Beating a Finite Automaton in the Big Match

We look at the Big Match game, a variation of the repeated Matching Pennies game where if the rst player plays tails the game ends with the rst player receiving the last round's payo . We study this game when the second player is implemented as a nite automaton. We show several results including: If the rst 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 rst player does not know the number of states of the second player then he can not guarantee himself more than the minimumscore. 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 rst player cannot have an even close to dominant strategy.

• Type: Conference
• Year: 1998
• Where: TARK
• Authors: Lance Fortnow, Peter G. Kimmel
• Keywords: Automated Reasoning, Deterministic Rst Player, Player Plays Tails, Rst Player, TARK 1998