On the evolution of optimizing behavior

Abstract We investigate whether replicator dynamics justify “survival of the fittest” when players inherit pure strategies, mixed strategies, or rules for choosing strategies. A strategy that never is a best reply can survive replicator dynamics if only pure strategies are heritable, but only rationalizable strategies survive if mixed strategies are heritable. Now suppose agents can inherit the rule of choosing a best reply to the last period's population, rather than inheriting a strategy itself. Such optimizers need not drive out players who inherit a dominated strategy. If we interpret replicator dynamics as a learning process, this means that non-optimizing behavior can survive.

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

[2]  D. Fudenberg,et al.  Evolution and Cooperation in Noisy Repeated Games , 1990 .

[3]  John Nachbar.  “Evolutionary” selection dynamics in games: Convergence and limit properties , 1990 .

[4]  D. E. Matthews.  Evolution and the Theory of Games , 1977 .

[5]  J. Sobel,et al.  On the limit points of discrete selection dynamics , 1992 .

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  Paul R. Milgrom,et al.  Adaptive and sophisticated learning in normal form games , 1991 .

[8]  E. Zeeman.  Dynamics of the evolution of animal conflicts , 1981 .

[9]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[10]  Larry Samuelson,et al.  Evolutionary Foundations of Solution Concepts for Finite, Two-Player, Normal-Form Games , 1988, TARK.

[11]  W. G. S. Hines,et al.  Strategy stability in complex populations , 1980, Journal of Applied Probability.

[12]  D. Friedman.  EVOLUTIONARY GAMES IN ECONOMICS , 1991 .

[13]  W. Hines.  Three characterizations of population strategy stability , 1980 .

[14]  L. Samuelson,et al.  Evolutionary stability in repeated games played by finite automata , 1992 .

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

[16]  David Canning.  Convergence to Equilibrium in a Sequence for Games with Learning , 1989 .

[17]  L. Samuelson,et al.  Evolutionary Stability in Asymmetric Games , 1992 .

[18]  Josef Hofbauer,et al.  The theory of evolution and dynamical systems , 1988 .

[19]  E. Damme.  Stability and perfection of Nash equilibria , 1987 .

[20]  J. Jordan,et al.  Bayesian learning in normal form games , 1991 .

[21]  B. Bernheim.  Rationalizable Strategic Behavior , 1984 .

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

[23]  L. Samuelson,et al.  EVOLUTIONARY STABILITY IN SYMMETRIC GAMES , 1990 .

[24]  E. Vandamme.  Stability and perfection of nash equilibria , 1987 .

[25]  David Pearce.  Rationalizable Strategic Behavior and the Problem of Perfection , 1984 .