{"id":"https://openalex.org/W2070298923","doi":"https://doi.org/10.1145/1807406.1807467","title":"On the complexity of equilibria in markets with additively separable utilities","display_name":"On the complexity of equilibria in markets with additively separable utilities","publication_year":2010,"publication_date":"2010-05-14","ids":{"openalex":"https://openalex.org/W2070298923","doi":"https://doi.org/10.1145/1807406.1807467","mag":"2070298923"},"language":"en","primary_location":{"id":"doi:10.1145/1807406.1807467","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1807406.1807467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions","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/A5100329834","display_name":"Xi Chen","orcid":"https://orcid.org/0000-0001-5661-515X"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I2800817003","display_name":"California Southern University","ror":"https://ror.org/058zz0t50","country_code":"US","type":"education","lineage":["https://openalex.org/I2800817003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xi Chen","raw_affiliation_strings":["University of Southern California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southern California","institution_ids":["https://openalex.org/I2800817003","https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023820841","display_name":"Decheng Dai","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Decheng Dai","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100783342","display_name":"Ye Du","orcid":"https://orcid.org/0000-0002-3057-1862"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ye Du","raw_affiliation_strings":["University of Michigan","(University of Michigan)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"(University of Michigan)","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102005063","display_name":"Shang\u2010Hua Teng","orcid":"https://orcid.org/0000-0001-5011-4514"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I2800817003","display_name":"California Southern University","ror":"https://ror.org/058zz0t50","country_code":"US","type":"education","lineage":["https://openalex.org/I2800817003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shang-Hua Teng","raw_affiliation_strings":["University of Southern California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Southern California","institution_ids":["https://openalex.org/I2800817003","https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0481,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87569632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9976999759674072,"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":0.9976999759674072,"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":0.9894999861717224,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9663000106811523,"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/separable-space","display_name":"Separable space","score":0.8321589231491089},{"id":"https://openalex.org/keywords/arrow","display_name":"Arrow","score":0.7691428661346436},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6252888441085815},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5686427354812622},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5674963593482971},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5605820417404175},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4684132933616638},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3600751757621765},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35585710406303406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06834915280342102}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.8321589231491089},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.7691428661346436},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6252888441085815},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5686427354812622},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5674963593482971},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5605820417404175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4684132933616638},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3600751757621765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35585710406303406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06834915280342102},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1807406.1807467","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1807406.1807467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1975043454","https://openalex.org/W2089884390","https://openalex.org/W2181860688","https://openalex.org/W2761826362","https://openalex.org/W1973761269","https://openalex.org/W1540792735","https://openalex.org/W1989829660","https://openalex.org/W3124251588","https://openalex.org/W4235221255","https://openalex.org/W3131134472"],"abstract_inverted_index":{"We":[0,26],"show":[1],"that":[2],"the":[3,30],"problem":[4],"of":[5,32],"computing":[6],"an":[7],"approximate":[8],"Arrow-Debreu":[9],"market":[10],"equilibrium":[11],"is":[12],"PPAD-hard,":[13],"even":[14],"when":[15],"all":[16],"traders":[17],"use":[18],"additively":[19],"separable,":[20],"piecewise-linear,":[21],"and":[22],"concave":[23],"utility":[24],"functions.":[25],"will":[27],"also":[28],"discuss":[29],"extension":[31],"this":[33],"result":[34],"to":[35],"Fisher's":[36],"model.":[37]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
