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Dominance Solvability in Random Games

Author

Listed:
  • Noga Alon

    (Princeton University)

  • Kirill Rudov

    (Princeton University)

  • Leeat Yariv

    (Princeton University)

Abstract

We study the effectiveness of iterated elimination of strictly dominated actions in random two-player 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, at least when one of the players has a small action set, iterated elimination simplifies the game substantially by ruling out a sizable fraction of actions. This is no longer the case as both players’ action sets expand. With more than two players, iterated elimination becomes even less potent in altering the game players need to consider. Technically, we illustrate the usefulness of recent combinatorial methods for the analysis of general games.

Suggested Citation

  • Noga Alon & Kirill Rudov & Leeat Yariv, 2021. "Dominance Solvability in Random Games," Working Papers 2021-84, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2021-84
    as

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    File URL: http://lyariv.mycpanel.princeton.edu//papers/DominanceSolvability.pdf
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    Cited by:

    1. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    2. 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.
    3. 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.
    4. 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.
    5. 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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    More about this item

    Keywords

    Random Games; Dominance Solvability; Iterated Elimination;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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