No Cover Image

Journal article 752 views 104 downloads

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

  • 48674.pdf

    PDF | Version of Record

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

    Download (522.79KB)

Check full text

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...

Full description

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
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2019-02-04T14:04:27Z
last_indexed 2023-01-11T14:24:25Z
id cronfa48674
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2022-12-05T12:44:46.1174298</datestamp><bib-version>v2</bib-version><id>48674</id><entry>2019-02-04</entry><title>A Semi-Potential for Finite and Infinite Games in Extensive Form</title><swanseaauthors><author><sid>17a56a78ec04e7fc47b7fe18394d7245</sid><ORCID>0000-0002-0173-3295</ORCID><firstname>Arno</firstname><surname>Pauly</surname><name>Arno Pauly</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2019-02-04</date><deptcode>SCS</deptcode><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 &#x394;02-sets.</abstract><type>Journal Article</type><journal>Dynamic Games and Applications</journal><volume>10</volume><journalNumber>1</journalNumber><paginationStart>120</paginationStart><paginationEnd>144</paginationEnd><publisher>Springer Science and Business Media LLC</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>2153-0785</issnPrint><issnElectronic>2153-0793</issnElectronic><keywords>Sequential games; Convergence; Belief learning; Infinite games</keywords><publishedDay>1</publishedDay><publishedMonth>3</publishedMonth><publishedYear>2020</publishedYear><publishedDate>2020-03-01</publishedDate><doi>10.1007/s13235-019-00301-7</doi><url/><notes/><college>COLLEGE NANME</college><department>Computer Science</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SCS</DepartmentCode><institution>Swansea University</institution><apcterm/><funders/><projectreference/><lastEdited>2022-12-05T12:44:46.1174298</lastEdited><Created>2019-02-04T08:49:15.5707302</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Computer Science</level></path><authors><author><firstname>St&#xE9;phane Le</firstname><surname>Roux</surname><order>1</order></author><author><firstname>Arno</firstname><surname>Pauly</surname><orcid>0000-0002-0173-3295</orcid><order>2</order></author></authors><documents><document><filename>0048674-18042019124522.pdf</filename><originalFilename>48674.pdf</originalFilename><uploaded>2019-04-18T12:45:22.2600000</uploaded><type>Output</type><contentLength>625340</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><embargoDate>2019-04-17T00:00:00.0000000</embargoDate><documentNotes>Released under the terms of a Creative Commons Attribution 4.0 International License (CC-BY).</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>http://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807>
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 SCS 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 Computer Science COLLEGE CODE SCS 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
hierarchytype
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
active_str 0
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 2020-03-01T03:59:15Z
_version_ 1763753019856388096
score 11.013776

Similar Items