{"id":"https://openalex.org/W2585927126","doi":"https://doi.org/10.4086/toc.2016.v012a020","title":"","display_name":"","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2585927126","doi":"https://doi.org/10.4086/toc.2016.v012a020","mag":"2585927126"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2016.v012a020","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2016.v012a020","pdf_url":"https://theoryofcomputing.org/articles/v012a020/v012a020.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v012a020/v012a020.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077432617","display_name":"Jugal Garg","orcid":"https://orcid.org/0000-0001-6439-7308"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jugal Garg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070267732","display_name":"Ruta Mehta","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruta Mehta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007368382","display_name":"Vijay V. Vazirani","orcid":"https://orcid.org/0000-0002-4106-9077"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vijay V. Vazirani","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2692,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90959379,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":"1","first_page":"1","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9706000089645386,"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":0.9706000089645386,"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":0.9470000267028809,"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":0.9412999749183655,"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/dichotomy","display_name":"Dichotomy","score":0.585818886756897},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5573263168334961},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5128722190856934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4864666163921356},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.48145145177841187},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.44960975646972656},{"id":"https://openalex.org/keywords/arrow","display_name":"Arrow","score":0.4446040987968445},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41520610451698303},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3648262023925781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34673094749450684},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3252406716346741},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11942219734191895}],"concepts":[{"id":"https://openalex.org/C59462968","wikidata":"https://www.wikidata.org/wiki/Q10361123","display_name":"Dichotomy","level":2,"score":0.585818886756897},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5573263168334961},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5128722190856934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4864666163921356},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.48145145177841187},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.44960975646972656},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.4446040987968445},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41520610451698303},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3648262023925781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34673094749450684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3252406716346741},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11942219734191895},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2016.v012a020","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2016.v012a020","pdf_url":"https://theoryofcomputing.org/articles/v012a020/v012a020.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2016.v012a020","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2016.v012a020","pdf_url":"https://theoryofcomputing.org/articles/v012a020/v012a020.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G310766843","display_name":null,"funder_award_id":"CCF-0914732","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6482526725","display_name":"ICES:  Large: Collaborative Research:  Markets, Algorithms, Applications and the Digital Economy","funder_award_id":"1216019","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8180203186","display_name":"AF: Small:  Algorithmic and Game-Theoretic Issues in Bargaining and Markets","funder_award_id":"0914732","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2585927126.pdf","grobid_xml":"https://content.openalex.org/works/W2585927126.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W159399628","https://openalex.org/W584634945","https://openalex.org/W1571051474","https://openalex.org/W1980813953","https://openalex.org/W1991624978","https://openalex.org/W1995573091","https://openalex.org/W1997649256","https://openalex.org/W1999625879","https://openalex.org/W2002373723","https://openalex.org/W2013815105","https://openalex.org/W2034053794","https://openalex.org/W2041985481","https://openalex.org/W2057913812","https://openalex.org/W2068845983","https://openalex.org/W2070264122","https://openalex.org/W2077181719","https://openalex.org/W2089649903","https://openalex.org/W2095954749","https://openalex.org/W2097048499","https://openalex.org/W2104375208","https://openalex.org/W2108614294","https://openalex.org/W2117290960","https://openalex.org/W2118008360","https://openalex.org/W2151192928","https://openalex.org/W2152122625","https://openalex.org/W2155954950","https://openalex.org/W2169359757","https://openalex.org/W2201641266","https://openalex.org/W2234020812","https://openalex.org/W2292587149","https://openalex.org/W2301555989","https://openalex.org/W2951836131","https://openalex.org/W4226347946","https://openalex.org/W4234277722","https://openalex.org/W4234761190","https://openalex.org/W4380884450"],"related_works":["https://openalex.org/W2042568131","https://openalex.org/W3149432069","https://openalex.org/W1437213286","https://openalex.org/W2011564139","https://openalex.org/W2083151571","https://openalex.org/W102771113","https://openalex.org/W2403473672","https://openalex.org/W2460650438","https://openalex.org/W2467911613","https://openalex.org/W2118769481"],"abstract_inverted_index":{"Piecewise-linear,":[0],"concave":[1],"(PLC)":[2],"utility":[3],"functions":[4],"play":[5],"an":[6,26],"important":[7],"role":[8],"in":[9,28,39],"work":[10],"done":[11],"at":[12],"the":[13,22,40,59,63],"intersection":[14],"of":[15,24,62,65,75,81],"economics":[16],"and":[17,34],"algorithms.":[18],"We":[19],"prove":[20],"that":[21,47],"problem":[23,89],"computing":[25],"equilibrium":[27],"Arrow-Debreu":[29],"markets":[30,77],"with":[31],"PLC":[32,35],"utilities":[33],"production":[36],"sets":[37],"is":[38,72],"class":[41],"FIXP.":[42],"Recently":[43],"it":[44],"was":[45],"shown":[46],"these":[48,76],"problems":[49],"are":[50],"also":[51],"FIXP-hard":[52],"(Garg":[53],"et":[54],"al.,":[55],"arXiv:1411.5060),":[56],"hence":[57],"settling":[58],"long-standing":[60],"question":[61],"complexity":[64],"this":[66],"problem.":[67],"Central":[68],"to":[69],"our":[70],"proof":[71],"capturing":[73],"equilibria":[74],"as":[78],"fixed":[79],"points":[80],"a":[82,86],"continuous":[83],"function":[84],"via":[85],"nonlinear":[87],"complementarity":[88],"(NCP)":[90],"formulation.":[91]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-12-17T22:08:43.090829","created_date":"2017-02-10T00:00:00"}
