Equilibria in Non‐cooperative Games Ii: Deviations Based Refinements of Nash Equilibrium

Abstract

In any Nash equilibrium no player will unilaterally deviate. However, many games have multiple Nash equilibria. In this paper, we survey some refinements of Nash equilibria based on the hypothesis that any player may consider a deliberate deviation from a Nash equilibrium vector while expecting other players to respond optimally to this deviation. The concepts studied here differ in the expectations players have about other players' responses to a deviation. This sort of deviations philosophy is predicated on the thought process of players. Therefore, the validity of a particular equilibrium concept to an economic model may depend upon the relevance of the thought process implied by the concept.

Equilibria in Non‐cooperative Games I: Perturbations Based Refinements of Nash Equilibrium

“…The normal form game corresponding to this reinterpreted extensive form is called the agent normal form. This agent normal form of an extensive form game is useful (as we shall see in Sadanand and Sadanand (1992)) in understanding the importance of deviations based refinements.…”

“…We begin by developing the basic definitions and notation that will be used in this paper and in the second part of this survey in Sadanand and Sadanand (1992). For a detailed description, the reader is referred to Kuhn (1 953), Luce and Raiffa (1956), Shubik (1983) among others.…”

“…A strategy i, is a weakly dominant strategy for player i if This observation is crucial to the development of some deviations based solution concepts in the second part of this survey in Sadanand and Sadanand (1992). for every s-, and s, f S: , .…”

“…However, there are some problems as we shall see. The definition of a sequential equilibrium and the issues raised therein provide a basis for looking into other refinements (see Sadanand and Sadanand ( 1992)) that are based not on perturbations of strategies but on deliberate deviations by the players from the equilibrium path.…”

“…One is to introduce criteria restricting the formation of beliefs using some (intuitive) arguments. We will examine some of these in Sadanand and Sadanand ( 1992). The other, is to reconsider the consistency requirement o n beliefs.…”