Generalizing Better Response Paths and Weakly Acyclic Games

Bora Yongacoglu, G\"urdal Arslan, Lacra Pavel and Serdar Y\"uksel

Papers from arXiv.org

Abstract: Weakly acyclic games generalize potential games and are fundamental to the study of game theoretic control. In this paper, we present a generalization of weakly acyclic games, and we observe its importance in multi-agent learning when agents employ experimental strategy updates in periods where they fail to best respond. While weak acyclicity is defined in terms of path connectivity properties of a game's better response graph, our generalization is defined using a generalized better response graph. We provide sufficient conditions for this notion of generalized weak acyclicity in both two-player games and $n$-player games. To demonstrate that our generalization is not trivial, we provide examples of games admitting a pure Nash equilibrium that are not generalized weakly acyclic. The generalization presented in this work is closely related to the recent theory of satisficing paths, and the counterexamples presented here constitute the first negative results in that theory.

Date: 2024-03
New Economics Papers: this item is included in nep-gth, nep-inv and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2403.18086 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2403.18086

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().