{"id":"https://openalex.org/W4386928656","doi":"https://doi.org/10.1080/02331934.2023.2259925","title":"A differentiable path-following method to compute Nash equilibria in robust normal-form games","display_name":"A differentiable path-following method to compute Nash equilibria in robust normal-form games","publication_year":2023,"publication_date":"2023-09-21","ids":{"openalex":"https://openalex.org/W4386928656","doi":"https://doi.org/10.1080/02331934.2023.2259925"},"language":"en","primary_location":{"id":"doi:10.1080/02331934.2023.2259925","doi":"https://doi.org/10.1080/02331934.2023.2259925","is_oa":false,"landing_page_url":"https://doi.org/10.1080/02331934.2023.2259925","pdf_url":null,"source":{"id":"https://openalex.org/S158016561","display_name":"Optimization","issn_l":"0233-1934","issn":["0233-1934","1026-7662","1029-4945"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-c","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5025264293","display_name":"Lingyuan Liu","orcid":"https://orcid.org/0000-0002-7674-7843","observed_orcids":["https://orcid.org/0000-0002-7674-7843"]},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Lingyuan Liu","raw_affiliation_strings":["City University of Hong Kong","Department of Systems Engineering, City University of Hong Kong, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Department of Systems Engineering, City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100430547","display_name":"Yin Chen","orcid":"https://orcid.org/0000-0001-5389-2821","observed_orcids":["https://orcid.org/0000-0001-5389-2821"]},"institutions":[{"id":"https://openalex.org/I4210152380","display_name":"Shenzhen Technology University","ror":"https://ror.org/04qzpec27","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152380"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yin Chen","raw_affiliation_strings":["Shenzhen Technology University","College of Big Data and Internet, Shenzhen Technology University, Shenzhen, Guangdong, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shenzhen Technology University","institution_ids":["https://openalex.org/I4210152380"]},{"raw_affiliation_string":"College of Big Data and Internet, Shenzhen Technology University, Shenzhen, Guangdong, People's Republic of China","institution_ids":["https://openalex.org/I4210152380"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085575860","display_name":"Chuangyin Dang","orcid":"https://orcid.org/0000-0003-4731-4616","observed_orcids":["https://orcid.org/0000-0003-4731-4616"]},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Chuangyin Dang","raw_affiliation_strings":["City University of Hong Kong","Department of Systems Engineering, City University of Hong Kong, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of Hong Kong","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Department of Systems Engineering, City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100430547"],"corresponding_institution_ids":["https://openalex.org/I4210152380"],"apc_list":null,"apc_paid":null,"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":null,"biblio":{"volume":"74","issue":"3","first_page":"549","last_page":"588"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9926999807357788,"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":0.9926999807357788,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.0020000000949949026,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium-computation","display_name":"Nash equilibrium computation","score":0.968999981880188},{"id":"https://openalex.org/keywords/payoff-uncertainty","display_name":"payoff uncertainty","score":0.8510000109672546},{"id":"https://openalex.org/keywords/logarithmic-barrier","display_name":"logarithmic barrier","score":0.675000011920929},{"id":"https://openalex.org/keywords/global-convergence","display_name":"global convergence","score":0.4480000138282776}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8130730986595154},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6105956435203552},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5915218591690063},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5653566122055054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5565226674079895},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.5066378712654114},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.5040294528007507},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4948682188987732},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.4747909903526306},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.42714792490005493},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.37289607524871826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2684699296951294},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08064472675323486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06590616703033447},{"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:10.1080/02331934.2023.2259925","doi":"https://doi.org/10.1080/02331934.2023.2259925","is_oa":false,"landing_page_url":"https://doi.org/10.1080/02331934.2023.2259925","pdf_url":null,"source":{"id":"https://openalex.org/S158016561","display_name":"Optimization","issn_l":"0233-1934","issn":["0233-1934","1026-7662","1029-4945"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-c","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5546748033","display_name":null,"funder_award_id":"2021A1515110099","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G8361734564","display_name":null,"funder_award_id":"12201427","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320332587","display_name":"Natural Science Foundation of Ningbo","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W11559153","https://openalex.org/W1500898274","https://openalex.org/W1543439990","https://openalex.org/W1544688354","https://openalex.org/W1572204513","https://openalex.org/W1607862333","https://openalex.org/W1969768653","https://openalex.org/W1981305496","https://openalex.org/W1987011264","https://openalex.org/W1987592874","https://openalex.org/W2005252069","https://openalex.org/W2008968905","https://openalex.org/W2019128548","https://openalex.org/W2035681301","https://openalex.org/W2039867343","https://openalex.org/W2041180287","https://openalex.org/W2060186712","https://openalex.org/W2066111511","https://openalex.org/W2070994188","https://openalex.org/W2080995113","https://openalex.org/W2089649903","https://openalex.org/W2094689434","https://openalex.org/W2100791203","https://openalex.org/W2153961011","https://openalex.org/W2170628846","https://openalex.org/W2177295793","https://openalex.org/W2332980573","https://openalex.org/W2619435297","https://openalex.org/W2690472105","https://openalex.org/W2963804264","https://openalex.org/W2974942783","https://openalex.org/W3023735859","https://openalex.org/W3088115742","https://openalex.org/W3118337689","https://openalex.org/W3121814859","https://openalex.org/W3133055261","https://openalex.org/W3179832012","https://openalex.org/W3182017764","https://openalex.org/W3195048711","https://openalex.org/W3201036065","https://openalex.org/W3204324417","https://openalex.org/W4210390072","https://openalex.org/W4214944398","https://openalex.org/W4223514112","https://openalex.org/W4233058511","https://openalex.org/W4234761190","https://openalex.org/W4283837014","https://openalex.org/W4285587674","https://openalex.org/W4288695994","https://openalex.org/W4301791716","https://openalex.org/W4306928238","https://openalex.org/W4312848642"],"related_works":["https://openalex.org/W4407420023","https://openalex.org/W3182017764","https://openalex.org/W1792585234","https://openalex.org/W4411385422","https://openalex.org/W3191750423","https://openalex.org/W1556093069","https://openalex.org/W4387539971","https://openalex.org/W4415020582","https://openalex.org/W6999732351","https://openalex.org/W7006235951"],"abstract_inverted_index":{"The":[0,32],"robust":[1,79,106,178],"normal-form":[2,80,107,179],"game":[3,10,108],"formulated":[4],"by":[5],"Aghassi":[6],"and":[7,25,52,157],"Bertsimas":[8],"[Robust":[9],"theory.":[11],"Math":[12],"Program.":[13],"2006;107(1-2):231-273.":[14],"doi:10.1007/s10107-005-0686-0]":[15],"makes":[16],"an":[17,38,61,99,151],"effective":[18],"paradigm":[19],"to":[20,49,58,74],"deal":[21],"with":[22,98,126],"payoff":[23,84,96],"uncertainty":[24,85],"has":[26],"many":[27],"applications":[28],"in":[29,41,78,109],"decision":[30],"analysis.":[31],"computation":[33],"of":[34,121,144,166],"Nash":[35,76,161],"equilibria":[36,77],"plays":[37],"important":[39],"role":[40],"these":[42],"applications.":[43],"Nonetheless,":[44],"the":[45,83,122,127,142,164,185,191],"existing":[46],"method":[47,73,188],"fails":[48],"converge":[50],"globally":[51],"it":[53],"remains":[54],"a":[55,70,90,104,114,131,145,160,176],"challenging":[56],"problem":[57],"find":[59],"such":[60],"equilibrium.":[62,162],"To":[63],"meet":[64],"this":[65,67,136],"challenge,":[66],"paper":[68],"develops":[69],"differentiable":[71],"path-following":[72,187,193],"compute":[75],"games":[81],"when":[82],"can":[86],"be":[87],"characterized":[88],"as":[89],"polytope.":[91],"Incorporating":[92],"logarithmic-barrier":[93,105,186],"terms":[94],"into":[95],"functions":[97],"extra":[100],"variable,":[101],"we":[102,140,169],"constitute":[103],"which":[110],"each":[111],"player":[112],"solves":[113],"strictly":[115],"convex":[116],"optimization":[117],"problem.":[118],"An":[119],"application":[120],"optimality":[123],"conditions":[124],"together":[125],"equilibrium":[128,133,138],"condition":[129],"yields":[130],"polynomial":[132,137],"system.":[134],"With":[135],"system,":[139],"establish":[141],"existence":[143],"smooth":[146,173],"path":[147,174],"that":[148,184],"starts":[149],"from":[150,175],"arbitrary":[152],"totally":[153],"mixed":[154],"strategy":[155],"profile":[156],"ends":[158],"at":[159],"For":[163],"purpose":[165],"numerical":[167],"comparison,":[168],"secure":[170],"one":[171],"more":[172],"convex-quadratic-penalty":[177,192],"game.":[180],"Numerical":[181],"results":[182],"show":[183],"significantly":[189],"outperforms":[190],"method.":[194]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2023-09-22T00:00:00"}