Promotion of cooperation in evolutionary game dynamics with local information.

In this paper, we propose a strategy-updating rule driven by local information, which is called Local process. Unlike the standard Moran process, the Local process does not require global information about the strategic environment. By analyzing the dynamical behavior of the system, we explore how the local information influences the fixation of cooperation in two-player evolutionary games. Under weak selection, the decreasing local information leads to an increase of the fixation probability when natural selection does not favor cooperation replacing defection. In the limit of sufficiently large selection, the analytical results indicate that the fixation probability increases with the decrease of the local information, irrespective of the evolutionary games. Furthermore, for the dominance of defection games under weak selection and for coexistence games, the decreasing of local information will lead to a speedup of a single cooperator taking over the population. Overall, to some extent, the local information is conducive to promoting the cooperation.

[1]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[2]  Long Wang,et al.  Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[4]  M. Nowak,et al.  Evolutionary game dynamics in a Wright-Fisher process , 2006, Journal of mathematical biology.

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

[6]  C. Hauert,et al.  Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game , 2005 .

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

[8]  G. Szabó,et al.  Cooperation in spatial prisoner's dilemma with two types of players for increasing number of neighbors. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  A. Traulsen,et al.  Non-Gaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  A. Traulsen,et al.  Fixation times in evolutionary games under weak selection , 2008, 0812.0851.

[11]  Bin Wu,et al.  Evolutionary stability and quasi-stationary strategy in stochastic evolutionary game dynamics. , 2010, Journal of theoretical biology.

[12]  Jörg Oechssler,et al.  Cooperation as a Result of Learning with Aspiration Levels , 2002 .

[13]  Tadeusz Platkowski.  Aspiration-based full cooperation in finite systems of players , 2015, Appl. Math. Comput..

[14]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[15]  A. Cabrales.  Stochastic replicator dynamics , 2000 .

[16]  R. Boyd,et al.  The evolution of altruistic punishment , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[17]  J. S. GALE,et al.  Logic of animal conflict , 1975, Nature.

[18]  Brauchli,et al.  Evolution of cooperation in spatially structured populations , 1999, Journal of theoretical biology.

[19]  L. Imhof,et al.  Stochasticity and evolutionary stability. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Drew Fudenberg,et al.  Evolutionary game dynamics in finite populations , 2004, Bulletin of mathematical biology.

[21]  J. Deneubourg,et al.  Collective Decision-Making and Foraging Patterns in Ants and Honeybees , 2008 .

[22]  G. Szabó,et al.  Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Chaitanya S. Gokhale,et al.  Stochastic slowdown in evolutionary processes. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M. Nowak,et al.  A symmetry of fixation times in evoultionary dynamics. , 2006, Journal of theoretical biology.

[25]  Long Wang,et al.  Aspiration dynamics in structured population acts as if in a well-mixed one , 2015, Scientific Reports.

[26]  Attila Szolnoki,et al.  Topology-independent impact of noise on cooperation in spatial public goods games. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Chaitanya S. Gokhale,et al.  Dynamic Properties of Evolutionary Multi-player Games in Finite Populations , 2013, Games.

[28]  M. Nowak,et al.  Stochastic dynamics of invasion and fixation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[30]  Yibin Kang,et al.  Fixation times in evolutionary games with the Moran and Fermi processes. , 2015, Journal of theoretical biology.

[31]  Dale O. Stahl,et al.  Aspiration-based and reciprocity-based rules in learning dynamics for symmetric normal-form games , 2002 .

[32]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

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

[34]  Christine Taylor,et al.  COOPERATION MAINTAINED BY FITNESS ADJUSTMENT. , 2007, Evolutionary ecology research.

[35]  Martin A Nowak,et al.  Evolutionary games on cycles , 2006, Proceedings of the Royal Society B: Biological Sciences.

[36]  Yibin Kang,et al.  Fixation probabilities in evolutionary games with the Moran and Fermi processes. , 2015, Journal of theoretical biology.

[37]  Arne Traulsen,et al.  The mechanics of stochastic slowdown in evolutionary games. , 2012, Journal of theoretical biology.

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

[39]  C. Hauert,et al.  Evolutionary games and population dynamics: maintenance of cooperation in public goods games , 2006, Proceedings of the Royal Society B: Biological Sciences.

[40]  J. Deneubourg,et al.  Probabilistic behaviour in ants: A strategy of errors? , 1983 .

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

[42]  Tadeusz Płatkowski,et al.  Cooperation in aspiration-based N -person prisoner's dilemmas. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  K Sigmund,et al.  A note on evolutionary stable strategies and game dynamics. , 1979, Journal of theoretical biology.

[44]  D. H. Janzen,et al.  Ecology of Foraging by Ants , 1973 .

[45]  T. Antal,et al.  Fixation of Strategies for an Evolutionary Game in Finite Populations , 2005, Bulletin of mathematical biology.

[46]  Zhen Wang,et al.  Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game , 2010, PloS one.

[47]  H. Ohtsuki,et al.  Evolutionary stability on graphs. , 2008, Journal of theoretical biology.

[48]  B. Wang,et al.  Role of aspiration-induced migration in cooperation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  J. Traniello.  Recruitment behavior, orientation, and the organization of foraging in the carpenter ant Camponotus pennsylvanicus degeer (Hymenoptera: Formicidae) , 1977, Behavioral Ecology and Sociobiology.

[50]  Tadeusz Platkowski,et al.  Enhanced cooperation in prisoner's dilemma with aspiration , 2009, Appl. Math. Lett..

[51]  F. Ratnieks,et al.  Decision making in ant foragers (Lasius niger) facing conflicting private and social information , 2011, Behavioral Ecology and Sociobiology.

[52]  Long Wang,et al.  Universality of weak selection. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  S. Kurokawa,et al.  Emergence of cooperation in public goods games , 2009, Proceedings of the Royal Society B: Biological Sciences.

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