Bilinear programming and structured stochastic games
Journal of Optimization Theory and Applications
On complexity as bounded rationality (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Optimality and domination in repeated games with bounded players
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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We look at the Big Match game, a variation of the repeated Matching Pennies game where if the first player plays tails the game ends with the first player receiving the last round's payoff. We study this game when the second player is implemented as a finite automation. We show several results including: • If the first player knows the number of states of the second player's automaton then he can achieve the maximum score with a deterministic polynomial-time algorithm. • If a deterministic first player does not know the number of states of the second player then he can not guarantee himself more than the minimum score. • If we allow player one to run in probabilistic polynomial-time then he still cannot achieve the maximum score but he can get arbitrarily close. • In a slight variation of the Big Match, the first player cannot have an even close to dominant strategy.