{"id":"https://openalex.org/W2062563163","doi":"https://doi.org/10.1155/2013/879325","title":"Game Perspectives of DEA Models and Their Duals","display_name":"Game Perspectives of DEA Models and Their Duals","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2062563163","doi":"https://doi.org/10.1155/2013/879325","mag":"2062563163"},"language":"en","primary_location":{"id":"doi:10.1155/2013/879325","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/879325","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/879325.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/879325.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089090107","display_name":"Fang Xu","orcid":"https://orcid.org/0000-0002-0777-1911"},"institutions":[{"id":"https://openalex.org/I114218197","display_name":"Chinese Academy of Social Sciences","ror":"https://ror.org/05bxbmy32","country_code":"CN","type":"facility","lineage":["https://openalex.org/I114218197"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210135514","display_name":"Research Institute of Forestry Policy and Information","ror":"https://ror.org/044snpb24","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210128615","https://openalex.org/I4210134523","https://openalex.org/I4210135514"]},{"id":"https://openalex.org/I4210159876","display_name":"Institute of Physics","ror":"https://ror.org/05cvf7v30","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210159876"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fang Xu","raw_affiliation_strings":["Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080, China","Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080 China"],"raw_orcid":"https://orcid.org/0000-0002-0777-1911","affiliations":[{"raw_affiliation_string":"Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I4210135514","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080 China","institution_ids":["https://openalex.org/I4210159876","https://openalex.org/I114218197"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083974405","display_name":"Daqun Zhang","orcid":"https://orcid.org/0000-0002-1351-9691"},"institutions":[{"id":"https://openalex.org/I84392919","display_name":"Temple University","ror":"https://ror.org/00kx1jb78","country_code":"US","type":"education","lineage":["https://openalex.org/I84392919"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DaQun Zhang","raw_affiliation_strings":["Department of Accounting, Temple University, Philadelphia, PA 19122, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Accounting, Temple University, Philadelphia, PA 19122, USA","institution_ids":["https://openalex.org/I84392919"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077217484","display_name":"Guo-liang Yang","orcid":"https://orcid.org/0000-0001-9781-4446"},"institutions":[{"id":"https://openalex.org/I114218197","display_name":"Chinese Academy of Social Sciences","ror":"https://ror.org/05bxbmy32","country_code":"CN","type":"facility","lineage":["https://openalex.org/I114218197"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210135514","display_name":"Research Institute of Forestry Policy and Information","ror":"https://ror.org/044snpb24","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210128615","https://openalex.org/I4210134523","https://openalex.org/I4210135514"]},{"id":"https://openalex.org/I4210159876","display_name":"Institute of Physics","ror":"https://ror.org/05cvf7v30","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210159876"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"GuoLiang Yang","raw_affiliation_strings":["Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080, China","Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080, China","institution_ids":["https://openalex.org/I4210135514","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100080 China","institution_ids":["https://openalex.org/I4210159876","https://openalex.org/I114218197"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017938877","display_name":"Wenbin Liu","orcid":"https://orcid.org/0000-0003-0390-8455"},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"WenBin Liu","raw_affiliation_strings":["Kent Business School, University of Kent, Canterbury CT 7PE, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kent Business School, University of Kent, Canterbury CT 7PE, UK","institution_ids":["https://openalex.org/I20581793"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15042199,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9997000098228455,"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/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9997000098228455,"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/T11161","display_name":"Consumer Market Behavior and Pricing","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1406","display_name":"Marketing"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10841","display_name":"Economic and Environmental Valuation","score":0.9786999821662903,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.8297343850135803},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.6303525567054749},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.5700069069862366},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.564826250076294},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4369601011276245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4221174716949463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38382488489151},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3797655999660492},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36962902545928955},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.337066113948822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14952519536018372}],"concepts":[{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.8297343850135803},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6303525567054749},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.5700069069862366},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.564826250076294},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4369601011276245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4221174716949463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38382488489151},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3797655999660492},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36962902545928955},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.337066113948822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14952519536018372},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2013/879325","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/879325","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/879325.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394807449","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1394807449","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:879325","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/879325.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:36dc4db55bc646f794d9f62c120e5dc9","is_oa":true,"landing_page_url":"https://doaj.org/article/36dc4db55bc646f794d9f62c120e5dc9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"},{"id":"pmh:oai:kar.kent.ac.uk:40798","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/40798/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1155/2013/879325","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/879325","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/879325.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2062563163.pdf","grobid_xml":"https://content.openalex.org/works/W2062563163.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W87988210","https://openalex.org/W1982127619","https://openalex.org/W1998946919","https://openalex.org/W2005057945","https://openalex.org/W2005482717","https://openalex.org/W2012265316","https://openalex.org/W2017268155","https://openalex.org/W2017959480","https://openalex.org/W2048039127","https://openalex.org/W2052874123","https://openalex.org/W2055034726","https://openalex.org/W2076452041","https://openalex.org/W2129763896","https://openalex.org/W2138907550","https://openalex.org/W2144765793","https://openalex.org/W2732805988"],"related_works":["https://openalex.org/W2803931294","https://openalex.org/W2282604764","https://openalex.org/W2500870930","https://openalex.org/W2218535193","https://openalex.org/W4389370903","https://openalex.org/W2468739564","https://openalex.org/W2501065092","https://openalex.org/W1554758635","https://openalex.org/W2171981925","https://openalex.org/W2955320052"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"series":[3],"of":[4],"two-person":[5],"games,":[6],"which":[7],"lead":[8],"to":[9],"various":[10],"DEA":[11,17,39,53,60,66],"models.":[12,67],"The":[13],"relationship":[14,46],"between":[15,47],"the":[16,20,28,37,48],"models":[18,61],"and":[19,50,62],"games":[21,49],"is":[22],"explicit":[23,45],"in":[24],"our":[25],"setting,":[26],"although":[27],"Nash":[29],"equilibrium":[30],"solutions":[31],"do":[32],"not":[33],"generally":[34],"exist.":[35],"Besides":[36],"classic":[38],"models,":[40,54],"we":[41],"also":[42],"establish":[43],"an":[44],"some":[51],"extended":[52],"such":[55],"as":[56],"free":[57],"disposable":[58],"hull":[59],"\u201cnegative\u201d":[63],"or":[64],"\u201cinverted\u201d":[65]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}