Rationalizable Strategic Behavior and the Problem of Perfection
David G. Pearce
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 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.”
The paper introduces the concept of rationalizability, which is a solution concept for finite noncooperative games. Rationalizability is based on three assumptions: (A1) players form subjective priors that do not contradict any of the information at their disposal; (A2) each player maximizes his expected utility relative to his subjective priors regarding the strategic choices of others; and (A3) the structure of the game is common knowledge. Rationalizability is defined as the set of strategies that are best responses to some conjecture over strategies that have not been removed at an earlier stage. The paper also introduces the concept of cautious rationalizability, which is a stronger form of rationalizability that requires players to exercise prudence when it is costless to do so.
The paper discusses the implications of rationalizability for the analysis of noncooperative games. It shows that rationalizability allows for a broader set of strategies than Nash equilibrium, and that it can exclude certain Nash equilibria that are intuitively unreasonable. The paper also discusses the limitations of rationalizability, particularly in the context of extensive form games, where the concept of imperfection arises. The paper concludes that rationalizability provides a useful solution concept for analyzing noncooperative games, but that it is not sufficient to capture all aspects of strategic behavior.Rationalizable Strategic Behavior and the Problem of Perfection
David G. Pearce
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 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.”
The paper introduces the concept of rationalizability, which is a solution concept for finite noncooperative games. Rationalizability is based on three assumptions: (A1) players form subjective priors that do not contradict any of the information at their disposal; (A2) each player maximizes his expected utility relative to his subjective priors regarding the strategic choices of others; and (A3) the structure of the game is common knowledge. Rationalizability is defined as the set of strategies that are best responses to some conjecture over strategies that have not been removed at an earlier stage. The paper also introduces the concept of cautious rationalizability, which is a stronger form of rationalizability that requires players to exercise prudence when it is costless to do so.
The paper discusses the implications of rationalizability for the analysis of noncooperative games. It shows that rationalizability allows for a broader set of strategies than Nash equilibrium, and that it can exclude certain Nash equilibria that are intuitively unreasonable. The paper also discusses the limitations of rationalizability, particularly in the context of extensive form games, where the concept of imperfection arises. The paper concludes that rationalizability provides a useful solution concept for analyzing noncooperative games, but that it is not sufficient to capture all aspects of strategic behavior.