{"id":"https://openalex.org/W3189507281","doi":"https://doi.org/10.24963/ijcai.2021/504","title":"CFR-MIX: Solving Imperfect Information Extensive-Form Games with Combinatorial Action Space","display_name":"CFR-MIX: Solving Imperfect Information Extensive-Form Games with Combinatorial Action Space","publication_year":2021,"publication_date":"2021-08-01","ids":{"openalex":"https://openalex.org/W3189507281","doi":"https://doi.org/10.24963/ijcai.2021/504","mag":"3189507281"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2021/504","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2021/504","pdf_url":"https://www.ijcai.org/proceedings/2021/0504.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.ijcai.org/proceedings/2021/0504.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101976908","display_name":"Shuxin Li","orcid":"https://orcid.org/0009-0003-3039-8451"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Shuxin Li","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100629118","display_name":"Youzhi Zhang","orcid":"https://orcid.org/0000-0002-2984-734X"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG","US"],"is_corresponding":false,"raw_author_name":"Youzhi Zhang","raw_affiliation_strings":["Department of Computer Science, Dartmouth College, USA","School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Dartmouth College, USA","institution_ids":["https://openalex.org/I107672454"]},{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049783685","display_name":"Xinrun Wang","orcid":"https://orcid.org/0000-0003-3369-219X"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xinrun Wang","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081745865","display_name":"Wanqi Xue","orcid":"https://orcid.org/0000-0002-1069-9105"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Wanqi Xue","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017743551","display_name":"Bo An","orcid":"https://orcid.org/0000-0002-7064-7438"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Bo An","raw_affiliation_strings":["School of Computer Science and Engineering, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4396,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61502347,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"3663","last_page":"3669"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11674","display_name":"Sports Analytics and Performance","score":0.9692000150680542,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9674999713897705,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.9182256460189819},{"id":"https://openalex.org/keywords/counterfactual-thinking","display_name":"Counterfactual thinking","score":0.5769938230514526},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5703079700469971},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5644199848175049},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5614843964576721},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.4558292031288147},{"id":"https://openalex.org/keywords/imperfect","display_name":"Imperfect","score":0.41437941789627075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33733463287353516},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.23203185200691223},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.22820991277694702},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19961285591125488},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.19882875680923462},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12650015950202942},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.08277073502540588}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.9182256460189819},{"id":"https://openalex.org/C108650721","wikidata":"https://www.wikidata.org/wiki/Q1783253","display_name":"Counterfactual thinking","level":2,"score":0.5769938230514526},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5703079700469971},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5644199848175049},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5614843964576721},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.4558292031288147},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.41437941789627075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33733463287353516},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.23203185200691223},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.22820991277694702},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19961285591125488},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.19882875680923462},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12650015950202942},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.08277073502540588},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/ijcai.2021/504","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2021/504","pdf_url":"https://www.ijcai.org/proceedings/2021/0504.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/ijcai.2021/504","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2021/504","pdf_url":"https://www.ijcai.org/proceedings/2021/0504.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","score":0.41999998688697815,"display_name":"Partnerships for the goals"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320327962","display_name":"Singapore Telecommunications Limited","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3189507281.pdf","grobid_xml":"https://content.openalex.org/works/W3189507281.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W62682045","https://openalex.org/W1528676759","https://openalex.org/W2006791053","https://openalex.org/W2103315867","https://openalex.org/W2106975967","https://openalex.org/W2113351146","https://openalex.org/W2123018439","https://openalex.org/W2151123669","https://openalex.org/W2187559597","https://openalex.org/W2574978968","https://openalex.org/W2620873683","https://openalex.org/W2741375793","https://openalex.org/W2741536312","https://openalex.org/W2904639101","https://openalex.org/W2963931057","https://openalex.org/W2964934024","https://openalex.org/W2966397236","https://openalex.org/W2994855394","https://openalex.org/W4256636565","https://openalex.org/W4285364563","https://openalex.org/W4288626409","https://openalex.org/W4289360601","https://openalex.org/W4295237430","https://openalex.org/W4295598622","https://openalex.org/W4312534390"],"related_works":["https://openalex.org/W1983202944","https://openalex.org/W2132624896","https://openalex.org/W2802467175","https://openalex.org/W2022564137","https://openalex.org/W2035984254","https://openalex.org/W4291127980","https://openalex.org/W2118206667","https://openalex.org/W633344313","https://openalex.org/W2970365960","https://openalex.org/W1531245405"],"abstract_inverted_index":{"In":[0],"many":[1],"real-world":[2],"scenarios,":[3],"a":[4,60,69,75,86,125,152,164],"team":[5],"of":[6,20,24,38,45,63,82,160,167,171],"agents":[7,84],"must":[8],"coordinate":[9],"with":[10,35,99],"each":[11],"other":[12],"to":[13,89,113,133,155],"compete":[14],"against":[15],"an":[16],"opponent.":[17],"The":[18],"challenge":[19],"solving":[21],"this":[22,56],"type":[23],"game":[25],"is":[26],"that":[27,73,177],"the":[28,36,43,46,91,97,103,108,114,118,135,139],"team's":[29],"joint":[30,76,161],"action":[31,77],"space":[32],"grows":[33],"exponentially":[34],"number":[37],"agents,":[39],"which":[40,150],"results":[41,175],"in":[42],"inefficiency":[44],"existing":[47,180],"algorithms,":[48],"e.g.,":[49],"Counterfactual":[50],"Regret":[51],"Minimization":[52],"(CFR).":[53],"To":[54,95],"address":[55],"problem,":[57],"we":[58,67,106,123,144],"propose":[59,68,124],"new":[61,70,147],"framework":[62],"CFR:":[64],"CFR-MIX.":[65],"Firstly,":[66],"strategy":[71,78],"representation":[72],"represents":[74],"using":[79],"individual":[80,100,172],"strategies":[81,101,112],"all":[83],"and":[85],"consistency":[87,109,115,136],"relationship":[88,110,116,137],"maintain":[90],"cooperation":[92],"between":[93,111,117,138],"agents.":[94],"compute":[96],"equilibrium":[98],"under":[102],"CFR":[104],"framework,":[105],"transform":[107],"cumulative":[119,130,140,157,168],"regret":[120,131,141,158,169],"values.":[121,142],"Furthermore,":[122],"novel":[126],"decomposition":[127],"method":[128],"over":[129],"values":[132,159,170],"guarantee":[134],"Finally,":[143],"introduce":[145],"our":[146],"algorithm":[148],"CFR-MIX":[149,178],"employs":[151],"mixing":[153],"layer":[154],"estimate":[156],"actions":[162],"as":[163],"non-linear":[165],"combination":[166],"actions.":[173],"Experimental":[174],"show":[176],"outperforms":[179],"algorithms":[181],"on":[182],"various":[183],"games":[184],"significantly.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}