Rationalizable Strategic Behavior

THE NOTION OF EQUILIBRIUM proposed by Nash [19] has come to play a dominant role in economic applications of noncooperative games. While analyses of Nash equilibria have unquestionably contributed to our understanding of economic behavior, it would be unreasonably optimistic to maintain that Nash "solved" the problem of noncooperative strategic choice. There is a small literature (beginning with Ellsberg [6]) and a much larger oral tradition which argues that Nash behavior is neither a necessary consequence of rationality, nor a reasonable empirical proposition. In this paper I take the view that although there may be various reasons why an agent might select a Nash strategy, the notion of an equilibrium has little intrinsic appeal within a strategic context. When an agent reaches a decision in ignorance of the strategies adopted by other players, rationality consists of making a choice which is justifiable by an internally consistent system of beliefs, rather than one which is optimal, post hoc. This point of view is not original; indeed, most serious justifications of the Nash hypothesis embrace such an approach, arguing that agents will expect the game to yield a Nash outcome, and consequently will choose their equilibrium strategies. Nevertheless, when we think in terms of maximizing utility subject to expectations rather than realizations, it becomes clear that the Nash hypothesis, far from being a consequence of rationality, arises from certain restrictions on agents' expectations which may or may not be plausible, depending upon the game being played. We are then quite naturally led to ask: are there any restrictions of individuals' expectations (and hence choices) which are required by rationality alone, rather than by (subjective) plausibility? This paper is concerned with defining, justifying, characterizing, and refining a criterion for rational strategic choice, which I label "rationalizability."