Evolutionary Dynamics of the Nash Demand Game: A Diffusion Approach

Cooperation is fundamental in animal societies including humans, yet how to divide the resources obtained through cooperation is not a trivial question. The Nash demand game provides an excellent framework to study resource division between selfish agents. We herein study evolutionary dynamics of strategies in the Nash demand game. Our evolutionary model confirms the traditional prediction based on a Nash-equilibrium analysis that any possible resource division can be a stable outcome. Next, we study the effect of mutation (or exploration in cultural evolution). We model mutation as diffusion in the strategy space and analyze a pair of reaction diffusion equations. We find that the introduction of mutation to the system dramatically alters evolutionary outcomes and leads to a fair split of resources between two agents. We also study the effect of asymmetry in selection intensity on the resulting pattern of resource division.

[1]  H. Ohtsuki,et al.  A simple rule for the evolution of cooperation on graphs and social networks , 2006, Nature.

[2]  A. Gardner,et al.  Altruism, Spite, and Greenbeards , 2010, Science.

[3]  M. Mobius,et al.  The Evolution of Work , 2006 .

[4]  J. Nash.  Two-Person Cooperative Games , 1953 .

[5]  K. Sigmund,et al.  Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity , 1998 .

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

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

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

[9]  A. Griffin,et al.  Evolutionary Explanations for Cooperation , 2007, Current Biology.

[10]  Carol Barner-Barry,et al.  The Biology of Moral Systems Richard D. Alexander New York: Aldine De Gruyter, 1987 , 1988, Politics and the Life Sciences.

[11]  D. Barash.  The Biology of Moral Systems, Richard D. Alexander. Aldine, Hawthorne, New York (1987), xx, +301. Price $34.95 hardback, $16.95 paperback , 1987 .

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

[13]  A. Gardner,et al.  Sixteen common misconceptions about the evolution of cooperation in humans , 2011 .

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

[15]  R. Trivers.  The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

[16]  A. Griffin,et al.  Social semantics : altruism , cooperation , mutualism , strong reciprocity and group selection , 2007 .

[17]  Theodore Stankowich,et al.  The African Wild Dog: Behavior, Ecology, and Conservation , 2003 .

[18]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[19]  Tim Clutton-Brock,et al.  Cooperation between non-kin in animal societies , 2009, Nature.

[20]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[21]  Y. Toquenaga,et al.  Evolution of generosity in the demand game , 2005, Population Ecology.

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

[23]  Ken Binmore.  Playing for Real: A Text on Game Theory , 2007 .

[24]  C. Feh.  Alliances and reproductive success in Camargue stallions , 1999, Animal Behaviour.

[25]  D. Watts.  Coalitionary mate guarding by male chimpanzees at Ngogo, Kibale National Park, Uganda , 1998, Behavioral Ecology and Sociobiology.

[26]  A. Rubinstein.  Perfect Equilibrium in a Bargaining Model , 1982 .

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

[28]  C. Packer,et al.  Egalitarianism in Female African Lions , 2001, Science.