Chimpanzee choice rates in competitive
games match equilibrium game theory
Christopher Flynn Martin
, Rahul Bhui
, Peter Bossaerts
, Tetsuro Matsuzawa
& Colin Camerer
Department of Brain and Behavioral Sciences, Kyoto University Primate Research Institute, Inuyama, Aichi 484-8506, Japan,
Division of the Humanities and Social Sciences, Caltech, Pasadena CA 91125, USA,
Department of Finance, University of Utah,
Salt Lake City, UT 84112 USA,
Computation & Neural Systems, Caltech.
The capacity for strategic thinking about the payoff-relevant actions of conspecifics is not well understood
across species. We use game theory to make predictions about choices and temporal dynamics in three
abstract competitive situations with chimpanzee participants. Frequencies of chimpanzee choices are
extremely close to equilibrium (accurate-guessing) predictions, and shift as payoffs change, just as
equilibrium theory predicts. The chimpanzee choices are also closer to the equilibrium prediction, and more
responsive to past history and payoff changes, than two samples of human choices from experiments in
which humans were also initially uninformed about opponent payoffs and could not communicate verbally.
The results are consistent with a tentative interpretation of game theory as explaining evolved behavior, with
the additional hypothesis that chimpanzees may retain or practice a specialized capacity to adjust strategy
choice during competition to perform at least as well as, or better than, humans have.
Interaction among organisms, in which each organism’s action influences the fitness reward of the other, is
ubiquitous in biological life. However, the ability of different species to think about payoff-relevant actions of
conspecifics and respond to action histories is not well understood. In this study, game theory is used to make
predictions about choices and temporal dynamics in three abstract competitive situations with chimpanzee and
human participants. We show that frequencies of chimpanzee choices are close to equilibrium game theory
predictions, and shift as payoffs change, just as equilibrium (accurate-guessing) theory predicts. This is a sur-
prising result. Equilibrium predictions assume mathematically that all organisms making choices correctly
anticipate what others do. Dozens of studies with human subjects show substantial deviations from that idealized
equilibrium state. However, chimpanzee choices in our data are also closer to the equilibrium prediction, and are
more responsive to past history and to payoff changes, than human choices. These results show how game theory
can be consistent with evolved behavior
, assuming that chimpanzees have a specialized capacity to adjust strategy
choice during competition, which appears to be practiced in ontogenetic development. This capacity makes their
choices at least as strategic as human choices
We see how our closest genetic relatives, chimpanzees (Pan troglodytes), behave as they make choices in
incentivized competitive strategic interactions in within-species competition. The interactions are referred to
as ‘‘games’’. Game theory is used to make predictions about possible behavioral outcomes. A chimpanzee-human
comparison in repeated competitive games is inspired by the ‘‘cognitive tradeoff hypothesis’’. This hypothesis is
that cortical growth and specialization for distinctly human cognitive capacities (such as language and categor-
ization) conceivably reduced more basic capacities, such as detailed perception and pattern recognition, useful for
tracking opponent choice during competition
. Those displaced capacities may be better preserved, and more
practiced during species development, in species for which those capacities are especially valuable (or ‘‘protean’’
Intra-group competition is clearly important in chimpanzee societies for establishing a dominance hierarchy
whereas large-scale cooperation is a human specialty. According to the cognitive tradeoff hypothesis, game theory
models may better describe chimpanzee behavior than human behavior.
Games are mathematical distillations of the basic action-payoff structures of ecologically valid situations.
Interactive experimental strategic games with payoffs have been used with primates and apes to assess prosociality
and coordination of mutually beneficial actions
and have been used in hundreds of human studies
We use a common protocol for both animals and humans (1; Methods), in which players were not initially
informed of their opponents’ payoffs. The games are direct and competitive: Joint actions create one winner and
11 April 2013
13 May 2014
5 June 2014
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SCIENTIFIC REPORTS | 4 : 5182 | DOI: 10.1038/srep05182 1
one loser. Both players can either press Left or Right touch-panel
buttons (Fig. 1). There are two roles: A Matcher player earns a payoff
if their choices match (e.g., Left-Left). A Mismatcher earns a payoff if
their choices mismatch (e.g., Right-Left). Joint actions of both players
immediately determine their payoff through the shared touch-panel
software (there is no subject-experimenter interaction; cf.
). Ours is
the first experiment in which chimpanzees compete directly with
other conspecifics for competitively-determined payoffs, and their
behavior is compared to human-human interaction.
Game theory offers a benchmark of optimal performance: Players
acting individually earn the most if they guess accurately what others
do, and if they choose strategies with maximal expected payoff given
those guesses. If both players do so, their choices form a ‘‘Nash
equilibrium’’ (NE), a pattern of play in which choices optimally
anticipate what others are likely to do.
The behavioral results answer two questions: (1) How close are the
frequencies of Left and Right choices, P(L) and P(R), to the game
theory NE predictions?; and (2) How predictably do current choices
respond to changes in the opponent’s history and to payoff changes?
Figs. 2a–c plot the overall frequencies of R choice, P(R), by indi-
vidual chimpanzee subjects in the three games, along with the Nash
equilibrium (NE) prediction. The theory predicts that Matchers will
choose the Right (R) box on the touch-panel half the time, P(R) 5
.50, in all three games. The theory also predicts that Mismatchers will
vary the frequency of choosing the Right box, P(R), across the three
games (see Supplementary Information). These NE predictions are
extremely counterintuitive: In this class of games, the payoffs of
Matcher subjects change. However, their predicted behavior should
not change across the games (they are predicted to choose P(R) 5.50
in all three treatments). Instead, the behavior of the Mismatcher
subjects should change, even though their payoffs do not change.
Fig. 2d plots cross-subject averages from all trials for all three
games. This plot shows whether the chimpanzees’ behavior changed
across the three payoff conditions as predicted by equilibrium theory.
The Matcher P(R) rates are generally close to half on average, as
equilibrium theory predicts (despite the fact that matcher payoffs
change across games). More strikingly, the Mismatchers’ P(R)
frequencies do shift numerically across games closely in line with
theory (though the Mismatchers’ payoffs did not change). The over-
all frequencies of P(R) for Mismatchers are .50, .73, and .79. These
frequencies are quite close to the NE predicted frequencies of .50, .75,
The close match of chimpanzee choice frequencies to game theory
predictions is generally closer than in most previous human experi-
ments (Fig. S2). Intrigued by this finding, we conducted additional
experiments with two human groups using a protocol to match the
chimpanzee and human conditions as closely as we feasibly could
(see Methods and Supplementary Information). Fig. 2c plots choice
frequencies for two different human groups in the Inspection game 3,
which is the only game that chimpanzees and humans both played.
Across Matcher and Mismatcher roles, the human average absolute
deviation from NE is .135, a number which is comparable to devia-
tions from NE in other competitive human experiments (see Fig. S2).
However, the chimpanzees’ average deviation is only .020 (cf. Table
S1). The chimpanzee choices are very close to the game theory pre-
diction, and are closer than both human groups’ choices are. Since
the chimpanzees played many more trials than the human groups
did, it is important to note that this difference in proximity to the NE
prediction also holds when the first 400 trials of the chimpanzee
group are matched to the 400 trials the human groups played in
the same game (Figs. S5–7).
Why do the chimpanzees so closely approximate game-theoretic
equilibrium? One clue is that working memory of experienced chim-
panzees is surprisingly good
. Chimpanzee choices may converge
more rapidly to the game theory prediction because they remember
patterns very well, and in some circumstances better than some
humans do. We test this hypothesis using statistical analyses to see
how strongly choices depend on beliefs based on previous opponent
choices (‘‘fictitious play’’ learning) and on different player roles. In
this analysis, choices depends on two behavioral parameters (
Supplementary Information): One is a ‘‘learning rate’’ (g), which
measures sensitivity to recent opponent choices, and influences
updates of the expected payoff of the L and R strategies. The second
measure is how well choices for each participant can be predicted
The trial progression, touch-panel setup, and game payoffs. (A) Two players interacting through touch-panel screens are shown a
self-start key (circle) at the beginning of each trial. After both players press the start key, two action choices are displayed, represented by squares on
the left and right sides of the screens. After both players make a choice, payoffs are dispensed to the winner and both players get feedback about their
opponent’s choice. (B) Payoff matrices for the 3 games in this study. (C) Subjects sit perpendicular to each other facing touch-panel screens that are
embedded in the walls of the experimental booth (photo credit: Chris Martin).
SCIENTIFIC REPORTS | 4 : 5182 | DOI: 10.1038/srep05182 2
based on the learning rate and on varying the frequency of R choice
in different role conditions (see Methods and Supplementary
Figures 3a–b compare learning rates and predictability across spe-
cies (excluding, however, one quarter of chimpanzee sessions with
extreme bias to one touch-panel side, though aggregate play remains
close to NE; see Supplementary Information, Table S4, and Fig. S8).
Learning rates and predictability are measured using a dynamic
model which accounts for how strongly choices in a trial adjust based
on the opponent’s previous history and the payoff structure (e.g.
Matcher vs Mismatcher role); see Methods and Supplementary
Information. The chimpanzees have a higher learning rate (p 5
.040, nonparametric ELR test; Supplementary Information IV) and
much higher predictability than humans (p 5.013, t-test;
Supplementary Information). These results suggest that the reason
the chimpanzees converge more sharply to mutually best-respond-
ing (i.e., are closer to NE) is because they adjust to opponent behavior
and to changes in incentives more strongly. This comparison does
not depend on differences in the numbers of trials the chimpanzee
and human groups faced (if anything, learning could be more evident
in the shorter trial lengths of the human groups).
Two empirical findings about response times (RTs) are notable.
First, chimpanzee RTs are much faster than human RTs (Fig. S9),
about 660 msec versus 900 msec. This may be due to the chimpan-
zees’ extended experience, or their previous experience with touch-
pad choice in other experiments at PRI. However, it is also consistent
with the cognitive tradeoff hypothesis that chimpanzees have
retained and developmentally trained skills for memory, computa-
tion and response in competitive games.
Second, Matcher RTs are faster than Mismatcher RTs. This
difference could arise if Mismatcher choices either involve more
complex calculations, or require override of an automatic motor
response to match. The motor-override interpretation is consistent
with recent evidence in human competitive games, showing that
Frequencies of R choices for all pairs in both roles show that chimpanzee behavior is close to game theoretic (NE) predictions.
(A, B) Chimpanzees in the symmetric and asymmetric MP games. (C) Chimpanzees and two human groups in the Inspection game. Deviations from
Nash equilibrium among chimpanzees average .02 (individual std error .025); deviations among humans average .13 (individual std error .059). Two-
sample t-test for the difference in absolute deviation is t(23) 56.38 (p ,.001). (D) Average behavior over all chimpanzees compared to NE for all three
SCIENTIFIC REPORTS | 4 : 5182 | DOI: 10.1038/srep05182 3
matching an opponent’s physical action is automatic—but,
remarkably, the difference disappears if both humans wear blind-
and persists with more control and incentives
Our experiments created strategic interactions between pairs of con-
specifics using a simple touch-panel protocol. The choice frequencies
of food-motivated chimpanzees match game theory predictions as
closely as in any species and comparable learning setting ever
observed, even when changes in rewards predict highly counterin-
tuitive changes in behavioral choice frequencies. The chimpanzees’
choices, compared to the human choices, are closer to those pre-
dicted by equilibrium game theory.
There are two broad hypotheses consistent with the facts that
chimpanzee choices are much closer to game theory than human
The first hypothesis is that there is a species-based confound in the
experimental protocols, and if this confound were eliminated the
chimpanzee and human results would then be closer.
There are some cross-species confounds in these experiments. We
do not think they fully account for direction or magnitude of the
chimpanzee-human difference. However, closer matches of human
and chimpanzee protocols are conceivable, and would be important
to establish more conclusively the differences our data simply
The chimpanzee subjects are genetically related mother-child
pairs and the human pairs are unrelated strangers. But the chimpan-
zees’ kinship should lead to less competitive behavior, away from
equilibrium; and the difference between chimpanzees and humans
does not go in that direction, and in fact goes in the opposite direction
(Supplementary Information Sect. VII). The chimpanzees were also
motivated by food reward. However, the two human groups were
either financially unmotivated (Japan) or very highly motivated
(Bossou), and exhibited very similar patterns of play (also compar-
able to other human groups
); so motivation does not explain the
Furthermore, the deviations from NE among humans observed in
this experiment are quite typical of deviations in other human experi-
ments with a variety of information and procedures (including
higher monetary stakes) (see 8; Fig. S2). The learning parameter
magnitudes for humans also closely match those from an earlier
human study with financial motivation using the same Inspection
game parameters with full participant knowledge of the game payoffs
; Fig. 3b; Supplementary Information). Thus, our results from two
human groups are not at all unusual compared to previous findings.
The second hypothesis is that chimpanzees actually are as good, or
better, at competitive interaction and at adjusting toward equilib-
rium choices from experience than humans are. Note that this tent-
ative conclusion certainly deserves further investigation since the
best evidence of an underlying mechanism — from statistical models
of learning — does exclude some unresponsive chimpanzee sessions;
then the difference in learning rate between chimpanzees and
humans is reasonably significant (p 5.040) (although overall pre-
dictability is different at p ,.001).
Nonetheless, a chimpanzee cognitive match or advantage is plaus-
ible because chimpanzees have clear physical advantages over humans
in strength and speed, which have fitness value in a dominance-
mediated social environment. In contrast, human society is relatively
egalitarian and non-agonistic, and there is less of a fitness benefit to
be gained from strength as a factor in intraspecific social interactions
That chimpanzees are close to NE (in our experiment) and humans
are further from NE (here and in other experiments) is consistent
with a possible parallel cognitive advantage for chimpanzees.
One cognitive advantage emerges in serial ordering tasks requiring
memory of briefly exposed spatial displays of Arabic numerals
one kind of memory masking task, when the lowest numeral of the
set is touched, the remaining eight numerals are masked by white
squares and subjects are required to touch the masked stimuli in
Chimpanzees respond to history and payoff structure more than humans do. (A) History-responsiveness of choices based on learning
rate (y-axis) and overall learning model fit which includes Matcher-Mismatcher response differences to payoff structure (x-axis). Chimpanzees have a
higher learning rate and a better model fit. (B) Cumulative distribution functions of the likelihood-ratio (LR) statistic (x-axis) showing the improvement
in fit of a model with learning compared to a no-learning benchmark. Higher LR numbers indicate more learning; one human outlier removed, see
Supplementary Information). The chimpanzee distribution is shifted to the right (i.e., it stochastically dominates the human distribution). This shift
means that for every level of detectable learning, more chimpanzees are likely to show that level of learning or greater, compared to humans (p 5.040 by
an ELR bootstrap test; see Supplementary Information Sect. IV).
SCIENTIFIC REPORTS | 4 : 5182 | DOI: 10.1038/srep05182 4
ascending order. One chimpanzee, Ayumu, could at 5.5 years old
perform this task above 80% accuracy while touching the first
numeral with an average latency of 670 msecs
. Humans have not
been shown to perform at his level of speed and accuracy on this
masking task, though in an easier memory task (the so-called
limited-hold task) in which five non-adjacent numerals are briefly
exposed for a duration of 210 msecs seconds before being auto-
matically masked, trained humans can achieve similar rates of
hypothesizes that chimpanzees are
better than humans at the masking memory task because human
evolution degraded certain memory skills to make room in the
brain for development of human language-related skills. The
notion that chimpanzees may display some superior cognitive
abilities due to a suggested lack of interference from language-
related processes is further supported by evidence from compar-
ative eye-tracking studies
. These studies have shown that
chimpanzees foveate on the same pictorial elements as humans,
but do so in less time by making quicker eye movements. Authors
suggest that longer fixation patterns displayed by humans are
caused by high-level semantic processing on objects as they are
viewed, and that the relative lack of such kinds of language pro-
cessing in chimpanzees gives them an advantage for making rapid
perceptual assessments of visual scenery.
The relatively poor performance of humans, together with the
conjectured importance of language for humans, raise issues about
the relevance of those game theory experiments in which humans
have traditionally been unable to talk to each other. If verbal com-
munication is indeed key to human strategic interaction, it seems
that external validity would be enhanced if one lets humans talk. Of
course, this challenges classical game theory, which has generally
struggled with how to model credibility of verbal communication
Ecological experience and development are likely to play an
important role too. In the wild, great apes engage in many compet-
itive strategic interactions such as predatory stalking
, young chim-
, border patrolling (which is very much like the
, raiding crops from human farms
, and play
). Because competitive payoff games are common
in chimpanzee life, evolutionary theory predicts that chimpanzees
would have developed cognitive adaptations to detect patterns in
opponent behavior and to create predictability in their own behavior.
More generally, chimpanzees are capable of strategic thinking in
, sneaky copulation
, future planning
many elements of theory of mind computation
. Some have argued
that the capacity to randomize effectively evolved because primate
predatory behavior and routine social interaction selects for unpre-
dictability in counter-strategies
. Experiments also show that chim-
panzees are better at competitive tasks than at comparable
In contrast, humans are relatively highly prosocial and coopera-
tive. As human children begin to speak and acculturate, their play
shifts between ages 2 to 4 from solitary and parallel play, to associat-
ive and cooperative play
. While young chimpanzees continue to
hone their competitive skills with constant practice, their young
human counterparts shift from competition to verbally-facilitated
Our new evidence of more responsive learning and adjustment
in competitive experiments by chimpanzees, and evidence of the
prevalence of competition in their ecology, supports the inter-
pretation of game theory as an evolutive theory. The evolutive
interpretation is that equilibrium game theory will apply particu-
larly well to strategy choices that are finely honed by evolutionary
value and (for the chimpanzees) regularly practiced in deve-
lopment and into adulthood. However, it is notable that in our
protocol humans are deliberately deprived of an extraordinary
cognitive ability -- language. In competitive games language can-
not increase group rewards. But in games requiring coordination
and cooperation, where language is particularly useful in our eco-
logy, the evolutive prediction is that humans will outperform
Methods (see also Supplementary Information)
Six chimpanzees (Pan Troglodytes) at the Kyoto University Primate Research
Institute voluntarily participated in the experiment. Each chimpanzee pair was a
mother and her offspring. They were matched together for all experimental games
reported here. These dual touch-panel competitive games were novel to the partici-
pants, but all six had previously participated in cognitive studies, including social
tasks involving food and token sharing
and observing and copying behavior of a
. The use of the chimpanzees during the experimental period adhered to
the Guide for the Care and Use of Laboratory Primates (2002) of the Primate Research
Institute of Kyoto University. The ethical committee of the Primate Research Institute
of Kyoto University approved the use of chimpanzee subjects. All experiments were
performed in accordance with the approved guidelines.
Sixteen students (13 female) of Gifu and Kyoto Universities also participated. Pairs
of subjects had 50 training trials in each of the Matcher and Mismatcher roles, to learn
the task and payoff structure. Then they played 200 rounds with a fixed counterpart,
once in each of the two roles, but only for the Inspection game.
Players made choices on pairs of computer touch-panel screens. Each screen dis-
played two identical stimuli (45 mm light blue square buttons) on the left and right
sides of the screen (Fig. 1a). If both subjects chose the button on the right, or if both
subjects chose the button on the left, then the Matcher earned a payoff. If the subjects
chose buttons on different sides, then the Mismatcher earned a payoff. Payoff
structures were different in three kinds of games, to test whether choices respond to
payoff changes as game theory predicted (Fig. 1c). Payoffs of apple cubes, or 1 Yen or
100 Guinean Franc bills were dispensed immediately after each trial (for chimpanzees
and humans respectively).
Additional human experimental sessions involved 12 adult males from the village
of Bossou in Guinea, West Africa. Subjects were pair-matched for 100 rounds of the
Inspection game. They played while sitting and facing each other across a table. Before
the game began, its rules were explained (though specific rewards were not described,
as in the chimpanzee protocol, and were instead learned over trials). On each round,
the experimenter counted out loud. At the count of three, each player placed a bottle
cap on the table in an upright or an inverted state. If the two bottle caps were in the
same state, the Matcher won the trial; otherwise, the Mismatcher won. Money was
immediately added to the pile of the winner in full view of both players, followed by
the next round. Players earned an average of 10,000 Guinean Francs (GF; $1.40 USD)
over the course of the game. This sum had large purchasing power in the village. A loaf
of bread costs 2,500 GF, and estimated annual GDP per capita is $503. Scaling up
based on the stakes as a fraction of GDP, the equivalent sums in the UK and US would
be £69 and $134 (as of 1/2013). These stakes are therefore substantial. The ethical
committee of Primate Research Institute of Kyoto University approved the use of
human subjects. All experiments were performed in accordance with the approved
guidelines. Written informed consent was provided by all human subjects. Several
illiterate Bossou subjects couldn’t read the consent form. The procedure was
explained to them verbally, then they signed a consent form (during video recording).
Model analysis: The model used to estimate responses of subjects to history is a
weighted form of ‘‘fictitious play’’. In this model, players update histories of what
other players have done in the recent past, to forecast future play and choose strategies
which are high-value (‘‘best responses’’) to those forecasts. In formal terms,
twhere the prediction error dp
tis the difference between an
indicator representing whether action awas taken by the opponent in trial t(P
or not (P
50), and the belief p
t. Hence, p
. This belief, which
changes on each trial, is then used to compute an expected value of each strategy.
Strategies are chosen using a softmax response function based on these expected value
differences, plus a ‘‘lever bias’’ term (reflecting a value bonus for choosing Right) that
can vary in Matcher and Mismatcher roles (see Supplemental Material). Three
parameters -- the two lever bias terms and the learning rate g-- are then fit to the
actual data using maximum likelihood. A high value of gindicates responsiveness to
opponent history. A difference in the lever bias terms controlling bias toward Right in
the two player roles indicates that players are responding correctly to different player-
role incentives. Both variables are compactly expressed in LL/N, which is the general
predictability of a player’s choices based on responsiveness gand differences in lever
bias (capturing the response to the shift in incentives from Matcher to Mismatcher
role). A low value of -LL/N indicates good predictability.
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Funds were provided by The Ministry of Education, Sports Technology, and Culture
(MEXT) No. 24000001, No. 20002001, JSPS-GCOE (A06, Biodiversity) (T.M.), JSPS
grant-in-aid (C.M.), Tamagawa GCOE (C.C.), the Gordon and Betty Moore Foundation
(C.C., P.B.), and Caltech HSS and the Social Sciences and Humanities Research Council of
Canada (R.B.). Thanks to D. Biro for task design, to M. Tanaka for help in building the
touch-panel setup, to I. Adachi, M. Hayashi, and M. Tomonaga for overseeing chimpanzee
experiments, and to the Center for Human Evolution Modeling and Research and members
of the Section on Language and Intelligence of Primate Research Institute for daily care of
Design (C.M., C.C., P.B., T.M.); research (C.M.); new analyses (R.B., P.B.); analyzed data
(R.B., C.M., P.B., C.C.); wrote paper (C.C., C.M., T.M., R.B.).
Supplementary information accompanies this paper at http://www.nature.com/
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Martin, C.F., Bhui, R., Bossaerts, P., Matsuzawa, T. & Camerer, C.
Chimpanzee choice rates in competitive games match equilibrium game theory predictions.
Sci. Rep. 4, 5182; DOI:10.1038/srep05182 (2014).
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SCIENTIFIC REPORTS | 4 : 5182 | DOI: 10.1038/srep05182 6