{"id":"https://openalex.org/W7140223589","doi":"https://doi.org/10.1007/s10462-026-11533-6","title":"Nash equilibrium strategy solving in two-player imperfect-information games: a survey","display_name":"Nash equilibrium strategy solving in two-player imperfect-information games: a survey","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140223589","doi":"https://doi.org/10.1007/s10462-026-11533-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10462-026-11533-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10462-026-11533-6","pdf_url":null,"source":{"id":"https://openalex.org/S122814990","display_name":"Artificial Intelligence Review","issn_l":"0269-2821","issn":["0269-2821","1573-7462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10462-026-11533-6","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Huale Li","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huale Li","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, Gansu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, Gansu, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhaobin Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaobin Wang","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, Gansu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, Gansu, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhen Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Yang","raw_affiliation_strings":["School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, Gansu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, Gansu, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Shuhan Qi","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuhan Qi","raw_affiliation_strings":["School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jiajia Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiajia Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29860683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"6","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":0.9143000245094299,"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":0.9143000245094299,"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":0.009800000116229057,"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/T11182","display_name":"Auction Theory and Applications","score":0.009100000374019146,"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":0.6934000253677368},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.46799999475479126},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.4068000018596649},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.3278999924659729},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.2865999937057495}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6934000253677368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6061999797821045},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.487199991941452},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4846000075340271},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.46799999475479126},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.4068000018596649},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.3278999924659729},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28439998626708984},{"id":"https://openalex.org/C103382277","wikidata":"https://www.wikidata.org/wiki/Q282640","display_name":"General equilibrium theory","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.2590999901294708}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10462-026-11533-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10462-026-11533-6","pdf_url":null,"source":{"id":"https://openalex.org/S122814990","display_name":"Artificial Intelligence Review","issn_l":"0269-2821","issn":["0269-2821","1573-7462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Review","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10462-026-11533-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10462-026-11533-6","pdf_url":null,"source":{"id":"https://openalex.org/S122814990","display_name":"Artificial Intelligence Review","issn_l":"0269-2821","issn":["0269-2821","1573-7462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Review","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2732835952","display_name":null,"funder_award_id":"62406251","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W123800271","https://openalex.org/W1504512712","https://openalex.org/W1554808787","https://openalex.org/W1676440337","https://openalex.org/W1714211023","https://openalex.org/W1769087895","https://openalex.org/W2006791053","https://openalex.org/W2044667552","https://openalex.org/W2055537715","https://openalex.org/W2086312499","https://openalex.org/W2095353739","https://openalex.org/W2114793692","https://openalex.org/W2135730283","https://openalex.org/W2145339207","https://openalex.org/W2154207916","https://openalex.org/W2160124660","https://openalex.org/W2167957526","https://openalex.org/W2174009875","https://openalex.org/W2257979135","https://openalex.org/W2493063923","https://openalex.org/W2562576832","https://openalex.org/W2574978968","https://openalex.org/W2579486451","https://openalex.org/W2766447205","https://openalex.org/W2773381986","https://openalex.org/W2810602713","https://openalex.org/W2902907165","https://openalex.org/W2960876848","https://openalex.org/W2963372454","https://openalex.org/W2963527567","https://openalex.org/W2964263974","https://openalex.org/W2964934024","https://openalex.org/W2966397236","https://openalex.org/W2982316857","https://openalex.org/W2989847975","https://openalex.org/W3018036994","https://openalex.org/W3037507370","https://openalex.org/W3037719421","https://openalex.org/W3075945543","https://openalex.org/W3096065649","https://openalex.org/W3133947113","https://openalex.org/W3174079223","https://openalex.org/W3189507281","https://openalex.org/W4210505536","https://openalex.org/W4229019182","https://openalex.org/W4234761190","https://openalex.org/W4256046955","https://openalex.org/W4283817675","https://openalex.org/W4285364563","https://openalex.org/W4285606934","https://openalex.org/W4300893300","https://openalex.org/W4300920027","https://openalex.org/W4310705874","https://openalex.org/W4317038588","https://openalex.org/W4380758740","https://openalex.org/W4387415017","https://openalex.org/W4390381945","https://openalex.org/W4404205226","https://openalex.org/W4404710747","https://openalex.org/W4406380313","https://openalex.org/W7124139285","https://openalex.org/W7124160341","https://openalex.org/W7124207559","https://openalex.org/W7124220798","https://openalex.org/W7124257019"],"related_works":[],"abstract_inverted_index":{"Imperfect-information":[0],"games":[1],"(IIGs)":[2],"have":[3,39],"attracted":[4],"significant":[5],"attention":[6],"due":[7],"to":[8,112,131],"the":[9,137],"complexity":[10],"arising":[11],"from":[12,88],"hidden":[13],"information.":[14],"In":[15],"recent":[16],"years,":[17],"efficiently":[18],"solving":[19,63,98],"optimal":[20],"strategies":[21,66],"in":[22,52,67],"IIGs":[23],"has":[24],"become":[25],"a":[26,85,107],"major":[27],"challenge.":[28],"Equilibrium":[29],"strategies,":[30],"with":[31],"their":[32,80,117],"solid":[33],"theoretical":[34],"foundation":[35],"and":[36,47,75,96,115,125],"demonstrated":[37],"performance,":[38],"achieved":[40],"great":[41],"success.":[42],"The":[43],"agents":[44],"like":[45],"Libratus":[46],"DeepNash":[48],"demonstrate":[49],"superior":[50],"performance":[51],"public":[53],"evaluations.":[54],"This":[55],"survey":[56,121],"comprehensively":[57],"reviews":[58],"two":[59],"key":[60],"methods":[61],"for":[62,135],"Nash":[64],"equilibrium":[65],"two-player":[68],"zero-sum":[69],"IIGs:":[70],"counterfactual":[71],"regret":[72],"minimization":[73],"(CFR)":[74],"fictitious":[76],"self-play":[77],"(FSP),":[78],"including":[79,91],"improved":[81],"variants.":[82],"We":[83],"provide":[84,132],"detailed":[86],"overview":[87],"multiple":[89],"dimensions,":[90],"problem":[92],"modeling,":[93],"solution":[94],"paradigms,":[95],"classical":[97],"methods.":[99],"To":[100],"further":[101],"evaluate":[102],"these":[103],"methods,":[104],"we":[105],"conducted":[106],"series":[108],"of":[109],"evaluation":[110],"experiments":[111],"deeply":[113],"analyze":[114],"compare":[116],"performance.":[118],"Finally,":[119],"this":[120],"summarizes":[122],"current":[123],"challenges":[124],"outlines":[126],"future":[127],"research":[128],"directions,":[129],"aiming":[130],"useful":[133],"insights":[134],"advancing":[136],"field.":[138]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-03-25T00:00:00"}