Equilibria Detection in Non-cooperative Game Theory. An Evolutionary Approach

The most important task in non-cooperative Game Theory is the equilibria detection. A computational method is presented in order to detect different types of equilibria. The method is based on generative relations. Generative relations are an algebraic tool for describing game equilibria. The generative relations of Nash, Aumann, Berge-Zhukovskii, Pareto and Lorenz equilibria are presented. The concept of meta-strategy is described that allows players to have different rationality types. The joint NashPareto and Nash Berge-Zhukovskii equilibrium is presented. Numerical experiments indicate the potential of the proposed method.