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Limit-of-All-Finite equilibria in infinite normal-form games

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  • Dilmé, Francesc

Abstract

This paper introduces and examines limit-of-all-finite (LOAF) equilibria, defined as strategy profiles obtained as limits of ε-equilibria along all discretizations of an infinite game. We establish conditions under which any limit of ε-equilibria along one discretization is a LOAF equilibrium, and we show that these conditions are satisfied in many common infinite games, such as Bertrand competition, wars of attrition, and standard auctions. We also identify conditions that ensure that the sets of LOAF and Nash equilibria coincide, and we discuss how our findings relate to known results on limit-of-finite perfect equilibria, approximate equilibria, and solutions for sharing rules.

Suggested Citation

  • Dilmé, Francesc, 2026. "Limit-of-All-Finite equilibria in infinite normal-form games," Journal of Economic Theory, Elsevier, vol. 233(C).
    • Handle: RePEc:eee:jetheo:v:233:y:2026:i:c:s0022053126000256
    DOI: 10.1016/j.jet.2026.106161
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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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