MODELLING NOISY PLAYERS. Part I: The Theoretical Framework

Resumen

In the theory of evolutionary games, perturbations are placed in the dynamic process that lead players to equilibrium; these perturbations have been sometimes endogenized by making them responsive to changes in the expected payoffs.The present paper is concerned in modelling realistically such perturbations. We present a model where, at each period, there is a proportion of agents in each player population, who use a choice procedure,based on correlated similarities, to establish a preference relation in their particular expected payoff-strategy frequency space. We present a measure of the perturbations induced by the choice procedure itself which is sensitive to expected payoffs, strategy frequencies and the degree of risk aversion displayed by the agents. A perturbed replicator dynamics is then built for models in which learning is social, replication of behaviours from one agent to another, being engineered by imitation. The point of introducing a dependence on payoffs, strategy frequencies and risk aversion is that it becomes possible for the dynamics to converge on Nash equilibria that are consistent with the outcomes observed in some laboratory experiments