INTRODUCTION

This chapter discusses the notions of information and rationality of agents that are implicit in interpretations of formal definitions of simultaneous equilibrium in normal-form games. The examination of the nature of such notions as information and rationality aims in particular at ascertaining the possibility of regarding the definitions of equilibrium as welldefined instances of a theory of rational decision; in other words, we inquire into whether it is possible to characterize an equilibrium point of a normal-form game as the outcome of a rational decision process, that is, as a rational equilibrium.

The models that allow for some definitions of equilibrium can be classified as “topological” or “Boolean algebraic.” The former class allows for the definition of a Nash equilibrium, and the models are often interpreted as representing multiperson decision making “under conditions of certainty.” The latter class includes “neo-Bayesian” models and the notion of a “correlated equilibrium,” and are often construed as representing decision making “under uncertainty.”

NORMATIVE USE OF A NASH EQUILIBRIUM

Let Ai and Aj be the two sets of actions (or strategies) available to the players of a two-person, normal-form game. The Cartesian product Ω≔ Ai × Aj will be the preference-relevant set of states of things, or outcomes of the game. Assume the two players to have well-defined preference orderings of the points of Ω. There may be a point of Ω such that no unilateral change in either coordinate would lead to a point that is preferred by the corresponding player; the former point will then be a Nash equilibrium.