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Absorbing games with a clock and two bits of memory

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  • Hansen, Kristoffer Arnsfelt
  • Ibsen-Jensen, Rasmus
  • Neyman, Abraham

Abstract

An absorbing game is a two-person zero-sum repeated game. Some of the entries are “absorbing” in the sense that, following the play of an absorbing entry, with positive probability all future payoffs are equal to that entry's payoff. The outcome of the game is the long-run average payoff. We prove that a two-person zero-sum absorbing game, with either finite or compact action sets, has, for each ε>0, ε-optimal strategies with finite memory. In fact, we show that there is an ε-optimal strategy that depends on the clock and three states of memory.

Suggested Citation

  • Hansen, Kristoffer Arnsfelt & Ibsen-Jensen, Rasmus & Neyman, Abraham, 2021. "Absorbing games with a clock and two bits of memory," Games and Economic Behavior, Elsevier, vol. 128(C), pages 213-230.
    • Handle: RePEc:eee:gamebe:v:128:y:2021:i:c:p:213-230
    DOI: 10.1016/j.geb.2021.04.008
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    References listed on IDEAS

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    1. Jean-François Mertens & Abraham Neyman & Dinah Rosenberg, 2009. "Absorbing Games with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 257-262, May.
    2. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    3. Kristoffer Arnsfelt Hansen & Rasmus Ibsen-Jensen & Abraham Neyman, 2023. "The Big Match with a Clock and a Bit of Memory," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 419-432, February.
    4. Abraham Neyman & Sylvain Sorin, 1998. "Equilibria in repeated games of incomplete information: The general symmetric case," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 201-210.
    5. Ehud Lehrer & Sylvain Sorin, 1992. "A Uniform Tauberian Theorem in Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 303-307, May.
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    Cited by:

    1. Shravan Luckraz & Bruno Antonio Pansera, 2022. "A Note on the Concept of Time in Extensive Games," Mathematics, MDPI, vol. 10(8), pages 1-4, April.

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