The prisoner’s dilemma on co-evolving networks under perfect rationality

Abstract We consider the prisoner’s dilemma being played repeatedly on a dynamic network, where agents may choose their actions as well as their co-players. This leads to co-evolution of network structure and strategy patterns of the players. Individual decisions are made fully rationally and are based on local information only. They are made such that links to defecting agents are resolved and that cooperating agents build up new links. The exact form of the updating scheme is motivated by profit maximization and not by imitation. If players update their decisions in a synchronized way the system exhibits oscillatory dynamics: Periods of growing cooperation (and total linkage) alternate with periods of increasing defection. The cyclical behavior is reduced and the system stabilizes at significant total cooperation levels when players are less synchronized. In this regime we find emergent network structures resembling ‘complex’ and hierarchical topology. The exponent of the power-law degree distribution ( γ ∼ 8.6 ) perfectly matches empirical results for human communication networks.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[3]  Esther Hauk,et al.  Leaving the Prison: Permitting Partner Choice and Refusal in Prisoner's Dilemma Games , 2001 .

[4]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Charles K. Rowley,et al.  The social dilemma : of autocracy, revolution, coup d'etat, and war , 2005 .

[6]  G. J. Rodgers,et al.  Transport on Complex Networks: Flow, Jamming and Optimization , 2007, Int. J. Bifurc. Chaos.

[7]  György Szabó,et al.  Evolutionary prisoner's dilemma game on hierarchical lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[10]  L. Tesfatsion,et al.  Preferential partner selection in an evolutionary study of Prisoner's Dilemma. , 1994, Bio Systems.

[11]  F. C. Santos,et al.  Evolutionary dynamics of social dilemmas in structured heterogeneous populations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[12]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[13]  R. Mulet,et al.  Evolutionary prisoner’s dilemma in random graphs , 2003 .

[14]  M. Kuperman,et al.  Social games in a social network. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Ádám Kun,et al.  THE EFFECT OF CLONAL INTEGRATION ON PLANT COMPETITION FOR MOSAIC HABITAT SPACE , 2000 .

[16]  V. Eguíluz,et al.  Cooperation and the Emergence of Role Differentiation in the Dynamics of Social Networks1 , 2005, American Journal of Sociology.

[17]  B. Huberman,et al.  Social Dilemmas and Internet Congestions , 1997 .

[18]  Víctor M Eguíluz,et al.  Coevolution of dynamical states and interactions in dynamic networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[20]  Kunihiko Kaneko,et al.  Spontaneous structure formation in a network of chaotic units with variable connection strengths. , 2002, Physical review letters.

[21]  S. Bornholdt,et al.  Coevolutionary games on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Petter Holme,et al.  Prisoners' dilemma in real-world acquaintance networks: spikes and quasiequilibria induced by the interplay between structure and dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  S. Goldhor.  Ecology , 1964, The Yale Journal of Biology and Medicine.

[24]  B A Huberman,et al.  Evolutionary games and computer simulations. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[25]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[26]  John H. Miller,et al.  Communication and cooperation , 1998 .

[27]  Michael Boss,et al.  Network topology of the interbank market , 2003, cond-mat/0309582.

[28]  György Szabó,et al.  Evolutionary prisoner's dilemma games with voluntary participation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Geoffrey Brennan,et al.  The Reason of Rules: Constitutional Political Economy. , 1987 .

[30]  B. Bollobás.  The evolution of random graphs , 1984 .

[32]  Beom Jun Kim,et al.  Dynamic instabilities induced by asymmetric influence: prisoners' dilemma game in small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Djoerd Hiemstra,et al.  Network Topology , 2009, Encyclopedia of Database Systems.

[34]  HANS M. AMMAN.  What is Computational Economics? , 1997 .

[35]  M. Nowak,et al.  A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game , 1993, Nature.

[36]  Eizo Akiyama,et al.  Chaos in learning a simple two-person game , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[37]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[38]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[39]  James M. Buchanan,et al.  The limits of liberty: between anarchy and Leviathan , 1976 .

[40]  Víctor M Eguíluz,et al.  Cooperation, social networks, and the emergence of leadership in a prisoner's dilemma with adaptive local interactions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.