Three is a crowd in iterated prisoner's dilemmas: experimental evidence on reciprocal behavior

Reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas. Recent experimental findings on networked games suggest that conditional cooperation may also depend on the previous action of the player. We here report on experiments on iterated, multi-player Prisoner's dilemma, on groups of 2 to 5 people. We confirm the dependence on the previous step and that memory effects for earlier periods are not significant. We show that the behavior of subjects in pairwise dilemmas is qualitatively different from the cases with more players; After an initial decay, cooperation increases significantly reaching values above 80%. The strategy of the players is rather universal as far as their willingness to reciprocate cooperation is concerned, whereas there is much diversity in their initial propensity to cooperate. Our results indicate that, for cooperation to emerge and thrive, three is a crowd.

[1]  Eugene Demidenko.  Mixed Models: Theory and Applications (Wiley Series in Probability and Statistics) , 2004 .

[2]  W. Hamilton.  The genetical evolution of social behaviour. I. , 1964, Journal of theoretical biology.

[3]  BÓ Pedrodal,et al.  Cooperation under the Shadow of the Future : Experimental Evidence from Infinitely Repeated Games , 2005 .

[4]  H. Gintis,et al.  A Cooperative Species: Human Reciprocity and Its Evolution , 2011 .

[5]  A Rapoport,et al.  Sex differences in factors contributing to the level of cooperation in the prisoner's dilemma game. , 1965, Journal of personality and social psychology.

[6]  Hilla Peretz,et al.  Ju n 20 03 Schrödinger ’ s Cat : The rules of engagement , 2003 .

[7]  W. Hamilton,et al.  The evolution of cooperation. , 1984, Science.

[8]  Robert Kurzban,et al.  Experiments investigating cooperative types in humans: a complement to evolutionary theory and simulations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[9]  W. Press,et al.  Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent , 2012, Proceedings of the National Academy of Sciences.

[10]  J. Ledyard.  Public Goods: A Survey of Experimental Research , 1994 .

[11]  S. Gächter,et al.  The Long-Run Benefits of Punishment , 2008, Science.

[12]  U. Fischbacher,et al.  Are People Conditionally Cooperative? Evidence from a Public Goods Experiment , 2001 .

[13]  Ángel Sánchez,et al.  Human behavior in Prisoner's Dilemma experiments suppresses network reciprocity , 2012, Scientific Reports.

[14]  P. Richerson,et al.  Punishment allows the evolution of cooperation (or anything else) in sizable groups , 1992 .

[15]  Manfred Milinski,et al.  The Calculus of Selfishness , 2011 .

[16]  E. Demidenko,et al.  Mixed Models: Theory and Applications (Wiley Series in Probability and Statistics) , 2004 .

[17]  U. Fischbacher.  z-Tree: Zurich toolbox for ready-made economic experiments , 1999 .

[18]  A. Melis,et al.  How is human cooperation different? , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[19]  Donald E. Myers,et al.  Linear and Generalized Linear Mixed Models and Their Applications , 2008, Technometrics.

[20]  Wolfgang J. Luhan,et al.  Cedex Discussion Paper Series , 2022 .

[21]  Jörg Oechssler,et al.  Two are few and four are many: number effects in experimental oligopolies , 2004 .

[22]  Lourdes Araujo,et al.  Social Experiments in the Mesoscale: Humans Playing a Spatial Prisoner's Dilemma , 2010, PloS one.

[23]  J. Cuesta,et al.  Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma , 2012, Proceedings of the National Academy of Sciences.

[24]  C. Hauert,et al.  Punishing and abstaining for public goods , 2006, Proceedings of the National Academy of Sciences.

[25]  Ananish Chaudhuri.  Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature , 2011 .

[26]  Arne Traulsen,et al.  Human strategy updating in evolutionary games , 2010, Proceedings of the National Academy of Sciences.

[27]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

[28]  David G. Rand,et al.  Positive Interactions Promote Public Cooperation , 2009, Science.

[29]  U. Fischbacher,et al.  The nature of human altruism , 2003, Nature.

[30]  Rachel T. A. Croson.  Theories of Commitment, Altruism and Reciprocity: Evidence from Linear Public Goods Games , 2007 .

[31]  P. Richerson,et al.  The evolution of indirect reciprocity , 1989 .

[32]  M. Nowak.  Five Rules for the Evolution of Cooperation , 2006, Science.

[33]  K. Liang,et al.  Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions , 1987 .

[34]  T. D. Herdt,et al.  Cooperation and fairness: the flood–Dresher experiment revisited , 2003 .

[35]  M. Nowak,et al.  Evolution of indirect reciprocity by image scoring , 1998, Nature.

[36]  Rosemarie Nagel,et al.  Naive learning and cooperation in network experiments , 2007, Games Econ. Behav..

[37]  L. Keller,et al.  Human cooperation in social dilemmas: comparing the Snowdrift game with the Prisoner's Dilemma , 2007, Proceedings of the Royal Society B: Biological Sciences.

[38]  Xihong Lin,et al.  Variance Component Testing in Generalized Linear Mixed Models for Longitudinal/Clustered Data and other Related Topics , 2008 .

[39]  David G. Rand,et al.  Dynamic social networks promote cooperation in experiments with humans , 2011, Proceedings of the National Academy of Sciences.

[40]  J. Zelmer.  Linear Public Goods Experiments: A Meta-Analysis , 2003 .

[41]  Jelena Grujić,et al.  On the coexistence of cooperators,defectors and conditional cooperators in the multiplayer iterated Prisoner's Dilemma. , 2012, Journal of theoretical biology.

[42]  E. Fehr,et al.  Cooperation and Punishment in Public Goods Experiments , 1999, SSRN Electronic Journal.

[43]  Xin Yao,et al.  An Experimental Study of N-Person Iterated Prisoner's Dilemma Games , 1993, Informatica.

[44]  P. Richerson,et al.  The evolution of reciprocity in sizable groups. , 1988, Journal of theoretical biology.

[45]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[46]  Katrin Fehl,et al.  Co-evolution of behaviour and social network structure promotes human cooperation. , 2011, Ecology letters.

[47]  R. Trivers.  The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

[48]  Eörs Szathmáry,et al.  The Major Transitions in Evolution , 1997 .

[49]  Guillaume Fréchette,et al.  The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence , 2011 .

[50]  David G. Rand,et al.  Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World , 2010 .

[51]  E. Ostrom,et al.  Revisiting the commons: local lessons, global challenges. , 1999, Science.