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Subgame-perfection in free transition games

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  • Flesch, J.
  • Kuipers, J.
  • Schoenmakers, G.
  • Vrieze, K.

Abstract

We prove the existence of a subgame-perfect ε-equilibrium, for every ε>0, in a class of multi-player games with perfect information, which we call free transition games. The novelty is that a non-trivial class of perfect information games is solved for subgame-perfection, with multiple non-terminating actions, in which the payoff structure is generally not (upper or lower) semi-continuous. Due to the lack of semi-continuity, there is no general rule of comparison between the payoffs that a player can obtain by deviating a large but finite number of times or, respectively, infinitely many times. We introduce new techniques to overcome this difficulty.

Suggested Citation

  • Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2013. "Subgame-perfection in free transition games," European Journal of Operational Research, Elsevier, vol. 228(1), pages 201-207.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:1:p:201-207
    DOI: 10.1016/j.ejor.2013.01.034
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    Cited by:

    1. János Flesch & Arkadi Predtetchinski, 2017. "A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1162-1179, November.
    2. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
    3. Jeroen Kuipers & János Flesch & Gijs Schoenmakers & Koos Vrieze, 2021. "Subgame perfection in recursive perfect information games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 603-662, March.
    4. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    5. Dmitry Ryvkin, 2022. "To Fight or to Give Up? Dynamic Contests with a Deadline," Management Science, INFORMS, vol. 68(11), pages 8144-8165, November.

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