Recent Developments in Learning and Competition with Finite Automata (Extended Abstract)
Consider a repeated two-person game. The question is how much smarter should a player be to effectively predict the moves of the other player. The answer depends on the formal definition of effective prediction, the number of actions each player has in the stage game, as well as on the measure of smartness. Effective prediction means that, no matter what the stage-game payoff function, the player can play (with high probability) a best reply in most stages. Neyman and Spencer  provide a complete asymptotic solution when smartness is measured by the size of the automata that implement the strategies.
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