Efficient algorithms for learning to play repeated games against computationally bounded adversaries

We examine the problem of learning to play various games optimally against resource-bounded adversaries, with an explicit emphasis on the computational efficiency of the learning algorithm. We are especially interested in providing efficient algorithms for games other than penny-matching (in which payoff is received for matching the adversary\´s action in the current round), and for adversaries other than the classically studied finite automata. In particular, we examine games and adversaries for which the learning algorithm\´s past actions may strongly affect the adversary\´s future willingness to "cooperate" (that is, permit high payoff), and therefore require carefully planned actions on the part of the learning algorithm. For example, in the game we call contract, both sides play O or 1 on each round, but our side receives payoff only if we play 1 in synchrony with the adversary; unlike penny-matching, playing O in synchrony with the adversary pays nothing. The name of the game is derived from the example of signing a contract, which becomes valid only if both parties sign (play 1)