ON MARKOV PERFECT EQUILIBRIA IN BASEBALL

We formulate baseball as a finite Markov game with approximately 3.5 million states. The manager of each opposing team is the player who maximizes the probability of their team winning. We derive, using dynamic programming, a recursive formula which is satisfied by Markov perfect equilibria and the value functions of the game for both teams. By solving this recursive formula, we can obtain optimal strategies for each condition. We demonstrate with numerical experiments that these can be calculated in approximately 1 second per game.