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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa48674
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last_indexed 2023-01-11T14:24:25Z
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spelling 2022-12-05T12:44:46.1174298 v2 48674 2019-02-04 A Semi-Potential for Finite and Infinite Games in Extensive Form 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2019-02-04 MACS 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. Journal Article Dynamic Games and Applications 10 1 120 144 Springer Science and Business Media LLC 2153-0785 2153-0793 Sequential games; Convergence; Belief learning; Infinite games 1 3 2020 2020-03-01 10.1007/s13235-019-00301-7 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2022-12-05T12:44:46.1174298 2019-02-04T08:49:15.5707302 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Stéphane Le Roux 1 Arno Pauly 0000-0002-0173-3295 2 0048674-18042019124522.pdf 48674.pdf 2019-04-18T12:45:22.2600000 Output 625340 application/pdf Version of Record true 2019-04-17T00:00:00.0000000 Released under the terms of a Creative Commons Attribution 4.0 International License (CC-BY). true eng http://creativecommons.org/licenses/by/4.0/
title A Semi-Potential for Finite and Infinite Games in Extensive Form
spellingShingle A Semi-Potential for Finite and Infinite Games in Extensive Form
Arno Pauly
title_short A Semi-Potential for Finite and Infinite Games in Extensive Form
title_full A Semi-Potential for Finite and Infinite Games in Extensive Form
title_fullStr A Semi-Potential for Finite and Infinite Games in Extensive Form
title_full_unstemmed A Semi-Potential for Finite and Infinite Games in Extensive Form
title_sort A Semi-Potential for Finite and Infinite Games in Extensive Form
author_id_str_mv 17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv 17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author Arno Pauly
author2 Stéphane Le Roux
Arno Pauly
format Journal article
container_title Dynamic Games and Applications
container_volume 10
container_issue 1
container_start_page 120
publishDate 2020
institution Swansea University
issn 2153-0785
2153-0793
doi_str_mv 10.1007/s13235-019-00301-7
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
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description 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.
published_date 2020-03-01T04:56:26Z
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score 11.310851

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