{"id":"https://openalex.org/W2029825080","doi":"https://doi.org/10.1145/1993636.1993664","title":"Rank-1 bimatrix games","display_name":"Rank-1 bimatrix games","publication_year":2011,"publication_date":"2011-06-06","ids":{"openalex":"https://openalex.org/W2029825080","doi":"https://doi.org/10.1145/1993636.1993664","mag":"2029825080"},"language":"en","primary_location":{"id":"doi:10.1145/1993636.1993664","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1993636.1993664","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993664","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-third annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993664","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025486660","display_name":"Bharat Adsul","orcid":"https://orcid.org/0000-0002-0292-6670"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bharat Adsul","raw_affiliation_strings":["Indian Institute of Technology, Bombay, Mumbai, India","Indian Institute of Technology-Bombay, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology-Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077432617","display_name":"Jugal Garg","orcid":"https://orcid.org/0000-0001-6439-7308"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jugal Garg","raw_affiliation_strings":["Indian Institute of Technology, Bombay, Mumbai, India","Indian Institute of Technology-Bombay, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology-Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070267732","display_name":"Ruta Mehta","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ruta Mehta","raw_affiliation_strings":["Indian Institute of Technology, Bombay, Mumbai, India","Indian Institute of Technology-Bombay, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology-Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051477034","display_name":"Milind Sohoni","orcid":"https://orcid.org/0000-0003-0510-7109"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Milind Sohoni","raw_affiliation_strings":["Indian Institute of Technology, Bombay, Mumbai, India","Indian Institute of Technology-Bombay, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology-Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":7.1931,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.97473642,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"195","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9932000041007996,"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/T10646","display_name":"Experimental Behavioral Economics Studies","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7394320964813232},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7258279919624329},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7172724604606628},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5145046710968018},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4618043303489685},{"id":"https://openalex.org/keywords/homeomorphism","display_name":"Homeomorphism (graph theory)","score":0.42690759897232056},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4101604223251343},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37447410821914673},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.31561899185180664}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7394320964813232},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7258279919624329},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7172724604606628},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5145046710968018},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4618043303489685},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.42690759897232056},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4101604223251343},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37447410821914673},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.31561899185180664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1993636.1993664","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1993636.1993664","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993664","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-third annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/1993636.1993664","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1993636.1993664","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993664","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-third annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2029825080.pdf","grobid_xml":"https://content.openalex.org/works/W2029825080.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W159399628","https://openalex.org/W190441398","https://openalex.org/W582068683","https://openalex.org/W1511111380","https://openalex.org/W1597710076","https://openalex.org/W2014217859","https://openalex.org/W2026177035","https://openalex.org/W2035681301","https://openalex.org/W2062556595","https://openalex.org/W2083639782","https://openalex.org/W2088278769","https://openalex.org/W2089649903","https://openalex.org/W2108614294","https://openalex.org/W2112996611","https://openalex.org/W2125537511","https://openalex.org/W2127470768","https://openalex.org/W2130937741","https://openalex.org/W2131967794","https://openalex.org/W2154374772","https://openalex.org/W2169359757","https://openalex.org/W2266755976","https://openalex.org/W2330024298","https://openalex.org/W3121616661","https://openalex.org/W4234761190","https://openalex.org/W6606447652","https://openalex.org/W6635535278","https://openalex.org/W6654164968","https://openalex.org/W6678861937"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W2077009862","https://openalex.org/W2364594919","https://openalex.org/W3083563261","https://openalex.org/W4312141693","https://openalex.org/W1536009559","https://openalex.org/W1969185016","https://openalex.org/W2103821767","https://openalex.org/W2111030377","https://openalex.org/W2037619003"],"abstract_inverted_index":{"Given":[0],"a":[1,11,49,68,78,84,93,134,141,149],"rank-1":[2,17,50,79,130],"bimatrix":[3,51,98,124],"game":[4,18,80,137],"(A,B),":[5],"i.e.,":[6],"where":[7],"rank(A+B)=1,":[8],"we":[9,35,66,127],"construct":[10],"suitable":[12],"linear":[13,161],"subspace":[14,24],"of":[15,48,77,96,106,116],"the":[16,37,74,112,120,129,155,166],"space":[19],"and":[20,61,81,114,119,139,154,162],"show":[21,82],"that":[22,83],"this":[23,33],"is":[25],"homeomorphic":[26],"to":[27,71,133],"its":[28],"Nash":[29,46,75,94,117],"equilibrium":[30,47,95],"correspondence.":[31],"Using":[32],"homeomorphism,":[34],"give":[36,67,140],"first":[38],"polynomial":[39],"time":[40],"algorithm":[41,70],"for":[42,91,123,147],"computing":[43],"an":[44,55],"exact":[45],"game.":[52,99,151],"This":[53],"settles":[54],"open":[56],"question":[57],"posed":[58],"by":[59],"Kannan":[60],"Theobald":[62],"(SODA'07).":[63],"In":[64],"addition,":[65],"novel":[69],"enumerate":[72],"all":[73],"equilibria":[76],"similar":[85],"technique":[86],"may":[87],"also":[88,102],"be":[89],"applied":[90],"finding":[92],"any":[97],"Our":[100],"approach":[101],"provides":[103],"new":[104],"proofs":[105],"important":[107],"classical":[108,167],"results":[109],"such":[110],"as":[111],"existence":[113],"oddness":[115],"equilibria,":[118],"index":[121],"theorem":[122],"games.":[125],"Further,":[126],"extend":[128],"homeomorphism":[131,153],"result":[132],"fixed":[135,142,156],"rank":[136],"space,":[138],"point":[143,157],"formulation":[144,158],"on":[145],"[0,1]k":[146],"solving":[148],"rank-k":[150],"The":[152],"are":[159],"piece-wise":[160],"considerably":[163],"simpler":[164],"than":[165],"constructions.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}