{"id":"https://openalex.org/W1585643958","doi":"https://doi.org/10.1145/1132516.1132526","title":"Reducibility among equilibrium problems","display_name":"Reducibility among equilibrium problems","publication_year":2006,"publication_date":"2006-05-21","ids":{"openalex":"https://openalex.org/W1585643958","doi":"https://doi.org/10.1145/1132516.1132526","mag":"1585643958"},"language":"en","primary_location":{"id":"doi:10.1145/1132516.1132526","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-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/A5067662147","display_name":"Paul W. Goldberg","orcid":"https://orcid.org/0000-0002-5436-7890"},"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":false,"raw_author_name":"Paul W. Goldberg","raw_affiliation_strings":["University of Warwick, U.K","University of Warwick, U.K.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warwick, U.K","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"University of Warwick, U.K.#TAB#","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103200572","display_name":"Christos H. Papadimitriou","orcid":"https://orcid.org/0009-0000-7264-8015"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christos H. Papadimitriou","raw_affiliation_strings":["University of California, Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5631,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.94482866,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"61","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9994999766349792,"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/T11031","display_name":"Game Theory and Applications","score":0.9970999956130981,"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":0.9940000176429749,"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/nash-equilibrium","display_name":"Nash equilibrium","score":0.6921175122261047},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5672821998596191},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5102863311767578},{"id":"https://openalex.org/keywords/normal-form-game","display_name":"Normal-form game","score":0.4829782545566559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4751458168029785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45927128195762634},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.45388349890708923},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.40536484122276306},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.38025856018066406}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6921175122261047},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5672821998596191},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5102863311767578},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.4829782545566559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4751458168029785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45927128195762634},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45388349890708923},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.40536484122276306},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.38025856018066406},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1132516.1132526","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.163.2719","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.163.2719","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.uni-trier.de/report/2005/090/download/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.61.9632","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.9632","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.berkeley.edu/~christos/papers/nashreductions1.ps","raw_type":"text"},{"id":"mag:1585643958","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/journals/eccc/eccc12.html#TR05-090","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1576554202","https://openalex.org/W1588415355","https://openalex.org/W1972735418","https://openalex.org/W1977823909","https://openalex.org/W2010476628","https://openalex.org/W2073048734","https://openalex.org/W2140790422","https://openalex.org/W2144846366","https://openalex.org/W2145297839","https://openalex.org/W2160135758","https://openalex.org/W2169359757","https://openalex.org/W2170578451","https://openalex.org/W2292587149","https://openalex.org/W4234761190","https://openalex.org/W6601753753","https://openalex.org/W6604276451","https://openalex.org/W6637921819","https://openalex.org/W6683733446"],"related_works":["https://openalex.org/W2160135758","https://openalex.org/W324981204","https://openalex.org/W2094143906","https://openalex.org/W1584215157","https://openalex.org/W1505648921","https://openalex.org/W136875871","https://openalex.org/W1593159028","https://openalex.org/W2160745863","https://openalex.org/W1985447712","https://openalex.org/W2169359757","https://openalex.org/W2119471446","https://openalex.org/W2141154922","https://openalex.org/W3000690265","https://openalex.org/W3167752956","https://openalex.org/W1594313668","https://openalex.org/W2978686123","https://openalex.org/W3036536866","https://openalex.org/W2116445460","https://openalex.org/W831981842","https://openalex.org/W3151082510"],"abstract_inverted_index":{"We":[0,19],"address":[1],"the":[2,7,48],"fundamental":[3],"question":[4],"of":[5,10,35,50,58],"whether":[6],"Nash":[8],"equilibria":[9],"a":[11,32,52,64],"game":[12,53],"can":[13],"be":[14],"computed":[15],"in":[16],"polynomial":[17],"time.":[18],"describe":[20],"certain":[21],"efficient":[22],"reductions":[23],"between":[24],"this":[25],"problem":[26,49],"for":[27,54],"normal":[28],"form":[29],"games":[30,39],"with":[31,40],"fixed":[33,41],"number":[34,57],"players":[36],"and":[37],"graphical":[38],"degree.":[42],"Our":[43],"main":[44],"result":[45],"is":[46,60],"that":[47],"solving":[51,63],"any":[55],"constant":[56],"players,":[59],"reducible":[61],"to":[62],"4-player":[65],"game.":[66]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
