INTRODUCTION

Non-cooperative game theory studies the question of what constitutes rational behavior in situations of strategic interaction in which players cannot communicate nor sign binding agreements. The traditional answer to this question centers around the notion of Nash equilibrium. Such an equilibrium is a vector of strategies, one for each player in the game, with the property that no single player can increase his payoff by changing to a different strategy as long as the opponents do not change their strategies. The Nash equilibrium concept is motivated by the idea that a theory of rational decision-making should not be a self-destroying prophecy that creates an incentive to deviate for those who believe in it. To quote from Luce and Raiffa (1957, p. 173):

In other words, for a (commonly known) norm of behavior to be self-enforcing it is necessary that the norm (agreement) constitutes a Nash equilibrium.

The increased use of non-cooperative game theory in economics in the last decades has led to an increased awareness of the fact that not every Nash equilibrium can be considered as a self-enforcing norm of behavior. Very roughly, the Nash concept is unsatisfactory since it may prescribe irrational behavior in contingencies that arise when somebody has deviated from the norm. In applications, one typically finds many equilibria and intuitive, context depending arguments have been used to exclude the “unreasonable” ones. At the same time game theorists have tried to formalize and unify the intuitions conveyed by applications and examples by means of general refined equilibrium notions.