Stochastic shortest path games

We consider dynamic, two-player, zero-sum games where the "minimizing" player seeks to drive an underlying finite-state dynamic system to a special terminal state along a least expected cost path. The "maximizer" seeks to interfere with the minimizer's progress so as to maxi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on control and optimization 1999, Vol.37 (3), p.804-824
Hauptverfasser: PATEK, S. D, BERTSEKAS, D. P
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 824
container_issue 3
container_start_page 804
container_title SIAM journal on control and optimization
container_volume 37
creator PATEK, S. D
BERTSEKAS, D. P
description We consider dynamic, two-player, zero-sum games where the "minimizing" player seeks to drive an underlying finite-state dynamic system to a special terminal state along a least expected cost path. The "maximizer" seeks to interfere with the minimizer's progress so as to maximize the expected total cost. We consider, for the first time, undiscounted finite-state problems, with compact action spaces, and transition costs that are not strictly positive. We admit that there are policies for the minimizer which permit the maximizer to prolong the game indefinitely. Under assumptions which generalize deterministic shortest path problems, we establish (i) the existence of a real-valued equilibrium cost vector achievable with stationary policies for the opposing players and (ii) the convergence of value iteration and policy iteration to the unique solution of Bellmans equation.
doi_str_mv 10.1137/S0363012996299557
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_925834205</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2600554431</sourcerecordid><originalsourceid>FETCH-LOGICAL-c342t-645577f28206304cac0b8d1fdc32de755672643815d1bc330e7e5662d0a78c6a3</originalsourceid><addsrcrecordid>eNplUMtKw0AUHUTBWP0ANxLEbfTeeWcpxRcUXFTXw3QyMSltE2emC__eCS24cHG5i_PkEHKNcI_I1MMSmGSAtK5lPiHUCSkQalEpZPqUFBNcTfg5uYhxDYCcIy_IzTINrrMx9a6M3RCSj6kcberKL7v18ZKctXYT_dXxz8jn89PH_LVavL-8zR8XlWOcpkrynKhaqinkFtxZByvdYNs4RhuvhJCKSs40igZXjjHwygspaQNWaSctm5Hbg-8Yhu997mDWwz7scqSpqdA5BEQm4YHkwhBj8K0ZQ7-14ccgmGkF82-FrLk7Gtvo7KYNduf6-CfUDIUC9gujFlkb</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>925834205</pqid></control><display><type>article</type><title>Stochastic shortest path games</title><source>SIAM Journals Online</source><source>Business Source Complete</source><creator>PATEK, S. D ; BERTSEKAS, D. P</creator><creatorcontrib>PATEK, S. D ; BERTSEKAS, D. P</creatorcontrib><description>We consider dynamic, two-player, zero-sum games where the "minimizing" player seeks to drive an underlying finite-state dynamic system to a special terminal state along a least expected cost path. The "maximizer" seeks to interfere with the minimizer's progress so as to maximize the expected total cost. We consider, for the first time, undiscounted finite-state problems, with compact action spaces, and transition costs that are not strictly positive. We admit that there are policies for the minimizer which permit the maximizer to prolong the game indefinitely. Under assumptions which generalize deterministic shortest path problems, we establish (i) the existence of a real-valued equilibrium cost vector achievable with stationary policies for the opposing players and (ii) the convergence of value iteration and policy iteration to the unique solution of Bellmans equation.</description><identifier>ISSN: 0363-0129</identifier><identifier>EISSN: 1095-7138</identifier><identifier>DOI: 10.1137/S0363012996299557</identifier><identifier>CODEN: SJCODC</identifier><language>eng</language><publisher>Philadelphia, PA: Society for Industrial and Applied Mathematics</publisher><subject>Applied mathematics ; Applied sciences ; Costs ; Equilibrium ; Exact sciences and technology ; Game theory ; Games ; Operational research and scientific management ; Operational research. Management science ; Probability ; Scholarships &amp; fellowships</subject><ispartof>SIAM journal on control and optimization, 1999, Vol.37 (3), p.804-824</ispartof><rights>1999 INIST-CNRS</rights><rights>[Copyright] © 1999 Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c342t-645577f28206304cac0b8d1fdc32de755672643815d1bc330e7e5662d0a78c6a3</citedby><cites>FETCH-LOGICAL-c342t-645577f28206304cac0b8d1fdc32de755672643815d1bc330e7e5662d0a78c6a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,3182,4022,27922,27923,27924</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=1831570$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>PATEK, S. D</creatorcontrib><creatorcontrib>BERTSEKAS, D. P</creatorcontrib><title>Stochastic shortest path games</title><title>SIAM journal on control and optimization</title><description>We consider dynamic, two-player, zero-sum games where the "minimizing" player seeks to drive an underlying finite-state dynamic system to a special terminal state along a least expected cost path. The "maximizer" seeks to interfere with the minimizer's progress so as to maximize the expected total cost. We consider, for the first time, undiscounted finite-state problems, with compact action spaces, and transition costs that are not strictly positive. We admit that there are policies for the minimizer which permit the maximizer to prolong the game indefinitely. Under assumptions which generalize deterministic shortest path problems, we establish (i) the existence of a real-valued equilibrium cost vector achievable with stationary policies for the opposing players and (ii) the convergence of value iteration and policy iteration to the unique solution of Bellmans equation.</description><subject>Applied mathematics</subject><subject>Applied sciences</subject><subject>Costs</subject><subject>Equilibrium</subject><subject>Exact sciences and technology</subject><subject>Game theory</subject><subject>Games</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Probability</subject><subject>Scholarships &amp; fellowships</subject><issn>0363-0129</issn><issn>1095-7138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNplUMtKw0AUHUTBWP0ANxLEbfTeeWcpxRcUXFTXw3QyMSltE2emC__eCS24cHG5i_PkEHKNcI_I1MMSmGSAtK5lPiHUCSkQalEpZPqUFBNcTfg5uYhxDYCcIy_IzTINrrMx9a6M3RCSj6kcberKL7v18ZKctXYT_dXxz8jn89PH_LVavL-8zR8XlWOcpkrynKhaqinkFtxZByvdYNs4RhuvhJCKSs40igZXjjHwygspaQNWaSctm5Hbg-8Yhu997mDWwz7scqSpqdA5BEQm4YHkwhBj8K0ZQ7-14ccgmGkF82-FrLk7Gtvo7KYNduf6-CfUDIUC9gujFlkb</recordid><startdate>1999</startdate><enddate>1999</enddate><creator>PATEK, S. D</creator><creator>BERTSEKAS, D. P</creator><general>Society for Industrial and Applied Mathematics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7RQ</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope><scope>U9A</scope></search><sort><creationdate>1999</creationdate><title>Stochastic shortest path games</title><author>PATEK, S. D ; BERTSEKAS, D. P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c342t-645577f28206304cac0b8d1fdc32de755672643815d1bc330e7e5662d0a78c6a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Applied mathematics</topic><topic>Applied sciences</topic><topic>Costs</topic><topic>Equilibrium</topic><topic>Exact sciences and technology</topic><topic>Game theory</topic><topic>Games</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Probability</topic><topic>Scholarships &amp; fellowships</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>PATEK, S. D</creatorcontrib><creatorcontrib>BERTSEKAS, D. P</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Career &amp; Technical Education Database</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>Agricultural &amp; Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science 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><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>SIAM journal on control and optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>PATEK, S. D</au><au>BERTSEKAS, D. P</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stochastic shortest path games</atitle><jtitle>SIAM journal on control and optimization</jtitle><date>1999</date><risdate>1999</risdate><volume>37</volume><issue>3</issue><spage>804</spage><epage>824</epage><pages>804-824</pages><issn>0363-0129</issn><eissn>1095-7138</eissn><coden>SJCODC</coden><abstract>We consider dynamic, two-player, zero-sum games where the "minimizing" player seeks to drive an underlying finite-state dynamic system to a special terminal state along a least expected cost path. The "maximizer" seeks to interfere with the minimizer's progress so as to maximize the expected total cost. We consider, for the first time, undiscounted finite-state problems, with compact action spaces, and transition costs that are not strictly positive. We admit that there are policies for the minimizer which permit the maximizer to prolong the game indefinitely. Under assumptions which generalize deterministic shortest path problems, we establish (i) the existence of a real-valued equilibrium cost vector achievable with stationary policies for the opposing players and (ii) the convergence of value iteration and policy iteration to the unique solution of Bellmans equation.</abstract><cop>Philadelphia, PA</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/S0363012996299557</doi><tpages>21</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0363-0129
ispartof SIAM journal on control and optimization, 1999, Vol.37 (3), p.804-824
issn 0363-0129
1095-7138
language eng
recordid cdi_proquest_journals_925834205
source SIAM Journals Online; Business Source Complete
subjects Applied mathematics
Applied sciences
Costs
Equilibrium
Exact sciences and technology
Game theory
Games
Operational research and scientific management
Operational research. Management science
Probability
Scholarships & fellowships
title Stochastic shortest path games
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-13T07%3A15%3A30IST&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=Stochastic%20shortest%20path%20games&rft.jtitle=SIAM%20journal%20on%20control%20and%20optimization&rft.au=PATEK,%20S.%20D&rft.date=1999&rft.volume=37&rft.issue=3&rft.spage=804&rft.epage=824&rft.pages=804-824&rft.issn=0363-0129&rft.eissn=1095-7138&rft.coden=SJCODC&rft_id=info:doi/10.1137/S0363012996299557&rft_dat=%3Cproquest_cross%3E2600554431%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=925834205&rft_id=info:pmid/&rfr_iscdi=true