No Cover Image

Journal article 214 views 31 downloads

A Semi-Potential for Finite and Infinite Games in Extensive Form / Stéphane Le Roux; Arno Pauly

Dynamic Games and Applications

Swansea University Author: Arno, Pauly

  • 48674.pdf

    PDF | Version of Record

    Released under the terms of a Creative Commons Attribution 4.0 International License (CC-BY).

    Download (522.79KB)

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...

Full description

Published in: Dynamic Games and Applications
ISSN: 2153-0785 2153-0793
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa48674
Tags: Add Tag
No Tags, Be the first to tag this record!
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.