Pink-noise dynamics in an evolutionary game on a regular graph

We consider an iterated multiplayer prisoner's dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and obtain heat-maps of the fraction of cooperators and the correlation of neighboring pairs. In the heat-map, there is a mixed region where cooperators and defectors coexist, and in the mixed region the correlation between neighbors is enhanced. Moreover, we observe pink-noise behavior in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. We also find that the pink-noise behavior can be reproduced in a simple random-walk model. In particular, we propose a modified random-walk model which can reproduce not only the pink-noise behavior but also the deviation from it observed in a low-frequency region.

[1]  Jonathan Newton,et al.  Evolutionary Game Theory: A Renaissance , 2018, Games.

[2]  Martin A Nowak,et al.  Evolution of extortion in Iterated Prisoner’s Dilemma games , 2012, Proceedings of the National Academy of Sciences.

[3]  Matjaz Perc,et al.  Aspiring to the Fittest and Promotion of Cooperation in the Prisoner's Dilemma Game , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Jun Tanimoto,et al.  Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game , 2007, Biosyst..

[5]  Robert van Rooij,et al.  The Stag Hunt and the Evolution of Social Structure , 2007, Stud Logica.

[6]  Arne Traulsen,et al.  Coevolution of strategy and structure in complex networks with dynamical linking. , 2006, Physical review letters.

[7]  César A. Hidalgo,et al.  Scale-free networks , 2008, Scholarpedia.

[8]  Colin Camerer.  Behavioral Game Theory: Experiments in Strategic Interaction , 2003 .

[9]  W. E. Fann.  Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb , 1993 .

[10]  D. Buss,et al.  Sex differences in human mate preferences: Evolutionary hypotheses tested in 37 cultures , 1989, Behavioral and Brain Sciences.

[11]  Robert Forsythe,et al.  COMMUNICATION IN THE BATTLE OF THE SEXES GAME , 1989 .

[12]  M. Mézard,et al.  Spin Glass Theory And Beyond: An Introduction To The Replica Method And Its Applications , 1986 .

[13]  R M May,et al.  Coevolution of hosts and parasites , 1982, Parasitology.

[14]  Michael Boss.  Economic theory of democracy , 1974 .

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

[16]  Morton D. Davis,et al.  The kernel of a cooperative game , 1965 .

[17]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[18]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .

[19]  Michael Wainwright.  On the Theory of Games of Strategy , 2016 .

[20]  Klaudia Beich,et al.  Playing For Real A Text On Game Theory , 2016 .

[21]  Katharina Weiss,et al.  Game Theory And Animal Behavior , 2016 .

[22]  J. Bendor,et al.  Effective Choice in the Prisoner ' s Dilemma , 2007 .

[23]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[24]  R. Gibbons.  Game theory for applied economists , 1992 .

[25]  K. Vrieze,et al.  A course in game theory , 1992 .

[26]  A. W. Tucker,et al.  Contributions to the theory of games (AM-40) , 1959 .

[27]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.