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On Markov perfect equilibria in baseball

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  • Akifumi Kira
  • Keisuke Inakawa

Abstract

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.

Suggested Citation

  • Akifumi Kira & Keisuke Inakawa, 2014. "On Markov perfect equilibria in baseball," TMARG Discussion Papers 115, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:tmarga:115
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    File URL: http://hdl.handle.net/10097/57096
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    References listed on IDEAS

    as
    1. Turocy Theodore L., 2008. "In Search of the "Last-Ups" Advantage in Baseball: A Game-Theoretic Approach," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(2), pages 1-20, April.
    2. Bruce Bukiet & Elliotte Rusty Harold & José Luis Palacios, 1997. "A Markov Chain Approach to Baseball," Operations Research, INFORMS, vol. 45(1), pages 14-23, February.
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