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Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem

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  • Madjid Eshaghi Gordji
  • Esmaiel Abounoori
  • Mohamadali Berahman

Abstract

We extend the concept of meta-Nash equilibrium, introduced by Eshaghi Gordji and Bagha [2026] for complete-information games, to environments with incomplete information. We define a meta-Bayesian Nash equilibrium as a profile of type-dependent mixed meta-strategies together with an environmental move such that no player type can profitably deviate and the environment cannot improve its expected payoff. For each transformed game, meta-payoffs are determined by the unique Bayesian Nash equilibrium of that game. Using Kakutani's fixed point theorem, we establish existence under finiteness assumptions on type spaces, meta-actions, and transformations, together with the assumption that each transformed game admits a unique Bayesian Nash equilibrium. Several illustrative examples, including adaptive subsidy competition, cybersecurity protocol selection, and platform rule formation, demonstrate that private information at the meta-level plays an essential role in endogenous game transformation. The framework contains both classical Bayesian games and complete-information meta-games as special cases.

Suggested Citation

  • Madjid Eshaghi Gordji & Esmaiel Abounoori & Mohamadali Berahman, 2026. "Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem," Papers 2605.16926, arXiv.org.
    • Handle: RePEc:arx:papers:2605.16926
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    3. Madjid Eshaghi Gordji & Esmaiel Abounoori & Mohamadali Berahman, 2026. "Changing the Game: Status-Quo Inertia, Institutional Design, and Equilibrium Transition," Papers 2605.09083, arXiv.org, revised Jun 2026.
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