{"id":"https://openalex.org/W2008288183","doi":"https://doi.org/10.1145/2229012.2229081","title":"Computing a proper equilibrium of a bimatrix game","display_name":"Computing a proper equilibrium of a bimatrix game","publication_year":2012,"publication_date":"2012-06-04","ids":{"openalex":"https://openalex.org/W2008288183","doi":"https://doi.org/10.1145/2229012.2229081","mag":"2008288183"},"language":"en","primary_location":{"id":"doi:10.1145/2229012.2229081","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229012.2229081","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 13th ACM Conference on Electronic Commerce","raw_type":"proceedings-article"},"type":"conference-paper","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/A5066030240","display_name":"Troels Bjerre S\u00f8rensen","orcid":null},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Troels Bjerre S\u00f8rensen","raw_affiliation_strings":["University of Warwick, Coventry, United Kingdom","University of Warwick Coventry , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick, Coventry, United Kingdom","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"University of Warwick Coventry , United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066030240"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":2.273,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.88561798,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":null,"first_page":"916","last_page":"928"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9991999864578247,"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":0.9991999864578247,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9786999821662903,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7761560678482056},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5278627276420593},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.469809353351593},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4676819443702698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44977471232414246},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4492890536785126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44807082414627075},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3559004068374634},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3094062805175781},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07517057657241821}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7761560678482056},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5278627276420593},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.469809353351593},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4676819443702698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44977471232414246},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4492890536785126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44807082414627075},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3559004068374634},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3094062805175781},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07517057657241821},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2229012.2229081","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229012.2229081","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 13th ACM Conference on Electronic Commerce","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.708.3879","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.708.3879","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.itu.dk/%7Etrbj/papers/biproper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5561909342","display_name":null,"funder_award_id":"EP/G069034/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W189162697","https://openalex.org/W1515545478","https://openalex.org/W1522839481","https://openalex.org/W1549584663","https://openalex.org/W1966558378","https://openalex.org/W1971258090","https://openalex.org/W1986996840","https://openalex.org/W1998191601","https://openalex.org/W2000151369","https://openalex.org/W2006794473","https://openalex.org/W2015813577","https://openalex.org/W2026177035","https://openalex.org/W2033040247","https://openalex.org/W2064657832","https://openalex.org/W2076458424","https://openalex.org/W2077578341","https://openalex.org/W2079557194","https://openalex.org/W2086386133","https://openalex.org/W2092818757","https://openalex.org/W2107815843","https://openalex.org/W2125363721","https://openalex.org/W2130937741","https://openalex.org/W2140790422","https://openalex.org/W2151192928","https://openalex.org/W2152122625","https://openalex.org/W2165132479","https://openalex.org/W2498386205","https://openalex.org/W2611147814","https://openalex.org/W2911985665","https://openalex.org/W4248083116","https://openalex.org/W6723532536"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2625725254","https://openalex.org/W1774334694"],"abstract_inverted_index":{"We":[0],"provide":[1],"the":[2,56,77,80],"first":[3],"pivoting-type":[4],"algorithm":[5,22,50],"that":[6,36,62],"computes":[7,52],"an":[8,64],"exact":[9],"proper":[10,42],"equilibrium":[11,66],"of":[12,30,41,58,76,79],"a":[13,25,38,53,59,96],"bimatrix":[14,45],"game.":[15],"This":[16,33],"is":[17,47,63],"achieved":[18],"by":[19],"using":[20,103],"Lemke's":[21],"to":[23,89],"solve":[24],"linear":[26,104],"complementarity":[27],"problem":[28],"(LCP)":[29],"polynomial":[31,101],"size.":[32],"also":[34,51],"proves":[35],"computing":[37,95],"simple":[39],"refinement":[40],"equilibria":[43],"for":[44,67],"game":[46],"PPAD-complete.":[48],"The":[49,83],"witness":[54],"in":[55,100],"form":[57],"parameterized":[60,97],"strategy":[61,99],"epsilon-proper":[65,98],"any":[68],"given":[69],"sufficiently":[70],"small":[71],"epsilon,":[72],"allowing":[73],"polynomial-time":[74],"verification":[75],"properties":[78],"refined":[81],"equilibrium.":[82],"same":[84],"technique":[85],"can":[86],"be":[87],"applied":[88],"matrix":[90],"games":[91],"(two-player":[92],"zero-sum),":[93],"thereby":[94],"time":[102],"programming.":[105]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
