{"id":"https://openalex.org/W1975856502","doi":"https://doi.org/10.1137/s1064827598339086","title":"Enumeration of All Extreme Equilibria of Bimatrix Games","display_name":"Enumeration of All Extreme Equilibria of Bimatrix Games","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1975856502","doi":"https://doi.org/10.1137/s1064827598339086","mag":"1975856502"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827598339086","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827598339086","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089929904","display_name":"Charles Audet","orcid":"https://orcid.org/0000-0002-3043-5393"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Charles Audet","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038480864","display_name":"Pierre Hansen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierre Hansen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048080334","display_name":"Brigitte Jaumard","orcid":"https://orcid.org/0000-0003-3443-4918"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brigitte Jaumard","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017686425","display_name":"Gilles Savard","orcid":"https://orcid.org/0000-0002-0527-6730"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gilles Savard","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089929904"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0934,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.78786303,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"1","first_page":"323","last_page":"338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.837716817855835},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8248061537742615},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.7962751388549805},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.7185425162315369},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6503434181213379},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6339112520217896},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6186825633049011},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6020517349243164},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.47300177812576294},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4660519063472748},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4527570903301239},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41459932923316956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09298121929168701}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.837716817855835},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8248061537742615},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.7962751388549805},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7185425162315369},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6503434181213379},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6339112520217896},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6186825633049011},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6020517349243164},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.47300177812576294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4660519063472748},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4527570903301239},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41459932923316956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09298121929168701},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827598339086","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827598339086","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:publications.polymtl.ca:27663","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/27663/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1605726653","https://openalex.org/W1978865199","https://openalex.org/W1980955342","https://openalex.org/W1991287453","https://openalex.org/W1994401526","https://openalex.org/W2004329945","https://openalex.org/W2010169734","https://openalex.org/W2022537828","https://openalex.org/W2039355449","https://openalex.org/W2067050450","https://openalex.org/W2071094669","https://openalex.org/W2072777545","https://openalex.org/W2075075559","https://openalex.org/W2089649903","https://openalex.org/W2093361315","https://openalex.org/W2165132479","https://openalex.org/W2492353954","https://openalex.org/W3123286829","https://openalex.org/W3124735991","https://openalex.org/W4298314778"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W3042106073","https://openalex.org/W2112547390","https://openalex.org/W2071727445","https://openalex.org/W1990147836","https://openalex.org/W3124768822","https://openalex.org/W1543997539"],"abstract_inverted_index":{"The":[0,57,89],"set":[1],"of":[2,5,12,20,23,49,52,65,91,115,117],"equilibrium":[3],"points":[4],"a":[6],"bimatrix":[7],"game":[8],"is":[9,28,59,87],"the":[10,21,84,103,107],"union":[11],"polytopes":[13,25],"that":[14,38],"are":[15,75],"not":[16],"necessarily":[17],"disjoint.":[18],"Knowledge":[19],"vertices":[22],"these":[24],"(extreme":[26],"equilibria)":[27],"sufficient":[29],"to":[30,61,68,79],"identify":[31],"all":[32,40],"equilibria.":[33,119],"We":[34],"present":[35],"an":[36],"algorithm":[37,58],"enumerates":[39],"extreme":[41,92],"equilibria":[42,93],"by":[43],"exploiting":[44],"complementary":[45],"slackness":[46],"optimality":[47],"conditions":[48],"two":[50],"pairs":[51],"parameterized":[53],"linear":[54],"programming":[55],"problems.":[56],"applied":[60],"randomly":[62],"generated":[63],"problems":[64],"size":[66,98],"up":[67,78],"29":[69,71],"\u00d7":[70,81],"when":[72,83],"both":[73],"dimensions":[74],"equal,":[76],"and":[77],"700":[80],"5":[82],"second":[85],"dimension":[86],"fixed.":[88],"number":[90],"grows":[94],"exponentially":[95],"with":[96],"problem":[97],"but":[99],"remains":[100],"moderate":[101],"for":[102,112],"instances":[104],"considered.":[105],"Therefore,":[106],"results":[108],"could":[109],"be":[110],"useful":[111],"further":[113],"study":[114],"refinements":[116],"Nash":[118]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}