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Super-Nash performance in games

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  • Mehmet S. Ismail
Abstract
Since the 1990s, artificial intelligence (AI) systems have achieved 'superhuman performance' in major zero-sum games, where winning has an unambiguous definition. However, most economic and social interactions are non-zero-sum, where measuring 'performance' is a non-trivial task. In this paper, I introduce a novel benchmark, super-Nash performance, and a solution concept, optimin, whereby every player maximizes their minimal payoff under unilateral profitable deviations of the others. Optimin achieves super-Nash performance in that, for every Nash equilibrium, there exists an optimin where each player not only receives but also guarantees super-Nash payoffs, even if other players deviate unilaterally and profitably from the optimin. Further, optimin generalizes and unifies several key results across domains: it coincides with (i) the maximin strategies in zero-sum games, and (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty; additionally, optimin generalizes (iii) Nash equilibrium in $n$-person constant-sum games. Finally, optimin is consistent with the direction of non-Nash deviations in games in which cooperation has been extensively studied, including the finitely repeated prisoner's dilemma, the centipede game, the traveler's dilemma, and the finitely repeated public goods game.

Suggested Citation

  • Mehmet S. Ismail, 2019. "Super-Nash performance in games," Papers 1912.00211, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:1912.00211
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    References listed on IDEAS

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    Cited by:

    1. Mehmet S. Ismail, 2022. "Exploring the Constraints on Artificial General Intelligence: A Game-Theoretic No-Go Theorem," Papers 2209.12346, arXiv.org, revised Nov 2023.
    2. Mehmet S. Ismail, 2023. "Human and Machine Intelligence in n-Person Games with Partial Knowledge: Theory and Computation," Papers 2302.13937, arXiv.org, revised Feb 2024.
    3. Mehmet S. Ismail, 2022. "Optimin achieves super-Nash performance," Papers 2210.00625, arXiv.org.

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