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Mixed strategy equilibria in repeated games with one‐period memory

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  • Prajit K. Dutta
  • Paolo Siconolfi

Abstract

Infinitely repeated games is the pre‐dominant paradigm within which economists study long‐term strategic interaction. The standard framework allows players to condition their strategies on all past actions; that is, assumes that they have unbounded memory. That is clearly a convenient simplification that is at odds with reality. In this paper we restrict attention to one‐period memory and characterize all totally mixed equilibria. In particular, we focus on strongly mixed equilibria. We provide conditions that are necessary and sufficient for a game to have such an equilibrium. We further demonstrate the exact set of payoffs that can be generated by such equilibria.

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  • Prajit K. Dutta & Paolo Siconolfi, 2010. "Mixed strategy equilibria in repeated games with one‐period memory," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 167-187, March.
    • Handle: RePEc:bla:ijethy:v:6:y:2010:i:1:p:167-187
    DOI: 10.1111/j.1742-7363.2009.00128.x
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    1. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    2. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    3. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    4. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
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    Cited by:

    1. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2016. "Bounded memory Folk Theorem," Journal of Economic Theory, Elsevier, vol. 163(C), pages 728-774.
    2. Artem Baklanov, 2021. "Reactive Strategies: An Inch of Memory, a Mile of Equilibria," Games, MDPI, vol. 12(2), pages 1-28, May.

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