{"id":"https://openalex.org/W4391021997","doi":"https://doi.org/10.1109/cdc49753.2023.10383475","title":"Differential Game with Mixed Strategies: A Weak Approximation Approach","display_name":"Differential Game with Mixed Strategies: A Weak Approximation Approach","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391021997","doi":"https://doi.org/10.1109/cdc49753.2023.10383475"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383475","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383475","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5019905578","display_name":"Tao Xu","orcid":"https://orcid.org/0000-0001-8254-7912"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"government","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Xu","raw_affiliation_strings":["Shanghai Jiao Tong University,Department of Automation","Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","Department of Automation, Shanghai Jiao Tong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University,Department of Automation","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]},{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040077369","display_name":"Xi Wang","orcid":"https://orcid.org/0000-0003-1872-5969"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"government","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang Xi","raw_affiliation_strings":["Shanghai Jiao Tong University,Department of Automation","Department of Automation, Shanghai Jiao Tong University","Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University,Department of Automation","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004668792","display_name":"Jianping He","orcid":"https://orcid.org/0000-0002-6253-7802"},"institutions":[{"id":"https://openalex.org/I1327237609","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934","country_code":"CN","type":"government","lineage":["https://openalex.org/I1327237609","https://openalex.org/I4210127390"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianping He","raw_affiliation_strings":["Shanghai Jiao Tong University,Department of Automation","Department of Automation, Shanghai Jiao Tong University","Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University,Department of Automation","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Department of Automation, Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China","institution_ids":["https://openalex.org/I1327237609"]}]}],"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":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"5216","last_page":"5221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9932000041007996,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T11031","display_name":"Game Theory and Applications","score":0.979200005531311,"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/stochastic-game","display_name":"Stochastic game","score":0.7158167958259583},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.6458860635757446},{"id":"https://openalex.org/keywords/strategy","display_name":"Strategy","score":0.5744062066078186},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5619056224822998},{"id":"https://openalex.org/keywords/symmetric-game","display_name":"Symmetric game","score":0.4987449645996094},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49691346287727356},{"id":"https://openalex.org/keywords/normal-form-game","display_name":"Normal-form game","score":0.47487160563468933},{"id":"https://openalex.org/keywords/extensive-form-game","display_name":"Extensive-form game","score":0.4734860360622406},{"id":"https://openalex.org/keywords/screening-game","display_name":"Screening game","score":0.4693012535572052},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4667879343032837},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.4579732120037079},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.41614145040512085},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.4142873287200928},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.37335917353630066},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3613009452819824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32694998383522034},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.28009188175201416}],"concepts":[{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.7158167958259583},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.6458860635757446},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.5744062066078186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5619056224822998},{"id":"https://openalex.org/C93733245","wikidata":"https://www.wikidata.org/wiki/Q3770642","display_name":"Symmetric game","level":5,"score":0.4987449645996094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49691346287727356},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.47487160563468933},{"id":"https://openalex.org/C146930158","wikidata":"https://www.wikidata.org/wiki/Q656416","display_name":"Extensive-form game","level":4,"score":0.4734860360622406},{"id":"https://openalex.org/C167573328","wikidata":"https://www.wikidata.org/wiki/Q7439054","display_name":"Screening game","level":4,"score":0.4693012535572052},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4667879343032837},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.4579732120037079},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.41614145040512085},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.4142873287200928},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.37335917353630066},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3613009452819824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32694998383522034},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.28009188175201416},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383475","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383475","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1581842928","https://openalex.org/W1659904137","https://openalex.org/W1978500102","https://openalex.org/W2015553626","https://openalex.org/W2026994882","https://openalex.org/W2041700247","https://openalex.org/W2048917716","https://openalex.org/W2171564854","https://openalex.org/W2549252642","https://openalex.org/W2803785256","https://openalex.org/W2898866127","https://openalex.org/W2907920236","https://openalex.org/W2963177798","https://openalex.org/W3104028495","https://openalex.org/W4250750844","https://openalex.org/W6739826692","https://openalex.org/W6756528052"],"related_works":["https://openalex.org/W2910530315","https://openalex.org/W1643208677","https://openalex.org/W2085538682","https://openalex.org/W2089306405","https://openalex.org/W3125878904","https://openalex.org/W2391693198","https://openalex.org/W3144134336","https://openalex.org/W2160036449","https://openalex.org/W1629081884","https://openalex.org/W4391021997"],"abstract_inverted_index":{"This":[0],"paper":[1],"utilizes":[2],"the":[3,18,40,48,53,56,82,94,97,104,116,120,126,133,139],"weak":[4,83,134],"approximation":[5,84],"method":[6,85],"to":[7,20,86,92,137,149],"analyze":[8,138],"differential":[9,90],"games":[10,33],"that":[11,103],"involve":[12],"mixed":[13,49,65,98],"strategies.":[14],"Mixed":[15],"strategies":[16],"have":[17],"potential":[19],"produce":[21],"unique":[22],"strategic":[23],"behaviors,":[24],"whereas":[25],"traditional":[26],"models":[27],"and":[28,59,73,128,151],"tools":[29],"in":[30,69],"pure":[31],"strategy":[32,50,58,66,99],"cannot":[34],"be":[35,109],"directly":[36],"applied.":[37],"Based":[38],"on":[39,153],"stochastic":[41,89],"processes":[42],"with":[43,112],"independent":[44],"increments,":[45],"we":[46,80,124,145],"define":[47],"without":[51],"assuming":[52],"knowledge":[54],"of":[55,96,115,132,141],"opponents'":[57],"system":[60],"state.":[61],"However,":[62],"this":[63],"general":[64],"poses":[67],"challenges":[68],"evaluating":[70],"game":[71,74,91,136,142],"payoff":[72,106],"value.":[75,143],"To":[76],"overcome":[77],"these":[78],"challenges,":[79],"utilize":[81],"employ":[87],"a":[88],"characterize":[93],"dynamics":[95],"game.":[100],"We":[101],"demonstrate":[102],"game's":[105],"function":[107],"can":[108],"precisely":[110],"approximated":[111,135],"an":[113],"error":[114],"same":[117],"scale":[118],"as":[119],"step":[121],"size.":[122],"Furthermore,":[123],"estimate":[125],"upper":[127],"lower":[129],"value":[130],"functions":[131],"existence":[140],"Finally,":[144],"provide":[146],"numerical":[147],"examples":[148],"illustrate":[150],"elaborate":[152],"our":[154],"findings.":[155]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
