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A Semi-Potential for Finite and Infinite Games in Extensive Form

Stéphane Le Roux, Arno Pauly Orcid Logo

Dynamic Games and Applications, Volume: 10, Issue: 1, Pages: 120 - 144

Swansea University Author: Arno Pauly Orcid Logo

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DOI (Published version): 10.1007/s13235-019-00301-7

Abstract

We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction of better-response dynamics will converge to a Nash e...

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Published in: Dynamic Games and Applications
ISSN: 2153-0785 2153-0793
Published: Springer Science and Business Media LLC 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa48674
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Abstract: We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction of better-response dynamics will converge to a Nash equilibrium in quadratic (finite) time. Convergence happens on a per-player basis, and even in the presence of players with cyclic preferences, the players with acyclic preferences will stabilize. Thus, we obtain a candidate notion for rationality in the presence of irrational agents. Moreover, the restriction of convertibility can be justified by a conservative updating of beliefs about the other players strategies.For infinite games in extensive form we can retain convergence to a Nash equilibrium (in some sense), if the preferences are given by continuous payoff functions; or obtain a transfinite convergence if the outcome sets of the game are Δ02-sets.
Keywords: Sequential games; Convergence; Belief learning; Infinite games
College: Faculty of Science and Engineering
Issue: 1
Start Page: 120
End Page: 144

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