This chapter examines a case in which players are very sophisticated in order to see how much can be gained from a high rationality perspective. The major positive result here is due to Kalai and Lehrer (1993), who show that Bayesian learning leads to Nash equilibrium behaviour provided the players’ prior beliefs capture the set of actual play paths with positive probability (the ‘absolute continuity’ condition). One limitation of this result is that absolute continuity assumes away a significant amount of the uncertainty inherent in the situation. In effect, it presupposes that players already have partial knowledge of their opponents’ strategies, which allows them to eliminate many possibilities ex ante. This assumption is obviously problematic in situations where players are completely ignorant of their opponents’ payoffs, for then they have no handle on the strategies that their opponents might be using.
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