Coevolutionary Instability in Games:An Analysis Based on Genetic Algorithms

Abstract

Recently, genetic algorithms have been extensively applied to modeling bounded rationality in game theory. While these applications advance our understanding or game theory, they have generated some new phenomena which have not been well treated in conventional game theory. We systemize the study of one of these new phenomena, namely, coevolutionary instability. We exemplify the basic properties of coevolutionary instability by the chain store game, which is the game frequently used to study the role of reputation effects in economics. In addition, we point out that, while, due to uncertainty effects, Nash equilibria can no longer be stable, they can still help us predict the dynamic process of the game. In particular, we can see that the dynamic process of the game is well captured by a few Nash equilibria and the transition among them. A careful study can uncover several interesting patterns. We show the impact of uncertainty on these patterns