A Sufficient Condition for Weakly Acyclic games with Applications

Guo Zhao and Yingming Chai

MPRA Paper from University Library of Munich, Germany

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.

Keywords: pure-strategy Nash equilibrium; weakly acyclicity; better reply dynamics; better-reply security (search for similar items in EconPapers)
JEL-codes: C72 D01 (search for similar items in EconPapers)
Date: 2024-04-01
New Economics Papers: this item is included in nep-gth
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