{"id":"https://openalex.org/W2072951587","doi":"https://doi.org/10.1145/1273340.1273348","title":"Convergence time to Nash equilibrium in load balancing","display_name":"Convergence time to Nash equilibrium in load balancing","publication_year":2007,"publication_date":"2007-08-01","ids":{"openalex":"https://openalex.org/W2072951587","doi":"https://doi.org/10.1145/1273340.1273348","mag":"2072951587"},"language":"en","primary_location":{"id":"doi:10.1145/1273340.1273348","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1273340.1273348","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-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/A5071856218","display_name":"Eyal Even-Dar","orcid":null},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eyal Even-Dar","raw_affiliation_strings":["University of Pennsylvania, Philadelphia, PA"],"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113507867","display_name":"Alex Kesselman","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alex Kesselman","raw_affiliation_strings":["Max-Planck Institut fur Informatik, Saarbrucken, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck Institut fur Informatik, Saarbrucken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113902158","display_name":"Yishay Mansour","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yishay Mansour","raw_affiliation_strings":["Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071856218"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":36.5563,"has_fulltext":false,"cited_by_count":132,"citation_normalized_percentile":{"value":0.99608788,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"3","issue":"3","first_page":"32","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9986000061035156,"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/T11182","display_name":"Auction Theory and Applications","score":0.9902999997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7819554805755615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6366170048713684},{"id":"https://openalex.org/keywords/load-balancing","display_name":"Load balancing (electrical power)","score":0.6117104291915894},{"id":"https://openalex.org/keywords/potential-game","display_name":"Potential game","score":0.5481259822845459},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5390706658363342},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5245426297187805},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5029594302177429},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.487533301115036},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.42996129393577576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31307125091552734},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.2566998600959778}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7819554805755615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6366170048713684},{"id":"https://openalex.org/C138959212","wikidata":"https://www.wikidata.org/wiki/Q1806783","display_name":"Load balancing (electrical power)","level":3,"score":0.6117104291915894},{"id":"https://openalex.org/C2778079155","wikidata":"https://www.wikidata.org/wiki/Q288500","display_name":"Potential game","level":3,"score":0.5481259822845459},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5390706658363342},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5245426297187805},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5029594302177429},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.487533301115036},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.42996129393577576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31307125091552734},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2566998600959778},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1273340.1273348","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1273340.1273348","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.102.5090","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102.5090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.seas.upenn.edu/~evendar/papers/convergence.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.182.6934","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.6934","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/%7Ecswamy/courses/co759/even-darkm-nashconv.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.6700000166893005,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W296036654","https://openalex.org/W1526250527","https://openalex.org/W1577419414","https://openalex.org/W1605188341","https://openalex.org/W1665632678","https://openalex.org/W1753330597","https://openalex.org/W1870008972","https://openalex.org/W1982142541","https://openalex.org/W2001330785","https://openalex.org/W2002089154","https://openalex.org/W2017227260","https://openalex.org/W2030914480","https://openalex.org/W2054129049","https://openalex.org/W2058013927","https://openalex.org/W2075113319","https://openalex.org/W2077066745","https://openalex.org/W2088559962","https://openalex.org/W2102736491","https://openalex.org/W2112269231","https://openalex.org/W2113692632","https://openalex.org/W2125537511","https://openalex.org/W2136388527","https://openalex.org/W2152520757","https://openalex.org/W2153541270","https://openalex.org/W2330024298","https://openalex.org/W2591957553","https://openalex.org/W2913711002","https://openalex.org/W3022321359","https://openalex.org/W4206871748","https://openalex.org/W4212808824","https://openalex.org/W4234761190","https://openalex.org/W4389615663"],"related_works":["https://openalex.org/W2100142613","https://openalex.org/W4300514062","https://openalex.org/W2949715110","https://openalex.org/W3161911778","https://openalex.org/W2095833558","https://openalex.org/W4214835929","https://openalex.org/W1582112020","https://openalex.org/W1598931193","https://openalex.org/W2047323392","https://openalex.org/W2132438287"],"abstract_inverted_index":{"We":[0,35,62,75,131],"study":[1],"the":[2,57,83,104,125],"number":[3],"of":[4,39,113,128],"steps":[5],"required":[6],"to":[7,25,27,60,91,108],"reach":[8],"a":[9,14,28,37,53,88,92,118,140,151],"pure":[10],"Nash":[11],"equilibrium":[12],"in":[13,136,147,158],"load":[15,40,134,145,156],"balancing":[16,41,135,146,157],"scenario":[17],"where":[18],"each":[19],"job":[20,89,107],"behaves":[21],"selfishly":[22],"and":[23,47,71,98,124,155,161],"attempts":[24],"migrate":[26],"machine":[29,93],"which":[30,94],"will":[31],"minimize":[32],"its":[33,96],"cost.":[34],"consider":[36,63],"variety":[38],"models,":[42],"including":[43],"identical,":[44],"restricted,":[45],"related,":[46],"unrelated":[48,137],"machines.":[49],"Our":[50],"results":[51,115],"have":[52],"crucial":[54],"dependence":[55],"on":[56],"weights":[58],"assigned":[59],"jobs.":[61],"arbitrary":[64,80],"weights,":[65,67,70],"integer":[66],"k":[68],"distinct":[69],"identical":[72],"(unit)":[73],"weights.":[74],"look":[76],"both":[77],"at":[78],"an":[79,166],"schedule":[81],"(where":[82],"only":[84],"restriction":[85],"is":[86,116,139,150,165],"that":[87,133],"migrates":[90],"lowers":[95],"cost)":[97],"specific":[99],"efficient":[100],"schedulers":[101],"(e.g.,":[102],"allowing":[103],"largest":[105],"weight":[106,163],"move":[109],"first).":[110],"A":[111],"by-product":[112],"our":[114],"establishing":[117],"connection":[119],"between":[120],"various":[121],"scheduling":[122],"models":[123],"game-theoretic":[126],"notion":[127],"potential":[129,143,153,168],"games.":[130],"show":[132],"machines":[138,149,160],"generalized":[141],"ordinal":[142],"game,":[144,154],"related":[148,159],"weighted":[152],"unit":[162],"jobs":[164],"exact":[167],"game.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"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":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":21}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
