Every normal-form game has a Pareto-optimal nonmyopic equilibrium

Steven J. Brams, Mehmet S. Ismail

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)349-362
    Number of pages14
    JournalTheory and Decision
    Issue number2
    StatePublished - Mar 2022


    • Cooperation
    • Dynamic analysis of games
    • Farsightedness
    • Game theory
    • Nonmyopic equilibrium

    ASJC Scopus subject areas

    • General Decision Sciences
    • Developmental and Educational Psychology
    • Arts and Humanities (miscellaneous)
    • General Economics, Econometrics and Finance
    • Applied Psychology
    • Computer Science Applications
    • General Social Sciences


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