{"id":"https://openalex.org/W2492477926","doi":"https://doi.org/10.1017/cbo9780511800481.007","title":"Combinatorial Algorithms for Market Equilibria","display_name":"Combinatorial Algorithms for Market Equilibria","publication_year":2007,"publication_date":"2007-09-24","ids":{"openalex":"https://openalex.org/W2492477926","doi":"https://doi.org/10.1017/cbo9780511800481.007","mag":"2492477926"},"language":"en","primary_location":{"id":"doi:10.1017/cbo9780511800481.007","doi":"https://doi.org/10.1017/cbo9780511800481.007","is_oa":false,"landing_page_url":"https://doi.org/10.1017/cbo9780511800481.007","pdf_url":null,"source":{"id":"https://openalex.org/S4306417653","display_name":"Algorithmic Game Theory","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmic Game Theory","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2508573783","display_name":"Algorithmic Game Theory"},"type":"book-chapter","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/A5007368382","display_name":"Vijay V. Vazirani","orcid":"https://orcid.org/0000-0002-4106-9077","observed_orcids":["https://orcid.org/0000-0002-4106-9077"]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vijay V. Vazirani","raw_affiliation_strings":["Georgia Institute of Technology","College of Computing Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"College of Computing Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007368382"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":20.8908,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.99326393,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"103","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.6923999786376953,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.6923999786376953,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.20360000431537628,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.05620000138878822,"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/market-equilibrium","display_name":"market equilibrium","score":0.8759999871253967},{"id":"https://openalex.org/keywords/combinatorial-algorithms","display_name":"combinatorial algorithms","score":0.8299999833106995},{"id":"https://openalex.org/keywords/fisher-markets","display_name":"Fisher markets","score":0.5139999985694885},{"id":"https://openalex.org/keywords/arrow-debreu-model","display_name":"Arrow-Debreu model","score":0.9200000166893005},{"id":"https://openalex.org/keywords/linear-utility","display_name":"linear utility","score":0.8270000219345093},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.6159999966621399},{"id":"https://openalex.org/keywords/auction-based-algorithm","display_name":"auction-based algorithm","score":0.6970000267028809},{"id":"https://openalex.org/keywords/primal-dual-algorithm","display_name":"primal-dual algorithm","score":0.7960000038146973},{"id":"https://openalex.org/keywords/strongly-polynomial-algorithms","display_name":"strongly polynomial algorithms","score":0.7979999780654907},{"id":"https://openalex.org/keywords/general-equilibrium","display_name":"general equilibrium","score":0.6309999823570251}],"concepts":[{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5435580611228943},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.541904866695404},{"id":"https://openalex.org/C52146309","wikidata":"https://www.wikidata.org/wiki/Q7431116","display_name":"Schema (genetic algorithms)","level":2,"score":0.532387375831604},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.5240647792816162},{"id":"https://openalex.org/C59919655","wikidata":"https://www.wikidata.org/wiki/Q5150821","display_name":"Combinatorial auction","level":3,"score":0.48393160104751587},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4760049283504486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4591900408267975},{"id":"https://openalex.org/C2988809283","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Combinatorial algorithms","level":2,"score":0.4466424882411957},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4457665681838989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4317009449005127},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4190785586833954},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41844695806503296},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.41552454233169556},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.41420263051986694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.384400874376297},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36772361397743225},{"id":"https://openalex.org/C163239763","wikidata":"https://www.wikidata.org/wiki/Q5153637","display_name":"Common value auction","level":2,"score":0.08569788932800293},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/cbo9780511800481.007","doi":"https://doi.org/10.1017/cbo9780511800481.007","is_oa":false,"landing_page_url":"https://doi.org/10.1017/cbo9780511800481.007","pdf_url":null,"source":{"id":"https://openalex.org/S4306417653","display_name":"Algorithmic Game Theory","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmic Game Theory","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1980938853","https://openalex.org/W1987497363","https://openalex.org/W2036174679","https://openalex.org/W2037710455","https://openalex.org/W2047880045","https://openalex.org/W2058858486","https://openalex.org/W2070150572","https://openalex.org/W2158733823","https://openalex.org/W2165807407","https://openalex.org/W2327315803","https://openalex.org/W2753542457"],"related_works":["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/W1901793333","https://openalex.org/W2460650438","https://openalex.org/W2791306776","https://openalex.org/W2135616721"],"abstract_inverted_index":{"Combinatorial":[0],"polynomial":[1,66],"time":[2],"algorithms":[3],"are":[4,60,117,167,176],"presented":[5,70],"for":[6,12,71,93],"finding":[7],"equilibrium":[8,224],"prices":[9,151,196,235],"and":[10,20,27,63,77,86,98,154,165,180],"allocations":[11],"the":[13,18,24,36,51,82,89,125,149,158,186,205,218,226,231,242],"linear":[14],"utilities":[15],"case":[16],"of":[17,35,73,84,100,152,185,233,241],"Fisher":[19],"Arrow\u2013Debreu":[21,227],"models":[22],"using":[23],"primal-dual":[25],"schema":[26],"an":[28,43],"auction-based":[29],"approach,":[30],"respectively.":[31],"An":[32],"intersting":[33],"feature":[34],"first":[37],"algorithm":[38,68],"is":[39,69,103,141,160,194,212],"that":[40,114,157,163,172,175,195,199,203,216],"it":[41],"finds":[42],"optimal":[44],"solution":[45],"to":[46,106,122,129,143,170],"a":[47,64,120,182,237],"nonlinear":[48],"convex":[49],"program,":[50],"Eisenberg-Gale":[52],"program.":[53],"Resource":[54],"allocation":[55],"markets":[56,85],"in":[57,162,178,191],"Kelly's":[58],"model":[59,240],"also":[61],"discussed":[62],"strongly":[65],"combinatorial":[67],"one":[72],"them.":[74],"Introduction":[75],"Thinkers":[76],"philosophers":[78],"have":[79],"pondered":[80],"over":[81],"notions":[83,102],"money":[87],"through":[88],"ages.":[90],"The":[91,112],"credit":[92],"initiating":[94],"formal":[95],"mathematical":[96,133],"modeling":[97],"study":[99,131],"these":[101],"generally":[104],"attributed":[105],"nineteenth-century":[107],"economist":[108],"Leon":[109],"Walras":[110],"(1874).":[111],"fact":[113],"Western":[115],"economies":[116],"capitalistic":[118],"had":[119],"lot":[121],"do":[123],"with":[124],"over-whelming":[126],"importance":[127],"given":[128],"this":[130],"within":[132,222],"economics":[134],"\u2013":[135],"essentially,":[136],"our":[137],"most":[138,177,219],"critical":[139],"decision-making":[140],"relegated":[142],"pricing":[144,192],"mechanisms.":[145],"They":[146],"largely":[147],"determine":[148],"relative":[150],"goods":[153,164],"services,":[155],"ensure":[156,181],"economy":[159,206],"efficient,":[161],"services":[166],"made":[168],"available":[169],"entities":[171],"produce":[173],"items":[174],"demand,":[179],"stable":[183],"operation":[184],"economy.":[187,243],"A":[188],"central":[189],"tenet":[190],"mechanisms":[193],"be":[197],"such":[198,234],"demand":[200],"equals":[201],"supply;":[202],"is,":[204],"should":[207],"operate":[208],"at":[209],"equilibrium.":[210],"It":[211],"not":[213],"surprising":[214],"therefore":[215],"perhaps":[217],"celebrated":[220],"theorem":[221],"general":[223,239],"theory,":[225],"Theorem,":[228],"establishes":[229],"precisely":[230],"existence":[232],"under":[236],"very":[238]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}