{"id":"https://openalex.org/W1597985172","doi":"https://doi.org/10.1007/11427391_130","title":"Stochastic Nash Equilibrium with a Numerical Solution Method","display_name":"Stochastic Nash Equilibrium with a Numerical Solution Method","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1597985172","doi":"https://doi.org/10.1007/11427391_130","mag":"1597985172"},"language":"en","primary_location":{"id":"doi:10.1007/11427391_130","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11427391_130","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"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/A5008929688","display_name":"Jinwu Gao","orcid":"https://orcid.org/0000-0003-4806-927X"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinwu Gao","raw_affiliation_strings":["Uncertain Systems Laboratory, School of Information, Renmin University of China, Beijing, 100872, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Uncertain Systems Laboratory, School of Information, Renmin University of China, Beijing, 100872, China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yankui Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yankui Liu","raw_affiliation_strings":["College of Mathematics and Computer Science, Hebei University, Baoding, 071002, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Hebei University, Baoding, 071002, China","institution_ids":["https://openalex.org/I43337087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"811","last_page":"816"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9912999868392944,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9912999868392944,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9850999712944031,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9706000089645386,"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":0.8036445379257202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.760978102684021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.570833683013916},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.49701789021492004},{"id":"https://openalex.org/keywords/stochastic-neural-network","display_name":"Stochastic neural network","score":0.4853285849094391},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.45749956369400024},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.420947790145874},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.41245827078819275},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2185351550579071},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16040650010108948},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.13835567235946655},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.11931279301643372}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8036445379257202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.760978102684021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.570833683013916},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.49701789021492004},{"id":"https://openalex.org/C86582703","wikidata":"https://www.wikidata.org/wiki/Q7617824","display_name":"Stochastic neural network","level":4,"score":0.4853285849094391},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.45749956369400024},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.420947790145874},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.41245827078819275},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2185351550579071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16040650010108948},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.13835567235946655},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.11931279301643372}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11427391_130","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11427391_130","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1497256448","https://openalex.org/W1536009559","https://openalex.org/W1569917448","https://openalex.org/W1966061878","https://openalex.org/W1989036492","https://openalex.org/W1992677797","https://openalex.org/W2001475848","https://openalex.org/W2049606892","https://openalex.org/W2101867594","https://openalex.org/W2103496339","https://openalex.org/W2137983211","https://openalex.org/W2152150600","https://openalex.org/W2517271243","https://openalex.org/W2976265969","https://openalex.org/W3023540311","https://openalex.org/W3146803896"],"related_works":["https://openalex.org/W2803931294","https://openalex.org/W2282604764","https://openalex.org/W2569414037","https://openalex.org/W2500870930","https://openalex.org/W2218535193","https://openalex.org/W4389370903","https://openalex.org/W2468739564","https://openalex.org/W1554758635","https://openalex.org/W4302558842","https://openalex.org/W2171981925"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}