The Evolution of Fuzzy Rules as Strategies in Two-Player Games

This paper describes simulations using fuzzy rules that show how Nash equilibrium behavior can be achieved by boundedly rational agents in two-player games with infinite strategy spaces. That is, we show how agents using simple “rules of thumb” can achieve near-equilibrium outcomes without any overt computation of the equilibrium. This is accomplished by using a genetic algorithm to approximate repeated play. Two games of differing complexities, both with analytic solutions, are examined: a repeated linear-demand Cournot game and a contestable rent game. When fuzzy rules used only the most recent information, the games we examined converged to outcomes similar to their respective Cournot-Nash equilibrium outcomes. When fuzzy rules “remembered” play from the more distant past, we found that the games converged more slowly, if at all.