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Blackwell Equilibrium in Repeated Games

Author

Listed:
  • Costas Cavounidis
  • Sambuddha Ghosh
  • Johannes Horner
  • Eilon Solan
  • Satoru Takahashi

Abstract

We apply Blackwell optimality to repeated games. An equilibrium whose strategy profile is sequentially rational for all high enough discount factors simultaneously is a Blackwell (subgame-perfect, perfect public, etc.) equilibrium. The bite of this requirement depends on the monitoring structure. Under perfect monitoring, a ``folk'' theorem holds relative to an appropriate notion of minmax. Under imperfect public monitoring, absent a public randomization device, any perfect public equilibrium generically involves pure action profiles or stage-game Nash equilibria only. Under private conditionally independent monitoring, in a class of games that includes the prisoner's dilemma, the stage-game Nash equilibrium is played in every round.

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  • Costas Cavounidis & Sambuddha Ghosh & Johannes Horner & Eilon Solan & Satoru Takahashi, 2025. "Blackwell Equilibrium in Repeated Games," Papers 2501.05481, arXiv.org.
    • Handle: RePEc:arx:papers:2501.05481
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    References listed on IDEAS

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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. Olivier GOSSNER, 2020. "The Robustness of Incomplete Penal Codes in Repeated Interactions," Working Papers 2020-29, Center for Research in Economics and Statistics.
    3. Christian Gollier & Richard Zeckhauser, 2005. "Aggregation of Heterogeneous Time Preferences," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 878-896, August.
    4. Matthew O. Jackson & Leeat Yariv, 2015. "Collective Dynamic Choice: The Necessity of Time Inconsistency," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 150-178, November.
    5. Kalai, Ehud & Samet, Dov & Stanford, William, 1988. "A Note on Reactive Equilibria in the Discounted Prisoner's Dilemma and Associated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(3), pages 177-186.
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