# Blog Archives

# Topic Archive: Nash equilibrium

# Definitive solutions of strategic games

In his dissertation of 1950, Nash based his concept of solution to a game on the principles that “a rational prediction should be unique, that the players should be able to deduce and make use of it.” In this paper, we address the issue of when Nash expectations of a definitive solution hold and whether the Nash Equilibrium (NE) solution concept is a match for such definitive solutions. We show that indeed, an existence of NE is a necessary condition for a definitive solution, and each NE σ is a definitive solution for some notion of rationality individually tuned for this σ. However, for specific notions of rationality, e.g., Aumann’s rationality, NE is not an exact match to definitive solutions, many games with NE do not have definitive solutions at all. In particular, strategic ordinal payoff games with two or more Nash equilibria, and even some games with a unique NE do not have definitive solutions. We also show that the iterated dominance approach is a better candidate for Nash’s definitive solution concept than the Nash Equilibrium.