{"id":"https://openalex.org/W1985860878","doi":"https://doi.org/10.1155/2014/747596","title":"Game Cross Efficiency for Systems with Two-Stage Structures","display_name":"Game Cross Efficiency for Systems with Two-Stage Structures","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1985860878","doi":"https://doi.org/10.1155/2014/747596","mag":"1985860878"},"language":"en","primary_location":{"id":"doi:10.1155/2014/747596","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/747596","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/747596.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/2014/747596.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019929472","display_name":"Chaoqun Ma","orcid":"https://orcid.org/0000-0001-5387-7357"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chaoqun Ma","raw_affiliation_strings":["School of Business Administration, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101739717","display_name":"Debin Liu","orcid":"https://orcid.org/0000-0002-5402-5751"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Debin Liu","raw_affiliation_strings":["School of Business Administration, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101679296","display_name":"Zhongbao Zhou","orcid":"https://orcid.org/0000-0002-6233-0422"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongbao Zhou","raw_affiliation_strings":["School of Business Administration, Hunan University, Changsha 410082, China"],"raw_orcid":"https://orcid.org/0000-0002-6233-0422","affiliations":[{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101859938","display_name":"Wei Zhao","orcid":"https://orcid.org/0000-0002-9186-3551"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhao","raw_affiliation_strings":["School of Business Administration, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100373250","display_name":"Wenbin Liu","orcid":"https://orcid.org/0000-0001-9369-9858"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"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":["CN","GB"],"is_corresponding":false,"raw_author_name":"Wenbin Liu","raw_affiliation_strings":["Kent Business School, University of Kent, Canterbury CT2 7PE, UK","School of Business Administration, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kent Business School, University of Kent, Canterbury CT2 7PE, UK","institution_ids":["https://openalex.org/I20581793"]},{"raw_affiliation_string":"School of Business Administration, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101739717"],"corresponding_institution_ids":["https://openalex.org/I16609230"],"apc_list":{"value":1130,"currency":"USD","value_usd":1130},"apc_paid":{"value":1130,"currency":"USD","value_usd":1130},"fwci":1.9571,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.86580863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10357","display_name":"Efficiency Analysis Using DEA","score":0.9995999932289124,"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":0.9995999932289124,"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/T11499","display_name":"ICT Impact and Policies","score":0.9674999713897705,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11161","display_name":"Consumer Market Behavior and Pricing","score":0.9333999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/data-envelopment-analysis","display_name":"Data envelopment analysis","score":0.8137282133102417},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.6744842529296875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6605105400085449},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5528091788291931},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5076843500137329},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4639999270439148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22417250275611877},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.12011480331420898},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.09728780388832092},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08305427432060242}],"concepts":[{"id":"https://openalex.org/C22088475","wikidata":"https://www.wikidata.org/wiki/Q647974","display_name":"Data envelopment analysis","level":2,"score":0.8137282133102417},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.6744842529296875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6605105400085449},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5528091788291931},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5076843500137329},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4639999270439148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22417250275611877},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.12011480331420898},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.09728780388832092},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08305427432060242}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2014/747596","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/747596","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/747596.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/1412177642","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1412177642","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:747596","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/747596.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:53a73b2ab3dd47a6bb570dd3d72e07ee","is_oa":true,"landing_page_url":"https://doaj.org/article/53a73b2ab3dd47a6bb570dd3d72e07ee","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 2014 (2014)","raw_type":"article"},{"id":"pmh:oai:kar.kent.ac.uk:40799","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/40799/","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:10.1155/2014/747596","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/747596","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/747596.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G3433888155","display_name":"\u4e0d\u786e\u5b9a\u6761\u4ef6\u4e0b\u7684\u7f51\u7edcDEA\u6a21\u578b\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"71371067","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3945766690","display_name":"\u57fa\u4e8e\u8d1d\u53f6\u65af\u7f51\u7edc\u7684\u590d\u6742\u7cfb\u7edf\u5b89\u5168\u98ce\u9669\u8bc4\u4f30\u65b9\u6cd5\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"70901024","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1985860878.pdf","grobid_xml":"https://content.openalex.org/works/W1985860878.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1966205558","https://openalex.org/W1969205463","https://openalex.org/W1988825474","https://openalex.org/W1993147828","https://openalex.org/W1996475019","https://openalex.org/W1997084088","https://openalex.org/W2012651708","https://openalex.org/W2021951270","https://openalex.org/W2022628441","https://openalex.org/W2022679355","https://openalex.org/W2024699854","https://openalex.org/W2029334685","https://openalex.org/W2029369144","https://openalex.org/W2044298016","https://openalex.org/W2051008436","https://openalex.org/W2061731337","https://openalex.org/W2068572713","https://openalex.org/W2069473059","https://openalex.org/W2074689476","https://openalex.org/W2076452041","https://openalex.org/W2085339553","https://openalex.org/W2090849644","https://openalex.org/W2094366331","https://openalex.org/W2095569416","https://openalex.org/W2122672261","https://openalex.org/W2139217221","https://openalex.org/W2141532588","https://openalex.org/W2156577211","https://openalex.org/W2167493478","https://openalex.org/W2363361506"],"related_works":["https://openalex.org/W2801360836","https://openalex.org/W2120745168","https://openalex.org/W2736559621","https://openalex.org/W2352291457","https://openalex.org/W2360317231","https://openalex.org/W4378625608","https://openalex.org/W2126538897","https://openalex.org/W2277194173","https://openalex.org/W1997433734","https://openalex.org/W3000540828"],"abstract_inverted_index":{"Data":[0],"envelopment":[1],"analysis":[2],"(DEA)":[3],"is":[4,43,116,127],"a":[5,105,110,168],"nonparametric":[6],"approach":[7],"for":[8,136,173],"measuring":[9],"the":[10,25,28,32,36,39,46,58,65,74,119,132,137,144,150,162],"relative":[11],"efficiencies":[12,59,67,84,135],"of":[13,48,60,68,87,121,152],"peer":[14],"decision-making":[15],"units":[16],"(DMUs).":[17],"For":[18],"systems":[19,69,139],"with":[20,70],"two-stage":[21,71],"structures,":[22],"where":[23],"all":[24],"outputs":[26],"from":[27,118],"first":[29],"stage":[30],"are":[31],"only":[33],"inputs":[34],"to":[35,56,79,90,108,130,148,167],"second":[37],"stage,":[38],"centralized":[40,75],"model,":[41],"which":[42,115],"based":[44],"on":[45,98],"concept":[47],"cooperative":[49],"game":[50,106,133,146,163],"theory,":[51],"has":[52],"been":[53],"widely":[54],"used":[55],"examine":[57],"such":[61],"systems.":[62],"We":[63,142],"define":[64],"cross":[66,83,112,134,171],"structures.":[72],"Since":[73],"model":[76,107,147,164],"may":[77],"lead":[78,166],"multiple":[80],"and":[81,85,100,140],"unacceptable":[82],"rankings":[86],"DMUs":[88],"due":[89],"its":[91],"high":[92],"flexibility":[93],"in":[94],"choosing":[95],"optimal":[96],"weights":[97],"input":[99],"output":[101],"factors,":[102],"we":[103],"develop":[104],"obtain":[109,131],"unique":[111,169],"efficiency":[113,172],"measure,":[114],"constructed":[117],"perspective":[120],"noncooperative":[122],"game.":[123],"An":[124],"iterative":[125],"algorithm":[126],"then":[128],"proposed":[129,145],"overall":[138],"subsystems.":[141],"use":[143],"evaluate":[149],"performance":[151],"top":[153],"30":[154],"US":[155],"commercial":[156],"banks.":[157],"The":[158],"results":[159],"show":[160],"that":[161],"can":[165],"reasonable":[170],"each":[174],"DMU.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
