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Best-Response dynamics in two-person random games with correlated payoffs

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Listed:
  • Hlafo Alfie Mimun
  • Matteo Quattropani
  • Marco Scarsini

Abstract

We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any action profile, player B's payoff coincides with player A's payoff with probability p and is i.i.d. from the same uniform distribution with probability 1-p. This model interpolates the model of i.i.d. random payoff used in most of the literature and the model of random potential games. First we study the number of pure Nash equilibria in the above class of games. Then we show that, for any positive p, asymptotically in the number of available actions, best response dynamics reaches a pure Nash equilibrium with high probability.

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  • Hlafo Alfie Mimun & Matteo Quattropani & Marco Scarsini, 2022. "Best-Response dynamics in two-person random games with correlated payoffs," Papers 2209.12967, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2209.12967
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    References listed on IDEAS

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    1. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, vol. 33(2), pages 274-293, November.
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    3. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2021. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," Papers 2101.04222, arXiv.org, revised Nov 2022.
    4. Samuel C. Wiese & Torsten Heinrich, 2022. "The Frequency of Convergent Games under Best-Response Dynamics," Dynamic Games and Applications, Springer, vol. 12(2), pages 689-700, June.
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    8. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
    9. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
    10. Noga Alon & Kirill Rudov & Leeat Yariv, 2021. "Dominance Solvability in Random Games," Papers 2105.10743, arXiv.org.
    11. Pangallo, Marco & Heinrich, Torsten & Jang, Yoojin & Scott, Alex & Tarbush, Bassel & Wiese, Samuel & Mungo, Luca, 2021. "Best-Response Dynamics, Playing Sequences, And Convergence To Equilibrium In Random Games," INET Oxford Working Papers 2021-23, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    12. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2023. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 703-735, September.
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    Cited by:

    1. Andrea Collevecchio & Hlafo Alfie Mimun & Matteo Quattropani & Marco Scarsini, 2024. "Basins of Attraction in Two-Player Random Ordinal Potential Games," Papers 2407.05460, arXiv.org.
    2. Andrea Collevecchio & Tuan-Minh Nguyen & Ziwen Zhong, 2024. "Finding pure Nash equilibria in large random games," Papers 2406.09732, arXiv.org, revised Aug 2024.

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