On Completely Mixed Stochastic Games

In this paper, we consider a two-person finite state stochastic games with finite number of pure actions for both players in all the states. In particular, for a large number of results we also consider one-player controlled transition probability and show that if all the optimal strategies of the u...

Full description

Saved in:
Bibliographic Details
Published in:Operations Research Forum 2022-12, Vol.3 (4), p.57, Article 57
Main Authors: Das, Purba, Parthasarathy, T., Ravindran, G.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Business and Management
Equilibrium
Game theory
Games
Math Applications in Computer Science
Mathematical analysis
Mathematical and Computational Engineering
Matrices (mathematics)
Operations Research/Decision Theory
Optimization
Original Research
Probability
Transition probabilities
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c286y-9dc55fd7b0d9768802472061dd3cda81379f02d69680fda5506dbe528dad80c53
container_end_page
container_issue 4
container_start_page 57
container_title Operations Research Forum
container_volume 3
creator Das, Purba
Parthasarathy, T.
Ravindran, G.
description In this paper, we consider a two-person finite state stochastic games with finite number of pure actions for both players in all the states. In particular, for a large number of results we also consider one-player controlled transition probability and show that if all the optimal strategies of the undiscounted stochastic game are completely mixed then for β sufficiently close to 1; all the optimal strategies of β -discounted stochastic games are also completely mixed. A counterexample is provided to show that the converse is not true. Further, for single-player controlled completely mixed stochastic games if the individual payoff matrices are symmetric in each state, then we show that the individual matrix games are also completely mixed. For the non-zerosum single-player controlled stochastic game under some non-singularity conditions, we show that if the undiscounted game is completely mixed, then the Nash equilibrium is unique. For non-zerosum β -discounted stochastic games when Nash equilibrium exists, we provide equalizer rules for corresponding value of the game.
doi_str_mv 10.1007/s43069-022-00150-y
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2932423029</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2932423029</sourcerecordid><originalsourceid>FETCH-LOGICAL-c286y-9dc55fd7b0d9768802472061dd3cda81379f02d69680fda5506dbe528dad80c53</originalsourceid><addsrcrecordid>eNp9kE1LxDAURYMoONT5A64Kuo2-vjRfSyk6I4zMQl2HNEm1MjMdkw7Yf2-1gq5c3be45z44hJwXcFUAyOtUMhCaAiIFKDjQ4YjMUAikyLk4_nOfknlKbQ1lKZUuGZuRy_Uur7rtfhP6sBnyh_Yj-Pyx79yrTX3r8oXdhnRGThq7SWH-kxl5vrt9qpZ0tV7cVzcr6lCJgWrvOG-8rMFrKZQCLCWCKLxnzltVMKkbQC-0UNB4yzkIXweOyluvwHGWkYtpdx-790NIvXnrDnE3vjSoGZbIYMyM4NRysUsphsbsY7u1cTAFmC8hZhJiRiHmW4gZRohNUBrLu5cQf6f_oT4BK6dhiw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2932423029</pqid></control><display><type>article</type><title>On Completely Mixed Stochastic Games</title><source>Springer Nature</source><source>Alma/SFX Local Collection</source><creator>Das, Purba ; Parthasarathy, T. ; Ravindran, G.</creator><creatorcontrib>Das, Purba ; Parthasarathy, T. ; Ravindran, G.</creatorcontrib><description>In this paper, we consider a two-person finite state stochastic games with finite number of pure actions for both players in all the states. In particular, for a large number of results we also consider one-player controlled transition probability and show that if all the optimal strategies of the undiscounted stochastic game are completely mixed then for β sufficiently close to 1; all the optimal strategies of β -discounted stochastic games are also completely mixed. A counterexample is provided to show that the converse is not true. Further, for single-player controlled completely mixed stochastic games if the individual payoff matrices are symmetric in each state, then we show that the individual matrix games are also completely mixed. For the non-zerosum single-player controlled stochastic game under some non-singularity conditions, we show that if the undiscounted game is completely mixed, then the Nash equilibrium is unique. For non-zerosum β -discounted stochastic games when Nash equilibrium exists, we provide equalizer rules for corresponding value of the game.</description><identifier>ISSN: 2662-2556</identifier><identifier>EISSN: 2662-2556</identifier><identifier>DOI: 10.1007/s43069-022-00150-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Business and Management ; Equilibrium ; Game theory ; Games ; Math Applications in Computer Science ; Mathematical analysis ; Mathematical and Computational Engineering ; Matrices (mathematics) ; Operations Research/Decision Theory ; Optimization ; Original Research ; Probability ; Transition probabilities</subject><ispartof>Operations Research Forum, 2022-12, Vol.3 (4), p.57, Article 57</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c286y-9dc55fd7b0d9768802472061dd3cda81379f02d69680fda5506dbe528dad80c53</cites><orcidid>0000-0002-2692-969X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Das, Purba</creatorcontrib><creatorcontrib>Parthasarathy, T.</creatorcontrib><creatorcontrib>Ravindran, G.</creatorcontrib><title>On Completely Mixed Stochastic Games</title><title>Operations Research Forum</title><addtitle>Oper. Res. Forum</addtitle><description>In this paper, we consider a two-person finite state stochastic games with finite number of pure actions for both players in all the states. In particular, for a large number of results we also consider one-player controlled transition probability and show that if all the optimal strategies of the undiscounted stochastic game are completely mixed then for β sufficiently close to 1; all the optimal strategies of β -discounted stochastic games are also completely mixed. A counterexample is provided to show that the converse is not true. Further, for single-player controlled completely mixed stochastic games if the individual payoff matrices are symmetric in each state, then we show that the individual matrix games are also completely mixed. For the non-zerosum single-player controlled stochastic game under some non-singularity conditions, we show that if the undiscounted game is completely mixed, then the Nash equilibrium is unique. For non-zerosum β -discounted stochastic games when Nash equilibrium exists, we provide equalizer rules for corresponding value of the game.</description><subject>Applications of Mathematics</subject><subject>Business and Management</subject><subject>Equilibrium</subject><subject>Game theory</subject><subject>Games</subject><subject>Math Applications in Computer Science</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Matrices (mathematics)</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Original Research</subject><subject>Probability</subject><subject>Transition probabilities</subject><issn>2662-2556</issn><issn>2662-2556</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAURYMoONT5A64Kuo2-vjRfSyk6I4zMQl2HNEm1MjMdkw7Yf2-1gq5c3be45z44hJwXcFUAyOtUMhCaAiIFKDjQ4YjMUAikyLk4_nOfknlKbQ1lKZUuGZuRy_Uur7rtfhP6sBnyh_Yj-Pyx79yrTX3r8oXdhnRGThq7SWH-kxl5vrt9qpZ0tV7cVzcr6lCJgWrvOG-8rMFrKZQCLCWCKLxnzltVMKkbQC-0UNB4yzkIXweOyluvwHGWkYtpdx-790NIvXnrDnE3vjSoGZbIYMyM4NRysUsphsbsY7u1cTAFmC8hZhJiRiHmW4gZRohNUBrLu5cQf6f_oT4BK6dhiw</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Das, Purba</creator><creator>Parthasarathy, T.</creator><creator>Ravindran, G.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0002-2692-969X</orcidid></search><sort><creationdate>20221201</creationdate><title>On Completely Mixed Stochastic Games</title><author>Das, Purba ; Parthasarathy, T. ; Ravindran, G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c286y-9dc55fd7b0d9768802472061dd3cda81379f02d69680fda5506dbe528dad80c53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Business and Management</topic><topic>Equilibrium</topic><topic>Game theory</topic><topic>Games</topic><topic>Math Applications in Computer Science</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Matrices (mathematics)</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Original Research</topic><topic>Probability</topic><topic>Transition probabilities</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Das, Purba</creatorcontrib><creatorcontrib>Parthasarathy, T.</creatorcontrib><creatorcontrib>Ravindran, G.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer science database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Operations Research Forum</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Das, Purba</au><au>Parthasarathy, T.</au><au>Ravindran, G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Completely Mixed Stochastic Games</atitle><jtitle>Operations Research Forum</jtitle><stitle>Oper. Res. Forum</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>3</volume><issue>4</issue><spage>57</spage><pages>57-</pages><artnum>57</artnum><issn>2662-2556</issn><eissn>2662-2556</eissn><abstract>In this paper, we consider a two-person finite state stochastic games with finite number of pure actions for both players in all the states. In particular, for a large number of results we also consider one-player controlled transition probability and show that if all the optimal strategies of the undiscounted stochastic game are completely mixed then for β sufficiently close to 1; all the optimal strategies of β -discounted stochastic games are also completely mixed. A counterexample is provided to show that the converse is not true. Further, for single-player controlled completely mixed stochastic games if the individual payoff matrices are symmetric in each state, then we show that the individual matrix games are also completely mixed. For the non-zerosum single-player controlled stochastic game under some non-singularity conditions, we show that if the undiscounted game is completely mixed, then the Nash equilibrium is unique. For non-zerosum β -discounted stochastic games when Nash equilibrium exists, we provide equalizer rules for corresponding value of the game.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s43069-022-00150-y</doi><orcidid>https://orcid.org/0000-0002-2692-969X</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2662-2556
ispartof Operations Research Forum, 2022-12, Vol.3 (4), p.57, Article 57
issn 2662-2556
2662-2556
language eng
recordid cdi_proquest_journals_2932423029
source Springer Nature; Alma/SFX Local Collection
subjects Applications of Mathematics
Business and Management
Equilibrium
Game theory
Games
Math Applications in Computer Science
Mathematical analysis
Mathematical and Computational Engineering
Matrices (mathematics)
Operations Research/Decision Theory
Optimization
Original Research
Probability
Transition probabilities
title On Completely Mixed Stochastic Games
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T14%3A48%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Completely%20Mixed%20Stochastic%20Games&rft.jtitle=Operations%20Research%20Forum&rft.au=Das,%20Purba&rft.date=2022-12-01&rft.volume=3&rft.issue=4&rft.spage=57&rft.pages=57-&rft.artnum=57&rft.issn=2662-2556&rft.eissn=2662-2556&rft_id=info:doi/10.1007/s43069-022-00150-y&rft_dat=%3Cproquest_cross%3E2932423029%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c286y-9dc55fd7b0d9768802472061dd3cda81379f02d69680fda5506dbe528dad80c53%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2932423029&rft_id=info:pmid/&rfr_iscdi=true