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Every Normal-Form Game Has a Pareto-Optimal Nonmyopic Equilibrium

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  • Brams, Steven J.
  • Ismail, Mehmet S.

Abstract

It is well-known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: Every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis.

Suggested Citation

  • Brams, Steven J. & Ismail, Mehmet S., 2021. "Every Normal-Form Game Has a Pareto-Optimal Nonmyopic Equilibrium," MPRA Paper 106718, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:106718
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    References listed on IDEAS

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    1. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
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    7. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
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    2. Giacomo Bonanno, 2022. "Rational Play in Extensive-Form Games," Games, MDPI, vol. 13(6), pages 1-20, October.
    3. Shacked Avrashi & Lior Givon & Ilan Fischer, 2025. "Integrating Strategic Properties with Social Perspectives: A Bipartite Classification of Two-by-Two Games," Games, MDPI, vol. 16(6), pages 1-22, October.

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • F50 - International Economics - - International Relations, National Security, and International Political Economy - - - General

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