PROPERTIES OF EVOLUTIONARILY STABLE LEARNING RULES

Suppose a strategy for learning the optimal behavior in repeatedly pla yed games is genetically determined. Then the animal is engaged in a l earning game as well as the repeatedly played game. Harley (1981, J. t heor. Biol. 89, 611-633) considers evolutionarily stable strategies in such learning games, called evolutionarily stable (ES) learning rules . Harley's work, though significant, is limited in that he does not es tablish the stochastic convergence of ES learning rules. Furthermore, his study of the relative payoff sum (RPS) approximation is limited to simulation experiments. Here, the stochastic convergence of ES learni ng rules and the RPS approximation is established. The ES learning rul es and the RPS approximation were found to converge to the same qualit y, the so-called matching ratio, with probability one. (C) 1995 Academ ic Press Limited