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Dominance Solvability in Random Games

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  • Noga Alon
  • Kirill Rudov
  • Leeat Yariv

Abstract

We study the effectiveness of iterated elimination of strictly-dominated actions in random games. We show that dominance solvability of games is vanishingly small as the number of at least one player's actions grows. Furthermore, conditional on dominance solvability, the number of iterations required to converge to Nash equilibrium grows rapidly as action sets grow. Nonetheless, when games are highly imbalanced, iterated elimination simplifies the game substantially by ruling out a sizable fraction of actions. Technically, we illustrate the usefulness of recent combinatorial methods for the analysis of general games.

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  • Noga Alon & Kirill Rudov & Leeat Yariv, 2021. "Dominance Solvability in Random Games," Papers 2105.10743, arXiv.org.
    • Handle: RePEc:arx:papers:2105.10743
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    References listed on IDEAS

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    1. Drew Fudenberg & Annie Liang, 2019. "Predicting and Understanding Initial Play," American Economic Review, American Economic Association, vol. 109(12), pages 4112-4141, December.
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    Cited by:

    1. Mimun, Hlafo Alfie & Quattropani, Matteo & Scarsini, Marco, 2024. "Best-response dynamics in two-person random games with correlated payoffs," Games and Economic Behavior, Elsevier, vol. 145(C), pages 239-262.
    2. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    3. Andrea Collevecchio & Tuan-Minh Nguyen & Ziwen Zhong, 2024. "Finding pure Nash equilibria in large random games," Papers 2406.09732, arXiv.org, revised Aug 2024.
    4. 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.
    5. 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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