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Correlated Equilibria and Mean Field Games: A Simple Model

Author

Listed:
  • Luciano Campi

    (Department of Mathematics “Federigo Enriques,” University of Milan, 20133 Milan, Italy)

  • Markus Fischer

    (Department of Mathematics “Tullio Levi-Civita,” University of Padua, 35121 Padova, Italy)

Abstract

In the context of simple finite-state discrete time systems, we introduce a generalization of a mean field game solution, called a correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium . Our notion of a solution is justified in two ways: we prove that correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying N -player games, and we show how to construct approximate N -player correlated equilibria starting from a correlated solution to the mean field game.

Suggested Citation

  • Luciano Campi & Markus Fischer, 2022. "Correlated Equilibria and Mean Field Games: A Simple Model," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2240-2259, August.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:3:p:2240-2259
    DOI: 10.1287/moor.2021.1206
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    References listed on IDEAS

    as
    1. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
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    3. Eilon Solan, 2001. "Characterization of correlated equilibria in stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 259-277.
    4. Robert J. Aumann, 2025. "Correlated Equilibrium as an Expression of Bayesian Rationality," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 7, pages 175-200, World Scientific Publishing Co. Pte. Ltd..
    5. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    6. repec:dau:papers:123456789/6019 is not listed on IDEAS
    7. repec:cup:cbooks:9781316779309 is not listed on IDEAS
    8. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    9. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781316624791.
    10. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781107172661.
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    Cited by:

    1. Ofelia Bonesini & Luciano Campi & Markus Fischer, 2025. "Correlated Equilibria for Mean Field Games with Progressive Strategies," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1072-1111, May.
    2. Sina Sanjari & Naci Saldi & Serdar Yüksel, 2023. "Optimality of Independently Randomized Symmetric Policies for Exchangeable Stochastic Teams with Infinitely Many Decision Makers," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1254-1285, August.

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