Generative relations for evolutionary equilibria detection

Abstract

A general technique for detecting equilibria in finite non cooperative games is proposed. Fundamental idea is that every equilibrium is characterized by a binary relation on the game strategies. This relation - called generative relation -- induces an appropriate domination concept. Game equilibrium is described as the set of non dominated strategies with respect to the generative relation. Slight generalizations of some well known equilibrium concepts are proposed. A population of strategies is evolved according to a domination-based ranking in oder to produce better and better equilibrium approximations. Eventually the process converges towards the game equilibrium. The proposed technique opens an way for qualitative approach of game equilibria. In order to illustrate the proposed evolutionary technique different equilibria for different continuous games are studied. Numerical experiments indicate the potential of the proposed concepts and technique.