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A classification of weakly acyclic games

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  • Krzysztof Apt
  • Sunil Simon

Abstract

Weakly acyclic games form a natural generalization of the class of games that have the finite improvement property (FIP). In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler introduced in Simon and Apt (Choosing products in social networks, 2012 ). We also show that finite games that can be solved by the iterated elimination of never best response strategies are weakly acyclic. Finally, we explain how the schedulers allow us to improve the bounds on finding a Nash equilibrium in a weakly acyclic game. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Krzysztof Apt & Sunil Simon, 2015. "A classification of weakly acyclic games," Theory and Decision, Springer, vol. 78(4), pages 501-524, April.
    • Handle: RePEc:kap:theord:v:78:y:2015:i:4:p:501-524
    DOI: 10.1007/s11238-014-9436-1
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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. Iimura, Takuya, 2016. "On the IENBR-solvability of two-person finite games," Economics Letters, Elsevier, vol. 146(C), pages 68-70.
    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. Arthur Dolgopolov & Cesar Martinelli, 2021. "Learning and Acyclicity in the Market Game," Working Papers 1084, George Mason University, Interdisciplinary Center for Economic Science.

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