Journal article 798 views 111 downloads
A Semi-Potential for Finite and Infinite Games in Extensive Form
Dynamic Games and Applications, Volume: 10, Issue: 1, Pages: 120 - 144
Swansea University Author:
Arno Pauly
-
PDF | Version of Record
Released under the terms of a Creative Commons Attribution 4.0 International License (CC-BY).
Download (522.79KB)
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...
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 Δ02-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>Stéphane 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 |
11.021648 |