Influence of Opinion Dynamics on the Evolution of Games

Under certain circumstances such as lack of information or bounded rationality, human players can take decisions on which strategy to choose in a game on the basis of simple opinions. These opinions can be modified after each round by observing own or others payoff results but can be also modified after interchanging impressions with other players. In this way, the update of the strategies can become a question that goes beyond simple evolutionary rules based on fitness and become a social issue. In this work, we explore this scenario by coupling a game with an opinion dynamics model. The opinion is represented by a continuous variable that corresponds to the certainty of the agents respect to which strategy is best. The opinions transform into actions by making the selection of an strategy a stochastic event with a probability regulated by the opinion. A certain regard for the previous round payoff is included but the main update rules of the opinion are given by a model inspired in social interchanges. We find that the fixed points of the dynamics of the coupled model are different from those of the evolutionary game or the opinion models alone. Furthermore, new features emerge such as the independence of the fraction of cooperators with respect to the topology of the social interaction network or the presence of a small fraction of extremist players.

[1]  M. Nowak,et al.  Evolutionary Dynamics of Biological Games , 2004, Science.

[2]  Arne Traulsen,et al.  Exploration dynamics in evolutionary games , 2009, Proceedings of the National Academy of Sciences.

[3]  H. Young,et al.  The Evolution of Conventions , 1993 .

[4]  L. Blume.  The Statistical Mechanics of Strategic Interaction , 1993 .

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

[6]  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.

[7]  Jens Christian Claussen,et al.  Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations , 2008, ArXiv.

[8]  Lawrence E. Blume,et al.  How noise matters , 2003, Games Econ. Behav..

[9]  John H. Miller,et al.  Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence , 1993 .

[10]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[11]  S. Galam,et al.  The role of inflexible minorities in the breaking of democratic opinion dynamics , 2007, physics/0703021.

[12]  H. Peyton Young,et al.  Stochastic Evolutionary Game Dynamics , 1990 .

[13]  Chao Wang,et al.  Imitating emotions instead of strategies in spatial games elevates social welfare , 2011, 1109.1712.

[14]  Naoki Masuda,et al.  Evolution of cooperation driven by zealots , 2012, Scientific Reports.

[15]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

[16]  Maxi San Miguel,et al.  Social and strategic imitation: the way to consensus , 2012, Scientific Reports.

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

[18]  M. Benaïm,et al.  Deterministic Approximation of Stochastic Evolution in Games , 2003 .

[19]  Garrett Hardin,et al.  Living Within Limits: Ecology, Economics, and Population Taboos , 1993 .

[20]  G. Hardin,et al.  The Tragedy of the Commons , 1968, Green Planet Blues.

[21]  S. Galam.  Contrarian deterministic effects on opinion dynamics: “the hung elections scenario” , 2003, cond-mat/0307404.

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

[23]  S. Galam.  Heterogeneous beliefs, segregation, and extremism in the making of public opinions. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  Duncan J. Watts,et al.  Cooperation and Contagion in Web-Based, Networked Public Goods Experiments , 2010, SECO.

[26]  C. Hauert,et al.  Coevolutionary dynamics: from finite to infinite populations. , 2004, Physical review letters.

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

[28]  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.

[29]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

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

[31]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[32]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[33]  K. Schlag.  Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits , 1998 .

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

[35]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

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

[37]  Daniel Gardner.  Risk: The Science and Politics of Fear , 2008 .

[38]  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.

[39]  J. Cuesta,et al.  Time scales in evolutionary dynamics. , 2006, Physical review letters.

[40]  Mauro Mobilia,et al.  Stochastic dynamics of the prisoner's dilemma with cooperation facilitators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Andrea Zaccaria,et al.  Critical Overview of Agent-Based Models for Economics , 2011, 1101.1847.

[42]  Daniele Vilone,et al.  Chaos and unpredictability in evolutionary dynamics in discrete time. , 2011, Physical review letters.

[43]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[44]  J. Hofbauer,et al.  Evolutionary game dynamics , 2011 .

[45]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[46]  Max M. Krasnow,et al.  Evolution of direct reciprocity under uncertainty can explain human generosity in one-shot encounters , 2011, Proceedings of the National Academy of Sciences.

[47]  P. Trout,et al.  Living within Limits: Ecology, Economics, and Population Taboos , 1995 .

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

[49]  Mauro Mobilia,et al.  Reply to "Comment on 'Stochastic dynamics of the prisoner's dilemma with cooperation facilitators' ". , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  K. Kaski,et al.  Spatial snowdrift game with myopic agents , 2005 .

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