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Correlated optimin

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  • Mehmet Mars Seven

Abstract

We extend the optimin notion of Ismail (2025) from mixed strategy profiles to correlated distributions. A correlated distribution is evaluated by the worst expected payoff each player can receive when opponents may either obey their private recommendations or make unilateral recommendation-contingent deviations that are strictly profitable under the posterior induced by the distribution. Correlated optimins are Pareto optimal with respect to this vector of guaranteed payoffs. We show that a correlated optimin exists in every finite game. In addition, for every correlated equilibrium, there exists a correlated optimin such that every player's guaranteed payoff is weakly higher than his or her correlated equilibrium payoff. In two-player zero-sum games, correlated optimin coincides with correlated equilibrium and yields the maximin value. Outside zero-sum games, correlated optimin may strictly improve upon all correlated equilibria. We illustrate this with a simple 2x2 game with a unique correlated and coarse correlated equilibrium, in which there exists a correlated optimin that strictly Pareto dominates the equilibrium payoff.

Suggested Citation

  • Mehmet Mars Seven, 2026. "Correlated optimin," Papers 2605.19129, arXiv.org.
    • Handle: RePEc:arx:papers:2605.19129
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    References listed on IDEAS

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    1. MOULIN, Hervé & VIAL, Jean-Philippe, 1978. "Strategically zero-sum games: the class of games whose completely mixed equilibria connot be improved upon," LIDAM Reprints CORE 359, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mehmet S. Ismail, 2025. "Super‐Nash Performance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 66(4), pages 1487-1503, October.
    3. 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..
    4. Mehmet S. Ismail, 2019. "Super-Nash Performance," Papers 1912.00211, arXiv.org, revised Oct 2025.
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