{"id":"https://openalex.org/W4386977919","doi":"https://doi.org/10.4230/lipics.itcs.2024.37","title":"Smooth Nash Equilibria: Algorithms and Complexity","display_name":"Smooth Nash Equilibria: Algorithms and Complexity","publication_year":2023,"publication_date":"2023-09-21","ids":{"openalex":"https://openalex.org/W4386977919","doi":"https://doi.org/10.4230/lipics.itcs.2024.37"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2309.12226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.12226","pdf_url":"https://arxiv.org/pdf/2309.12226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.12226","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034822411","display_name":"Constantinos Daskalakis","orcid":"https://orcid.org/0000-0002-5451-0490"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daskalakis, Constantinos","raw_affiliation_strings":["MIT, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089252105","display_name":"Noah Golowich","orcid":"https://orcid.org/0000-0003-2274-7861"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Golowich, Noah","raw_affiliation_strings":["MIT, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080772091","display_name":"Nika Haghtalab","orcid":"https://orcid.org/0000-0002-8612-2089"},"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":"Haghtalab, Nika","raw_affiliation_strings":["University of California at Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089291709","display_name":"Abhishek Shetty","orcid":"https://orcid.org/0000-0003-2693-0866"},"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":"Shetty, Abhishek","raw_affiliation_strings":["University of California at Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9994999766349792,"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/T12137","display_name":"Economic theories and models","score":0.9983000159263611,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9943000078201294,"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":0.8295606374740601},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.6761994957923889},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.6722602248191833},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.6170262098312378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5865482687950134},{"id":"https://openalex.org/keywords/risk-dominance","display_name":"Risk dominance","score":0.5495938658714294},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.5456441640853882},{"id":"https://openalex.org/keywords/trembling-hand-perfect-equilibrium","display_name":"Trembling hand perfect equilibrium","score":0.5239306092262268},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.38778156042099},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3867439925670624},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35160690546035767},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32035642862319946},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.24941834807395935},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.24025702476501465},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15259358286857605},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06952959299087524}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8295606374740601},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.6761994957923889},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.6722602248191833},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.6170262098312378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5865482687950134},{"id":"https://openalex.org/C22349654","wikidata":"https://www.wikidata.org/wiki/Q2039354","display_name":"Risk dominance","level":5,"score":0.5495938658714294},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.5456441640853882},{"id":"https://openalex.org/C16946829","wikidata":"https://www.wikidata.org/wiki/Q1039525","display_name":"Trembling hand perfect equilibrium","level":5,"score":0.5239306092262268},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.38778156042099},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3867439925670624},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35160690546035767},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32035642862319946},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.24941834807395935},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.24025702476501465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15259358286857605},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06952959299087524}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2309.12226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.12226","pdf_url":"https://arxiv.org/pdf/2309.12226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:drops-oai.dagstuhl.de:19565","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.37","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol287-itcs2024/LIPIcs.ITCS.2024.37/LIPIcs.ITCS.2024.37.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"doi:10.48550/arxiv.2309.12226","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.12226","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.4230/lipics.itcs.2024.37","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.itcs.2024.37","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.12226","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.12226","pdf_url":"https://arxiv.org/pdf/2309.12226","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2392833675","display_name":null,"funder_award_id":"DMS-2022448","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2649554787","display_name":"CAREER: Towards a theory of machine learning with strategic interactions","funder_award_id":"2145898","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4584308787","display_name":null,"funder_award_id":"CCF-2145898","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8294762899","display_name":"Foundations of Data Science Institute","funder_award_id":"2022448","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"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1553185561","https://openalex.org/W1554758635","https://openalex.org/W2068864510","https://openalex.org/W3125812435","https://openalex.org/W4301347782","https://openalex.org/W2122414948","https://openalex.org/W1502787658","https://openalex.org/W4299551322","https://openalex.org/W1667857601","https://openalex.org/W2274855902"],"abstract_inverted_index":{"A":[0],"fundamental":[1],"shortcoming":[2],"of":[3,6,28,36,94,154,260,283],"the":[4,26,152,177,205,254,290],"concept":[5],"Nash":[7,14,37,41,51,96,100,117,133,140,171,193,211,246,261],"equilibrium":[8,38,112,172,194,262],"is":[9,19,72,121,160,182,237,264,277],"its":[10],"computational":[11,137],"intractability:":[12],"approximating":[13],"equilibria":[15,134,247],"in":[16,102,173,195,202,216,289],"normal-form":[17,174,197],"games":[18],"PPAD-hard.":[20],"In":[21,48,176],"this":[22],"paper,":[23],"inspired":[24],"by":[25,84,229,279],"ideas":[27],"smoothed":[29],"analysis,":[30],"we":[31,275],"introduce":[32],"a":[33,44,49,68,73,161,167,183,189,196,242,258],"relaxed":[34],"variant":[35,259],"called":[39],"\u03c3-smooth":[40,50,69,95,99,109,116,132,170,192,245],"equilibrium,":[42,52],"for":[43,208],"{smoothness":[45],"parameter}":[46],"\u03c3.":[47],"players":[53,104,155,268],"only":[54],"need":[55],"to":[56,67,107,139,165,187,204,221,256,269],"achieve":[57],"utility":[58],"at":[59],"least":[60],"as":[61,63,144,146,274],"high":[62],"their":[64],"best":[65],"deviation":[66],"strategy,":[70],"which":[71,103,213,263],"distribution":[74],"that":[75,127,231],"does":[76],"not":[77],"put":[78],"too":[79],"much":[80],"mass":[81],"(as":[82],"parametrized":[83],"\u03c3)":[85],"on":[86,285],"any":[87],"fixed":[88],"action.":[89],"We":[90,125,224],"distinguish":[91],"two":[92],"variants":[93],"equilibria:":[97,141],"strong":[98,131,190],"equilibria,":[101,118,212],"are":[105,156,253],"required":[106],"play":[108],"strategies":[110],"under":[111],"play,":[113],"and":[114,130,151,272],"weak":[115,129,168,243],"where":[119],"there":[120,159,181],"no":[122],"such":[123],"requirement.":[124],"show":[126],"both":[128],"have":[135],"superior":[136],"properties":[138],"when":[142,232],"\u03c3":[143,234],"well":[145],"an":[147,238,280],"approximation":[148],"parameter":[149,179],"\u03f5":[150,236],"number":[153],"all":[157],"constants,":[158],"{constant-time}":[162],"randomized":[163],"algorithm":[164,186,207],"find":[166,188],"\u03f5-approximate":[169,191,210,244],"games.":[175],"same":[178],"regime,":[180],"polynomial-time":[184],"deterministic":[185],"game.":[198],"These":[199],"results":[200,252],"stand":[201],"contrast":[203],"optimal":[206],"computing":[209],"cannot":[214],"run":[215],"faster":[217],"than":[218],"quasipolynomial-time,":[219],"subject":[220],"complexity-theoretic":[222],"assumptions.":[223],"complement":[225],"our":[226],"upper":[227],"bounds":[228],"showing":[230],"either":[233],"or":[235],"inverse":[239],"polynomial,":[240],"finding":[241],"becomes":[248],"computationally":[249,265],"intractable.":[250],"Our":[251],"first":[255],"propose":[257],"tractable,":[266],"allows":[267],"act":[270],"independently,":[271],"which,":[273],"discuss,":[276],"justified":[278],"extensive":[281],"line":[282],"work":[284],"individual":[286],"choice":[287],"behavior":[288],"economics":[291],"literature.":[292]},"counts_by_year":[],"updated_date":"2026-07-16T13:24:37.021932","created_date":"2023-09-23T00:00:00"}