{"id":"https://openalex.org/W4387046540","doi":"https://doi.org/10.1016/j.tcs.2023.114218","title":"PPAD-complete approximate pure Nash equilibria in Lipschitz games","display_name":"PPAD-complete approximate pure Nash equilibria in Lipschitz games","publication_year":2023,"publication_date":"2023-09-26","ids":{"openalex":"https://openalex.org/W4387046540","doi":"https://doi.org/10.1016/j.tcs.2023.114218"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.tcs.2023.114218","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.tcs.2023.114218","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067662147","display_name":"Paul W. Goldberg","orcid":"https://orcid.org/0000-0002-5436-7890"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"funder","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Paul W. Goldberg","raw_affiliation_strings":["Department of Computer Science, University of Oxford, Oxford, England, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, England, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001933089","display_name":"Matthew J. Katzman","orcid":"https://orcid.org/0000-0001-8147-9110"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"funder","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Matthew Katzman","raw_affiliation_strings":["Department of Computer Science, University of Oxford, Oxford, England, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, England, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067662147","https://openalex.org/A5001933089"],"corresponding_institution_ids":["https://openalex.org/I40120149","https://openalex.org/I40120149"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":65},"biblio":{"volume":"980","issue":null,"first_page":"114218","last_page":"114218"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9998,"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":0.9998,"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":0.9972,"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":0.9963,"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":[],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8585522},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.72354317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.71325827},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5272797},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5253215},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.49885488},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47502786},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.42195094},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41507182},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38150263},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.37422708},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20352939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17668009},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06255308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06250921},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.tcs.2023.114218","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:26f81156-4c16-4001-952f-52dde92627ae","pdf_url":"https://ora.ox.ac.uk/objects/uuid:26f81156-4c16-4001-952f-52dde92627ae/files/r8c97kr31v","source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":["University of Oxford"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.tcs.2023.114218","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.42}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":23,"referenced_works":["https://openalex.org/W100324934","https://openalex.org/W1527197079","https://openalex.org/W1648820898","https://openalex.org/W193574887","https://openalex.org/W1980813953","https://openalex.org/W1998196694","https://openalex.org/W2044667552","https://openalex.org/W2057913812","https://openalex.org/W2065828765","https://openalex.org/W2083207585","https://openalex.org/W2087005894","https://openalex.org/W2103981148","https://openalex.org/W2127451547","https://openalex.org/W2168755209","https://openalex.org/W2169359757","https://openalex.org/W2336485875","https://openalex.org/W2396633455","https://openalex.org/W2511655436","https://openalex.org/W2740520762","https://openalex.org/W2811432292","https://openalex.org/W2913334655","https://openalex.org/W3118247429","https://openalex.org/W4234761190"],"related_works":["https://openalex.org/W3207342620","https://openalex.org/W3030822758","https://openalex.org/W2803932348","https://openalex.org/W2803931294","https://openalex.org/W2760737027","https://openalex.org/W2728657731","https://openalex.org/W2561139292","https://openalex.org/W2481143976","https://openalex.org/W2236801283","https://openalex.org/W2092374696"],"abstract_inverted_index":{"Lipschitz":[0,10,46,80,153],"games,":[1],"in":[2,127,147],"which":[3,111],"there":[4],"is":[5,89],"a":[6,18,76,114,134,138],"limit":[7],"\u03bb":[8],"(the":[9],"value":[11],"of":[12,79,94,100,107,125,133,152,184],"the":[13,41,63,68,105,123,131,190],"game)":[14],"on":[15],"how":[16],"much":[17],"player's":[19],"payoffs":[20,156,170],"may":[21],"change":[22],"when":[23],"some":[24],"other":[25],"player":[26,52],"deviates,":[27],"were":[28],"introduced":[29],"about":[30],"10":[31],"years":[32],"ago":[33],"by":[34],"Azrieli":[35],"and":[36,122,187],"Shmaya.":[37],"They":[38],"showed":[39],"via":[40],"probabilistic":[42],"method":[43],"that":[44,73,189],"n-player":[45],"games":[47,81,154,167],"with":[48],"m":[49],"strategies":[50],"per":[51],"have":[53],"\u03f5-approximate":[54,86],"pure":[55,87,135,172],"Nash":[56],"equilibria,":[57],"for":[58,67,75,91,149],"\u03f5\u2265\u03bb8nlog\u2061(2mn).":[59],"Here":[60],"we":[61,112,179],"provide":[62,180],"first":[64],"hardness":[65,109],"result":[66,102],"corresponding":[69],"computational":[70],"problem,":[71],"showing":[72],"even":[74],"simple":[77],"class":[78,151],"(Lipschitz":[82],"polymatrix":[83,120],"games),":[84],"finding":[85],"equilibria":[88],"PPAD-complete,":[90],"suitable":[92],"pairs":[93],"values":[95],"\u03f5(n),":[96],"\u03bb(n).":[97],"Novel":[98],"features":[99],"this":[101,195],"include":[103],"both":[104],"proof":[106,124],"PPAD":[108,128,148],"(in":[110],"apply":[113],"population":[115],"game":[116],"reduction":[117],"from":[118,137,157,171],"unrestricted":[119],"games)":[121],"containment":[126,146],"(by":[129],"derandomizing":[130],"selection":[132],"equilibrium":[136],"mixed":[139],"one).":[140],"In":[141],"fact,":[142],"our":[143],"approach":[144],"implies":[145],"any":[150],"where":[155,168],"mixed-strategy":[158],"profiles":[159,174],"can":[160,175],"be":[161,176],"deterministically":[162,177],"computed.":[163],"When":[164],"instead":[165],"considering":[166],"only":[169],"action":[173],"computed,":[178],"two":[181],"equivalent":[182],"definitions":[183],"\"randomized":[185],"PPAD\"":[186],"show":[188],"generalized":[191],"problem":[192],"belongs":[193],"to":[194],"class.":[196]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4387046540","counts_by_year":[],"updated_date":"2025-04-10T09:04:09.037916","created_date":"2023-09-27"}