Stochastic evolution with slow learning

Summary. This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making mutation rates small does not in general select a unique equilibrium but making selection strong does.

[1]  J. Gillespie.  Some Properties of Finite Populations Experiencing Strong Selection and Weak Mutation , 1983, The American Naturalist.

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

[3]  Glenn Ellison,et al.  Basins of Attraction, Long-Run Equilibria, and the Speed of Step-by-Step Evolution , 1995 .

[4]  M. Frank Norman,et al.  Limit theorems for stationary distributions , 1975, Advances in Applied Probability.

[5]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[6]  Ken Binmore,et al.  Muddling Through: Noisy Equilibrium Selection☆ , 1997 .

[7]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[8]  Siegfried K. Berninghaus,et al.  Another Approach to Mutation and Learning in Games , 1996 .

[9]  S. Ethier.  Limit theorems for Absorption Times of Genetic Models , 1979 .

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

[11]  R. Durrett.  Stochastic Calculus: A Practical Introduction , 1996 .

[12]  H. Kushner.  A cautionary note on the use of singular perturbation methods for “small noise” modelst † , 1982 .

[13]  W. Ewens.  Mathematical Population Genetics , 1980 .

[14]  Valentina Corradi,et al.  Continuous Approximations of Stochastic Evolutionary Game Dynamics , 2000, J. Econ. Theory.

[15]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[16]  W. Sandholm.  Markov evolution with inexact information , 1999 .

[17]  Barton L. Lipman,et al.  Evolution with State-Dependent Mutations , 1996 .

[18]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[19]  D. Fudenberg,et al.  Evolutionary Dynamics with Aggregate Shocks , 1992 .

[20]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[21]  William H. Sandholm,et al.  Evolution and equilibrium under inexact information , 2003, Games Econ. Behav..

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

[23]  S. Ethier.  A class of degenerate diffusion processes occurring in population genetics , 1976 .

[24]  P. A. P. Moran,et al.  Random processes in genetics , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[25]  L. Samuelson,et al.  Musical Chairs: Modeling Noisy Evolution , 1995 .

[26]  T. Shiga.  Diffusion processes in population genetics , 1981 .