Dynamic Properties of the Nash Equilibrium

Abstract

In this paper the authors examine the games with well-defined reaction functions. The focus is on the stability property of the Nash equilibria, i.e. the convergency in the strategy profile space to a Nash equilibrium when, beginning with some initial strategy choices in a neighborhood, players take turn to make improvements. Some interesting propositions on the dynamic properties have been established, which offer a kind of explanation as to why in general the outcomes of games and the economic dynamic process can be rather diversified.