Social Stability and Equilibrium - Gilboa, Itzhak; Matsui, Akihiko (Econometrica, 1991)
IN THE FIELD OF NONCOOPERATIVE GAME THEORY, Nash equilibrium (Nash (1951)) has played a central role as a solution concept. In bold strokes, one may discern two major interpretations of Nash equilibrium in the context of rational players. The first, which is close to the eductive interpretation of Binmore (1987, 1988) and the complete information interpretation of Kaneko (1987), assumes that the game is played exactly once (if it is a repeated game, the repetition occurs once), and the players have sufficient knowledge and ability to analyze the game in a rational manner. Sometimes it is assumed that all players have consistent hierarchies of beliefs, where the game and their priors are common knowledge. Bayesian interpretation such as proposed by Aumann (1987) advanced this idea to the level that the players have a common prior. From this point of view, however, Nash equilibrium seems far from being satisfactory