Properties of Evolutionarily Stable Learning Rules

Suppose a strategy for learning the optimal behaviour in repeatedly played games is genetically determined. Then the animal is engaged in a learning game as well as the repeatedly played game. Harley (1981,J. theor. Biol.89,611–633) considers evolutionarily stable strategies in such learning games, called evolutionarily stable (ES) learning rules. Harleyʹs work, though significant, is limited in that he does not establish 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 learning rules and the RPS approximation is established. The ES learning rules and the RPS approximation were found to converge to the same quality, the so-called matching ratio, with probability one.