expe imen s, he simula ion un is o e 10 yea s wi h he i s yea deno ed as i e a ion 0 being
he ini ializa ion un. The ewa d in his case is he cumula i e sum o i s equi y capi al o e he simula ion
un. We use cumula i e sum o equi y a he han inal equi y o encou age consis en imp o emen in a m
pe o mance ac oss i e a ions a he han ocusing only on he inal s a e. Emphasizing he inal equi y alue,
on he o he hand, could lead o iskie s a egies ha p io i ize highes p o i s in ce ain i e a ion, while
po en ially isk he a ms s abili y. In addi ion, models ained exclusi ely on inal equi y alues a e expec ed
o show inc eased sensi i i y o he numbe o i e a ions conside ed. In con as , he use o cumula i e ewa ds
mi iga es his sensi i i y by encou aging he agen o conside bo h sho - e m and long- e m p o i abili y,
and he eby assumingly p omo ing a balanced and obus lea ning cu e ha includes bo h immedia e gains
and sus ainable pe o mance.
Le ’s deno e he ansi ion om he s a e s o s′ by aking he ac ion a as (s, a, s′), hen he cumula i e ewa d
R can be desc ibed as
R
sas
i
(, , )
i s′ is a e minal s a e, o he wise R(s, a, s′) = 0. He e i is he equi y capi al o he DRL agen a e he i h
yea in he simula ion wi h Ag iPoliS.
3.2.6 The algo i hm and expe imen al se up
In Figu e 3, he de ailed p ocesses in he h ee componen s in he amewo k a e illus a ed. All da a lows
h ough COM-MQ a e indica ed wi h blue lines, whils he black lines show he da a lows wi hin a subsys em
APS-ENV o MLU. “pa ial ewa ds” wi hin COM-MQ means he equi y capi al a e e e y single yea .
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Figu e 8. E ec o lea ning on a m size o o he a ms.
I e a ion
(a) Baseline
Fa m size (ha)
I e a ion
(b) DRL
Fa m size (ha)
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Table 4. Compa ison o he cumula i e sum o equi y capi al o all he a ms.
Fa m agen Baseline cumula i e ewa d DRL maximum cumula i e ewa d Rela i e change (%)
F0 2 288 694 2 287 647 −0.05
F1 3 932 183 4 022 778 2.30
F2 6 850 762 6 976d853 1.84
F3 12 669 940 12 868 645 1.57
F4 7 387 073 7 925d292 7.29
F5 7 889 960 8 613 919 9.18
F6 8 354 720 9 120 867 9.17
Fo example, F5 expe ienced a decline in he a m size in he DRL scena io compa ed o he Baseline
scena io because o less en ed plo s due o he DRL bidding s a egy. The size o F0 emained ela i ely
low indica ing ha F0 was no ha ac i e on he land ma ke in bo h scena ios. The same e ec was also
obse ed o all he a ms as illus a ed in Fig. A1 in he Appendix.
4.2 Flexibili y o he amewo k
Based on he success o he aining p ocess in Sec ion 4.1, and o es he adap abili y and lexibili y o he
amewo k, expe imen s we e epea ed using he same ne wo k a chi ec u e and hype pa ame e s o all he
o he a ms. The esul s we e e alua ed based on he same ewa d s uc u e i.e. he a m agen ’s cumula i e
sum o equi y capi al and compa ed wi h he Baseline.
Based on he me ics in Table 4, i is e iden ha he e was an inc ease in he cumula i e sum o equi y
capi al o all he a ms in he DRL scena io compa ed o hei Baseline excep o Fa m 0 which showed
a sligh dec ease o 0.05% in he cumula i e sum o equi y capi al wi h DRL. F0, F1, F2 expe ienced a
modes inc ease o 2.30, 1.84 and 1.57%, espec i ely, in he cumula i e sum o equi y capi al. F4 o F6 saw
signi ican inc ease o 7.29, 9.18 and 9.17%, espec i ely, in he cumula i e sum o equi y capi al wi h DRL.
Figu e 9 displays he cumula i e sum o equi y capi al a e e y epoch ela i e o he Baseline. The esul s
ac oss 2000 epoch demons a e a ia ions in he speed o lea ning among he a m agen s. F0 howe e ,
pe o med wo se e en a e lea ning o e 2000 epochs. An in es iga ion as o whe he es ic ing aining
o 2000 epochs caused he lack o con e gence was conduc ed. A 2- old inc ease in he numbe o epochs
did no imp o e he lea ning o he agen . This shows ha he agen did no bene i om lea ning and his
is u he ein o ced by he ac ha he a m seemed o en ela i ely he same ( e y low) numbe o en al
plo s in bo h DRL and Baseline scena ios (Figu e 10a). In con as , F6 en ed signi ican ly mo e land when
using DRL as compa ed o he Baseline (Figu e 10b). This also led o a signi ican inc ease in hei a m
size and subsequen inc ease in hei cumula i e sum o equi y capi al (Table 4). Also, all he o he a ms
en ed mo e plo s o land by using DRL as compa ed o he Baseline. Howe e , a ms F1 o F3 showed
negligible inc emen in en ed plo s be ween he DRL and Baseline scena ios (Figu e A2 in he Appendix).
This is also e lec ed by a ela i ely low inc ease in hei cumula i e sum o equi y capi al. Like F6, F5
en ed signi ican ly mo e land when using DRL as compa ed o he Baseline which is also in line wi h hei
signi ican inc ease o cumula i e sum o equi y capi al.
In Figu e 11, an illus a ion o bidding s a egies o selec ed indi idual a ms indica es ha by a ying hei
bidding coe icien he a m agen s can maximize hei ewa ds (see Figu e A4 in he Appendix o he bes
bidding s a egy o he a ms no p esen ed he e). E e y a m had a unique bes bidding s a egy while all
he o he a ms main ained a ixed bidding s a egy in he DRL scena io.
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Cumula i e Rewa d ( ela i e % change o he Baseline)
Figu e 9. Rela i e change in cumula i e ewa d in DRL compa ed o he baseline o all a ms.
5. Discussion
In his pape , we explo ed how he in eg a ion o DRL in o he decision making o agen s in Ag iPoliS
enables s a egic beha iou and in e ac ions. The explo a ion began by cons uc ing an ad anced amewo k
consis ing o a lea ning uni (MLU), communica ion uni (COM-MQ) and an adap ed Ag iPoliS en i onmen
(APS-ENV). Th ough he amewo k, a single agen lea n a bidding s a egy ha maximized hei cumula i e
ewa d i.e. cumula i e sum o equi y capi al based on s a e a iables e lec ing a m and egional condi ions,
bid in e dependence, and long- e m planning. The esul s we e hen compa ed o a Baseline scena io (s anda d
Ag iPoliS agen ) whe e he agen used a ixed bidding coe icien . The DRL agen demons a ed supe io
adap abili y and s a egic decision-making compa ed o he s anda d Ag iPoliS agen .
The s a egic supe io i y o he a m agen is demons a ed by hei g ea e compe i i eness on he land
ma ke and s onge a m g ow h, as demons a ed by he inc eased a m size (Figu e 7b). Compa a i ely,
he DRL agen pe o med be e han he Baseline agen as shown by he inc ease in he cumula i e sum
o equi y capi al (Table 3 and Figu e 6). Addi ionally, he esul s indica e ha he bes s a egy based on
he s a e a iables signi ican ly di e om he use o a ixed bidding coe icien (Figu e 7a). On he o he
side, he bidding s a egy p o ed o be de imen al o o he a m agen s (wi h s anda d ixed β) as he DRL
agen ou bid hem in hei ques o en mo e land om he land en al ma ke (Figu e 8). O e all, he DRL
amewo k unde lines how adap i e decision-making can p omo e a a m’s long- e m g ow h.
To u he e alua e he adap abili y o he DRL amewo k, simula ions we e epea ed ac oss all a m agen s
using he same hype pa ame e s, allowing us o assess i s lexibili y o he e ogeneous a m ypes. The
esul s showed ha he amewo k could be applied e ec i ely o o he a ms exhibi ing di e en s uc u es
and inancial capabili ies (Figu e 9). Wi h he DRL bidding decisions being adap i e and d i en by pas
expe iences, cu en a m si ua ion, egional condi ions, and compe i i e in e ac ions, i is he e o e sensible
ha he bidding s a egies di e ed ac oss he a ms u he illus a ing how he he e ogenei y o a ms leads
hem o di e en bidding s a egies and hus di e ence in a m g ow h. Howe e , a his s age, he lea ning
p ocessed is mo e e ec i e o a m agen s wi h high ac i i y on he land ma ke and no o a ms wi h
minimal land ma ke ac i i y (Figu e 10). Al hough i should be heo e ically possible ha a ms wi h low
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I e a ion
(a) Fa m 0
I e a ion
(b) Fa m 6
Figu e 10. E olu ion o a m size(ha) o selec ed a ms.
Fa m size (ha)Fa m size (ha)
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Be a coe icien Be a coe icien
I e a ion
(a) Fa m 0
I e a ion
(b) Fa m 6
Figu e 11. Bes bidding s a egy o selec ed a ms.
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ac i i y on he land ma ke could bene i om addi ional uning o he hype pa ame e s o enhanced lea ning,
his migh no be oo ele an o s udying land ma ke in e ac ions. Land ma ke dynamics a e d i en by a
ew e y s ong ac o s (Appel and Balmann, 2023) and he e o e i should be su icien o model imp o ed
s a egic beha iou o some agen s while o he s show he de aul beha iou . These esul s unde line he
po en ial o he DRL amewo k o model he dynamics o land ma ke s mo e ealis ically by e lec ing he
s a egic he e ogenei y among a ms.
Building on hese indings, we can conside he b oade implica ions o adap ing s anda d Ag iPoliS agen s’
bidding s a egies beyond a ixed coe icien . The esul s could be unde s ood as an indica ion ha assuming
a cons an bidding coe icien o 0.5 o s anda d Ag iPoliS agen s migh jus be oo low. Howe e , G aubne
(2018) emphasizes he po en ial o spa ial p ice disc imina ion in he ag icul u al land ma ke s: Due o
dis ance cos s, a ms ace a con ex (p ice-elas ic) egional land supply, esul ing in impe ec compe i ion
and a educed sha e o income om land being ans e ed o en al p ices. This heo e ical wo k is also
unde pinned by empi ical s udies. Fo ins ance, Kilian e al. (2012) examined he sha e o expec ed income
om land (di ec paymen s) capi alized in o land p ices, inding incidences anging om 28 o 79% o
Ge many (Ba a ia), depending on he di ec paymen ype and land ca ego y. Al hough di ec paymen s
a e only a pa o he expec ed addi ional income used o de e mine shadow p ices and, consequen ly, land
ma ke bids, hese indings sugges ha a me s ypically bid only a ac ion o hei shadow p ice. Assuming
an op imized ixed bidding coe icien o each s anda d Ag iPoliS agen , we es ima e hese coe icien s o
ange be ween 0.44 and 0.77 (see Table A2 in he Appendix). The bidding s a egy employed by he DRL
agen su passes his op imized ixed coe icien by adap i ely adjus ing i s en ing coe icien o he speci ic
indi idual and land ma ke condi ions in each i e a ion. These esul s indica e ha s a egic ad an age in
he land ma ke is no simply a ma e o ha ing a highe o lowe bidding coe icien , bu a he lies in
adap i ely adjus ing bidding decisions based on pas expe iences, cu en a m si ua ion, egional condi ions,
and compe i i e in e ac ions, esul ing in op imized spa ial and empo al p ice disc imina ion.
While ou indings unde sco e he alue o he DRL amewo k o enabling adap i e bidding s a egies o
a mo e ealis ic modelling o land ma ke dynamics, ce ain limi a ions mus be acknowledged in e ms o
he s udy’s scope and compu a ional easibili y. In his s udy, he egion was modelled wi h 7 a m agen s,
whe eas a ypical eal-wo ld egion, would comp ise se e al hund ed a ms, c ea ing a mo e dynamic
en i onmen and equi ing simula ions ha could ex end o e se e al days, weeks o e en mon hs. This
simpli ica ion helped o educe complexi ies such as aining ime, compu a ional cos (memo y, p ocessing
powe ) and con e gence o a s able solu ion. Fu u e s udies could aim o model la ge egions by add essing
hese complexi ies h ough app oaches like pa allelized aining, au oma ed hype -pa ame e op imiza ion
and use o as e GPUs.
A key c i icism o DRL is ha he agen lea ns h ough epea ed simula ed in e ac ions wi h he en i onmen ,
allowing hem o expe ience millions o possible scena ios – an ad an age no a ailable o eal-li e a me s
who ace ex e nal cons ain s and limi ed in o ma ion. Howe e , in his amewo k, he in o ma ion p o ided
o he DRL agen (Table 1) mi o s wha a well-in o med and well-connec ed egional a m manage migh
ealis ically possess. Jus as a a m manage would ely on a combina ion o expe ience, knowledge, and
in ui ion o e ine hei bidding s a egies o e ime, he DRL agen e ines i s bidding s a egies o e ime
based on expe ience and e ol ing expe ise. These aspec s o expe ience and in ui ion canno be cap u ed by
adi ional no ma i e models (Buchholz e al., 2022). While DRL canno explici ly co e all hese aspec s
ei he , i enables agen s o lea n op imal s a egies h ough i e a i e adjus men s, c ea ing a o m o expe ience
o in ui ion. Fu he mo e, ou analysis (Figu e 6) illus a es ha he DRL agen e ec i ely le e aged he
a ailable in o ma ion o make compe i i e decisions, esul ing in inc eased cumula i e equi y capi al om
he ou se . This sugges s ha s a egic beha iou can eme ge e en wi hou ex ensi e in o ma ion (Sil e
e al., 2021). While indeed DRL has he heo e ical po en ial o p o ide i ually unlimi ed in o ma ion
h ough ex ensi e i e a ions and da a, ou s udy was cons ained by compu a ional limi a ions, p omp ing us
o only p o ide in o ma ion in Table 1 o he DRL agen which does no comple ely e lec he complexi y
o human decision making.
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Ano he c i ical aspec o he p esen ed DRL amewo k is he assump ion ha o he agen s adop a ixed
bidding s a egy h oughou he simula ion. This simpli ica ion c ea es a ela i ely s a iona y en i onmen ,
allowing he DRL o exploi he s a ic beha iou o he o he agen s. In eali y, howe e , o he a ms would
adjus hei beha iou in esponse o unsuccess ul bids. These adjus men s would ha e implica ions a
bo h he a m and egional le els, in oducing an addi ional laye o modelling complexi y ha has no
been e ec i ely add essed ye . To cap u e his addi ional laye o complexi y, u u e wo k will ocus on
ad ancing he cu en DRL amewo k owa ds a mul i-agen deep ein o cemen lea ning (MADRL)
app oach. In such an ad anced amewo k, mul iple agen s would use DRL o de e mine hei bidding
decision in he land ma ke , a he han elying on a ule-based heu is ic like he ixed bidding coe icien .
MADRL is pa icula ly use ul o modelling mo e complex in e ac ions, compe i ion, and dependencies
among agen s. Wi h MADRL, agen s can sense and espond o o he agen s’ s a egies, which may lead
o highe e iciency, ie ce compe i ion o e en collabo a ion among hem (Busoniu e al., 2008; Osoba
e al., 2020). This app oach would enable us o s udy op imal land alloca ion among a m agen s, po en ial
imp o emen s o land use and in es men planning, and possible inc eases in ea nings. Th ough imp o ed
beha iou al s a egies, i could also con ibu e o discussions on how a ms may adap o, o e en ci cum en
land ma ke egula ions. Despi e hese ad an ages, MADRL in oduces ce ain challenges, pa icula ly in
managing he complexi y o a con inuously changing en i onmen : as all agen s lea n simul aneously, he
en i onmen becomes non-s a iona y making i mo e challenging o he agen s o s a egically adjus hei
ac ions. Addi ionally, as he numbe o agen s inc eases, he ‘cu se o dimensionali y’ in ensi ies, wi h a
co esponding ise in he numbe o s a e and ac ion a iables o conside – in oducing compu a ional
challenges ha we a e ac i ely wo king on.
6. Conclusion
The aim o his pape was o explo e how a ms s a egic decision-making beha iou in land ma ke s could
be cap u ed mo e accu a ely by in eg a ing DRL as an al e na i e beha iou al app oach in Ag iPoliS. In his
amewo k, a single DRL agen lea ns adap i ely om he en i onmen , enabling hem o gene a e bids,
ocusing on long- e m g ow h. The agen ’s decisions a e in o med by s a e a iables ha cap u e he a m’s
s a us, egional condi ions, and compe i i e in e ac ions hus simula ing aspec s o long- e m planning,
expe ience, and adap i e decision making in he land ma ke s. Wi hin his se -up, he agen compe ed agains
he s anda d myopic beha iou o adi ional Ag iPoliS agen s.
The expe imen s demons a ed ha he DRL agen was mo e compe i i e in he land ma ke and managed
o inc ease hei long- e m g ow h as indica ed h ough inc eases in a m size and cumula i e sum o equi y
capi al. As he DRL agen ’s a m expanded h ough s a egic bidding, o he a ms aced a co esponding
dec ease in en ed land. Addi ionally, when di e en a ms designa ed as he DRL agen , hey adop ed
unique bidding s a egies esul ing in inc eased, hough a ied, g ow h o he espec i e a m. These esul s
unde sco e he po en ial o using DRL in cap u ing s a egic decision-making o he e ogeneous a ms, laying
he ounda ion o u he explo a ion o s a egic a m beha iou in ag icul u al modelling. The indings
p o ide aluable insigh in o imp o ing po en ials in modelling o a m decisions and beha iou s, add essing
a gap whe e mos models ely on ule-based heu is ics o myopic decision making in land ma ke s.
Fu u e wo k will expand he model o include a la ge egion wi h mo e a ms, in oducing g ea e compe i ion
and imp o ing he ealism o he ep esen a ion o egional a m s uc u es. Addi ionally, we plan o ex end
he amewo k o MADRL, enabling mul iple agen s o use DRL o lea n and adjus hei s a egies o e
ime. Such a model could se e as a aluable ool o modelle s, p ac i ione s and policymake s, helping o
explo e land ma ke dynamics and assess he e ec s o p oposed land ma ke egula ions.
Acknowledgemen s
This wo k was inancially suppo ed by he Ge man Resea ch Founda ion (DFG) h ough Resea ch Uni 2569
“Ag icul u al Land Ma ke s – E iciency and Regula ion”.
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Table A2. Compa ison be ween ixed, op imal ixed and lexible en al ac o (β).
Fa m agen Cumula i e ewa d
Baseline (β=0.5) Op imal ixed β (op imal β in pa en heses) DRL ( lexible β)*
F0 2 288 694 2 291 395 (0.51) 2 287 647
F1 3 932 183 4 023 643 (0.59) 4 022 778
F2 6 850 762 6 896 696 (0.44) 6 976 853
F3 12 669 940 12 833 917 (0.59) 12 868 645
F4 7 387 073 7 840 896 (0.62) 7 925 292
F5 7 889 960 8 211 464 (0.77) 8 613 919
F6 8 354 720 9 025 105 (0.75) 9 120 867
* See Figu e A2.
Figu e A4. Rela i e change in cumula i e ewa d in DRL compa ed o he Baseline o all a ms. *See
Figu e 10, Resul s.
