IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2607.06282.html

Axioms for Correlated Equilibrium

Author

Listed:
  • Florian Brandl

Abstract

We characterize correlated equilibrium in finite normal-form games. Interpreting correlated strategies as action recommendations, we show that correlated equilibrium is the unique solution concept that never recommends a pure-strategy dominated action, treats payoff-equivalent actions interchangeably, and respects the sure-thing principle under uncertainty about payoffs and the correlation device. A parallel characterization identifies coarse correlated equilibrium among solution concepts that recommend dominant actions whenever they exist and treat payoff-equivalent actions as strongly interchangeable.

Suggested Citation

  • Florian Brandl, 2026. "Axioms for Correlated Equilibrium," Papers 2607.06282, arXiv.org.
  • Handle: RePEc:arx:papers:2607.06282
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2607.06282
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    3. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    4. Brandl, Florian & Brandt, Felix, 2024. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society, vol. 19(4), November.
    5. Voorneveld, Mark, 2019. "An elementary axiomatization of the Nash equilibrium concept," SSE Working Paper Series in Economics 2019:1, Stockholm School of Economics.
    6. Barelli, Paulo, 2009. "Consistency of beliefs and epistemic conditions for Nash and correlated equilibria," Games and Economic Behavior, Elsevier, vol. 67(2), pages 363-375, November.
    7. Gilboa, Itzhak & Schmeidler, David, 2003. "A derivation of expected utility maximization in the context of a game," Games and Economic Behavior, Elsevier, vol. 44(1), pages 172-182, July.
    8. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
    9. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 133-154.
    10. Voorneveld, Mark, 2019. "An axiomatization of the Nash equilibrium concept," Games and Economic Behavior, Elsevier, vol. 117(C), pages 316-321.
    11. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    12. Kalai, Adam Tauman & Kalai, Ehud, 2024. "Beyond dominance and Nash: Ranking equilibria by critical mass," Games and Economic Behavior, Elsevier, vol. 144(C), pages 378-394.
    13. Florian Brandl & Felix Brandt & Hans Georg Seedig, 2016. "Consistent Probabilistic Social Choice," Econometrica, Econometric Society, vol. 84, pages 1839-1880, September.
    14. Shurojit Chatterji & Srihari Govindan, 2006. "Message spaces for perfect correlated equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 475-479, June.
    15. Luo, Xiao & Qiao, Yongchuan & Sun, Yang, 2022. "A revelation principle for correlated equilibrium under trembling-hand perfection," Journal of Economic Theory, Elsevier, vol. 200(C).
    16. Bach, Christian W. & Tsakas, Elias, 2014. "Pairwise epistemic conditions for Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 85(C), pages 48-59.
    17. Lackner, Martin & Skowron, Piotr, 2021. "Consistent approval-based multi-winner rules," Journal of Economic Theory, Elsevier, vol. 192(C).
    18. Eric Maskin, 1979. "Decision-Making Under Ignorance with Implications for Social Choice," Springer Books, in: H. W. Brock (ed.), Game Theory, Social Choice and Ethics, pages 319-337, Springer.
    19. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    20. Brandl, Florian & Brandt, Felix, 2019. "Justifying optimal play via consistency," Theoretical Economics, Econometric Society, vol. 14(4), November.
    21. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    22. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    23. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    24. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Florian Brandl & Felix Brandt, 2023. "A Robust Characterization of Nash Equilibrium," Papers 2307.03079, arXiv.org, revised Jun 2024.
    2. Brandl, Florian & Brandt, Felix, 2024. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society, vol. 19(4), November.
    3. Bach, Christian W. & Perea, Andrés, 2020. "Two definitions of correlated equilibrium," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 12-24.
    4. Michele Crescenzi, 2025. "A choice-based axiomatization of Nash equilibrium," Papers 2512.03930, arXiv.org.
    5. Atsushi Kajii & Stephen Morris, 2020. "Correction to: Refinements and higher-order beliefs: a unified survey," The Japanese Economic Review, Springer, vol. 71(2), pages 351-351, April.
    6. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    8. Bach, Christian W. & Perea, Andrés, 2020. "Generalized Nash equilibrium without common belief in rationality," Economics Letters, Elsevier, vol. 186(C).
    9. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    10. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    11. Lederer, Patrick, 2024. "Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule," Journal of Economic Theory, Elsevier, vol. 218(C).
    12. Luo, Xiao & Qiao, Yongchuan & Sun, Yang, 2022. "A revelation principle for correlated equilibrium under trembling-hand perfection," Journal of Economic Theory, Elsevier, vol. 200(C).
    13. Aziz, Haris & Lederer, Patrick & Lu, Xinhang & Suzuki, Mashbat & Vollen, Jeremy, 2025. "Approximately fair and population consistent budget division via simple payment schemes," Games and Economic Behavior, Elsevier, vol. 154(C), pages 208-225.
    14. Werner Güth, 2002. "On the Inconsistency of Equilibrium Refinement," Theory and Decision, Springer, vol. 53(4), pages 371-392, December.
    15. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    16. Florian Brandl & Felix Brandt, 2026. "Consistent Probabilistic Social Choice Revisited," Papers 2606.10998, arXiv.org.
    17. Yuval Heller, 2012. "Sequential Correlated Equilibria in Stopping Games," Operations Research, INFORMS, vol. 60(1), pages 209-224, February.
    18. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    19. Forges, Françoise & Ray, Indrajit, 2024. "“Subjectivity and correlation in randomized strategies”: Back to the roots," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    20. Haris Aziz & Patrick Lederer & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen, 2024. "Approximately Fair and Population Consistent Budget Division via Simple Payment Schemes," Papers 2412.02435, arXiv.org, revised Jul 2025.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2607.06282. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.