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A Sufficient Condition for Weakly Acyclic games with Applications

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  • zhao, guo
  • Chai, Yingming

Abstract

The class of weakly acyclic games captures many practical application domains, and is particularly relevant for multi-agent distributed control problems. However, reliably checking weak acyclicity is extremely computationally intractable (PSPACE-complete) in the worst case. The present paper identifies sufficient conditions for weak acyclicity by means of the transitive closure of individual conditional preference, which can be constructed in terms of better-reply improvement paths. This pure-ordinal approach leads to a novel connection between weak acyclic games and better-reply secure games. Specifically, a better-reply secure game is weakly acyclic if the better reply dynamics does not possess a dense orbit (in addition to the quasi-concavity of individual preferences as well as the usual convexity and compactness assumptions on strategy sets). These results give a partial answer to an open problem of finding applicable and tractable conditions for weak acyclicity, posed by Fabrikant, Jaggard, and Schapira in 2013.

Suggested Citation

  • zhao, guo & Chai, Yingming, 2024. "A Sufficient Condition for Weakly Acyclic games with Applications," MPRA Paper 120789, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:120789
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    File URL: https://mpra.ub.uni-muenchen.de/120789/1/MPRA_paper_120789.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    pure-strategy Nash equilibrium; weakly acyclicity; better reply dynamics; better-reply security;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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