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Correlated Equilibria for Mean Field Games with Progressive Strategies

Author

Listed:
  • Ofelia Bonesini

    (Department of Mathematics, Imperial College London, London SW7 1NE, United Kingdom; and Dipartimento di Matematica “Tullio Levi-Civita,” Università degli studi di Padova, 35121 Padova, Italy)

  • Luciano Campi

    (Dipartimento di Matematica “Federigo Enriques,” Università degli studi di Milano, 20133 Milano, Italy)

  • Markus Fischer

    (Dipartimento di Matematica “Tullio Levi-Civita,” Università degli studi di Padova, 35121 Padova, Italy)

Abstract

In a discrete space and time framework, we study the mean field game limit for a class of symmetric N -player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows us to construct approximate N -player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormoor:v:50:y:2025:i:2:p:1072-1111
    DOI: 10.1287/moor.2022.0357
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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.
    2. Robert J. Aumann, 2025. "Subjectivity and Correlation in Randomized Strategies," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 4, pages 73-113, World Scientific Publishing Co. Pte. Ltd..
    3. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    4. Eilon Solan, 2000. "Rationality and Extensive Form Correlated Equilibria in Stochastic Games," Discussion Papers 1298, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. 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..
    6. repec:dau:papers:123456789/6019 is not listed on IDEAS
    7. Arce M., Daniel G. & Sandler, Todd, 2001. "Transnational public goods: strategies and institutions," European Journal of Political Economy, Elsevier, vol. 17(3), pages 493-516, September.
    8. repec:cup:cbooks:9781316779309 is not listed on IDEAS
    9. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781316624791, Enero-Abr.
    10. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781107172661, Enero-Abr.
    11. 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.
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