Rationalizable Strategic Behavior and the Problem of Perfection

This paper explores the fundamental problem of what can be inferred about the outcome of a noncooperative game, from the rationality of the players and from the information they possess. The answer is summarized in a solution concept called rationalizability. Strategy profiles that are rationalizable are not always Nash equilibria; conversely, the information in an extensive form game often allows certain unreasonable Nash equilibria to be excluded from the set of rationalizable profiles. A stronger form of rationalizability is appropriate if players are known to be not merely rational but also cautious. WHAT CONSTITUTES RATIONAL BEHAVIOR in a noncooperative strategic situation? This paper explores the issue in the context of a wide class of finite noncooperative games in extensive form. The traditional answer relies heavily upon the idea of Nash equilibrium (Nash [17]). The position developed here, however, is that as a criterion for judging a profile of strategies to be choices for players in a game, the Nash equilibrium property is neither necessary nor sufficient. Some Nash equilibria are intuitively unreasonable, and not all reasonable strategy profiles are Nash equilibria. The fact that a Nash equilibrium can be intuitively unattractive is well-known: the equilibrium may be imperfect. Introduced into the literature by Selten [20], the idea of imperfect equilibria has prompted game theorists to search for a narrower definition of equilibrium. While this research, some of which will be discussed here, has been extremely instructive, it remains inconclusive. Theorists often agree about what should happen in particular games, but to capture this intuition in a general solution concept has proved to be very difficult. If this paper is successful it should make some progress in that direction. The other side of the coin has received less scrutiny. Can all non-Nash profiles really be excluded on logical grounds? I believe not. The standard justifications for considering only Nash profiles are circular in nature, or make gratuitous assumptions about players' decision criteria or beliefs. The following discussion of these points is extremely brief, due to space constraints; more detailed arguments may be found in Pearce [18].