Replicator dynamics with mutations for games with a continuous strategy space

A partial differential equation is derived, describing the replicator dynamics with mutations of games with a continuous strategy space. This equation is then applied to continuous versions of symmetric 2x2 games, such as the Prisoners Dilemma, Hawk-Dove and Coordination games, and to the Ultimatum Game. In the latter case, we find that adding even a small mutation term to the replicator equation leads to a solution where the average offer is significantly larger than zero.

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

[2]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[3]  G A Parker,et al.  Evolutionary Stable Strategies , 1984, Encyclopedia of Evolutionary Psychological Science.

[4]  Chia-Ven Pao,et al.  Nonlinear parabolic and elliptic equations , 1993 .

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

[6]  P. Maître.  PLAYING FAIR GAME THEORY AND THE SOCIAL CONTRACT , 1994 .

[7]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[8]  U Dieckmann,et al.  Can adaptive dynamics invade? , 1997, Trends in ecology & evolution.

[9]  L. Samuelson.  Evolutionary Games and Equilibrium Selection , 1997 .

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

[11]  J. Oechssler,et al.  Evolutionary dynamics on infinite strategy spaces , 2001 .

[12]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

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

[14]  E. Fehr,et al.  Fairness and Retaliation: The Economics of Reciprocity , 2000, SSRN Electronic Journal.

[15]  R. Seymour.  Stationary distributions of noisy replicator dynamics in the Ultimatum game , 2000 .

[16]  M. Nowak,et al.  A generalized adaptive dynamics framework can describe the evolutionary Ultimatum Game. , 2001, Journal of theoretical biology.

[17]  Odo Diekmann,et al.  A beginners guide to adaptive dynamics , 2002 .

[18]  Herbert Gintis,et al.  Behavioural science: Homo reciprocans , 2002, Nature.

[19]  R. Cressman.  Evolutionary Dynamics and Extensive Form Games , 2003 .

[20]  R. Vaughan,et al.  Evolutive equilibrium selection I: symmetric two player binary choice games , 2004 .

[21]  H. Gintis,et al.  The evolution of strong reciprocity: cooperation in heterogeneous populations. , 2004, Theoretical population biology.

[22]  Ross Cressman,et al.  Stability of the replicator equation with continuous strategy space , 2004, Math. Soc. Sci..

[23]  J. Fletcher.  Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics , 2006, Journal of Mammalian Evolution.