The Ultimatum Game in complex networks

We address the problem of how cooperative (altruistic-like) behavior arises in natural and social systems by analyzing an Ultimatum Game in complex networks. Specifically, players of three types are considered: (a) empathetic, whose aspiration levels, and offers, are equal, (b) pragmatic, who do not distinguish between the different roles and aim to obtain the same benefit, and (c) agents whose aspiration levels, and offers, are independent. We analyze the asymptotic behavior of pure populations with different topologies using two kinds of strategic update rules: natural selection, which relies on replicator dynamics, and social penalty, inspired by the Bak–Sneppen dynamics, in which players are subject to a social selection rule penalizing not only the less fit individuals, but also their first neighbors. We discuss the emergence of fairness in the different settings and network topologies.

[1]  M. Nowak,et al.  Empathy leads to fairness , 2002, Bulletin of mathematical biology.

[2]  R. Axelrod,et al.  Evolutionary Dynamics , 2004 .

[3]  J. Gómez-Gardeñes,et al.  From scale-free to Erdos-Rényi networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Henrik Jeldtoft Jensen,et al.  Prisoner's dilemma on a stochastic nongrowth network evolution model. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Günter Haag,et al.  Economic Evolution and Demographic Change , 1992 .

[7]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[8]  J. Gómez-Gardeñes,et al.  Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks , 2007, q-bio/0703019.

[9]  W. Güth,et al.  An experimental analysis of ultimatum bargaining , 1982 .

[10]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

[11]  M. Milinski,et al.  Reputation helps solve the ‘tragedy of the commons’ , 2002, Nature.

[12]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[13]  M. Nowak.  Evolutionary Dynamics: Exploring the Equations of Life , 2006 .

[14]  Angel Sánchez,et al.  Altruism may arise from individual selection. , 2004, Journal of theoretical biology.

[15]  Henrik Jeldtoft Jensen,et al.  Darwinian selection in a locally unstable Boolean network , 2004 .

[16]  M. Nowak,et al.  Fairness versus reason in the ultimatum game. , 2000, Science.

[17]  Gretchen Vogel,et al.  The Evolution of the Golden Rule , 2004, Science.

[18]  James H Fowler,et al.  Altruistic Punishment and the Origin of Cooperation , 2005, Proceedings of the National Academy of Sciences of the United States of America.

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

[20]  Dirk Helbing.  Interrelations between stochastic equations for systems with pair interactions , 1992 .

[21]  David G. Rand,et al.  Winners don’t punish , 2008, Nature.

[22]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  S. Gould.  The Structure of Evolutionary Theory , 2002 .

[24]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

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

[26]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[27]  J. Gómez-Gardeñes,et al.  Natural selection of cooperation and degree hierarchy in heterogeneous populations. , 2008, Journal of theoretical biology.

[28]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[29]  R. Boyd,et al.  Explaining altruistic behavior in humans , 2003 .

[30]  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.

[31]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

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

[33]  Yamir Moreno,et al.  The Bak-Sneppen model on scale-free networks , 2001, cond-mat/0108494.

[34]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[35]  Colin Camerer,et al.  Foundations of Human Sociality - Economic Experiments and Ethnographic: Evidence From Fifteen Small-Scale Societies , 2004 .

[36]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

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

[38]  J Gómez-Gardeñes,et al.  Dynamical organization of cooperation in complex topologies. , 2007, Physical review letters.

[39]  S. Gächter.  Behavioral Game Theory , 2008, Encyclopedia of Evolutionary Psychological Science.

[40]  E. Fehr,et al.  Altruistic punishment in humans , 2002, Nature.