{"id":"https://openalex.org/W3006529361","doi":"https://doi.org/10.1155/2020/6750805","title":"A Differential Game of Transboundary Pollution Control and Ecological Compensation in a River Basin","display_name":"A Differential Game of Transboundary Pollution Control and Ecological Compensation in a River Basin","publication_year":2020,"publication_date":"2020-02-12","ids":{"openalex":"https://openalex.org/W3006529361","doi":"https://doi.org/10.1155/2020/6750805","mag":"3006529361"},"language":"en","primary_location":{"id":"doi:10.1155/2020/6750805","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6750805","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6750805.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","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/complexity/2020/6750805.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013563840","display_name":"Yongxi Yi","orcid":"https://orcid.org/0000-0002-2479-4488"},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongxi Yi","raw_affiliation_strings":["School of Economics Management and Law, University of South China, Hengyang, China"],"affiliations":[{"raw_affiliation_string":"School of Economics Management and Law, University of South China, Hengyang, China","institution_ids":["https://openalex.org/I91935597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027958518","display_name":"Zhongjun Wei","orcid":"https://orcid.org/0000-0001-6942-1629"},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongjun Wei","raw_affiliation_strings":["School of Economics Management and Law, University of South China, Hengyang, China"],"affiliations":[{"raw_affiliation_string":"School of Economics Management and Law, University of South China, Hengyang, China","institution_ids":["https://openalex.org/I91935597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027478479","display_name":"Chunyan Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I91935597","display_name":"University of South China","ror":"https://ror.org/03mqfn238","country_code":"CN","type":"education","lineage":["https://openalex.org/I91935597"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chunyan Fu","raw_affiliation_strings":["School of Economics Management and Law, University of South China, Hengyang, China"],"affiliations":[{"raw_affiliation_string":"School of Economics Management and Law, University of South China, Hengyang, China","institution_ids":["https://openalex.org/I91935597"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027478479"],"corresponding_institution_ids":["https://openalex.org/I91935597"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":4.581,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9566149,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10471","display_name":"Climate Change Policy and Economics","score":0.9934999942779541,"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/T10471","display_name":"Climate Change Policy and Economics","score":0.9934999942779541,"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/T10841","display_name":"Economic and Environmental Valuation","score":0.991599977016449,"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/T10969","display_name":"Water resources management and optimization","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/upstream","display_name":"Upstream (networking)","score":0.8197234272956848},{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.7735810279846191},{"id":"https://openalex.org/keywords/investment","display_name":"Investment (military)","score":0.7278373837471008},{"id":"https://openalex.org/keywords/downstream","display_name":"Downstream (manufacturing)","score":0.6226159930229187},{"id":"https://openalex.org/keywords/compensation","display_name":"Compensation (psychology)","score":0.561010479927063},{"id":"https://openalex.org/keywords/environmental-science","display_name":"Environmental science","score":0.5398404598236084},{"id":"https://openalex.org/keywords/pollution","display_name":"Pollution","score":0.5310623645782471},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.5305655002593994},{"id":"https://openalex.org/keywords/upstream-and-downstream","display_name":"Upstream and downstream (DNA)","score":0.5176985263824463},{"id":"https://openalex.org/keywords/structural-basin","display_name":"Structural basin","score":0.5019989013671875},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.44877541065216064},{"id":"https://openalex.org/keywords/natural-resource-economics","display_name":"Natural resource economics","score":0.386050283908844},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.372546911239624},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3319167494773865},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.21255987882614136},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16893449425697327},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.10171005129814148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.0899716317653656},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08657380938529968},{"id":"https://openalex.org/keywords/operations-management","display_name":"Operations management","score":0.07933226227760315}],"concepts":[{"id":"https://openalex.org/C191172861","wikidata":"https://www.wikidata.org/wiki/Q7899321","display_name":"Upstream (networking)","level":2,"score":0.8197234272956848},{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.7735810279846191},{"id":"https://openalex.org/C27548731","wikidata":"https://www.wikidata.org/wiki/Q88272","display_name":"Investment (military)","level":3,"score":0.7278373837471008},{"id":"https://openalex.org/C2776207758","wikidata":"https://www.wikidata.org/wiki/Q5303302","display_name":"Downstream (manufacturing)","level":2,"score":0.6226159930229187},{"id":"https://openalex.org/C2780023022","wikidata":"https://www.wikidata.org/wiki/Q1338171","display_name":"Compensation (psychology)","level":2,"score":0.561010479927063},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.5398404598236084},{"id":"https://openalex.org/C521259446","wikidata":"https://www.wikidata.org/wiki/Q58734","display_name":"Pollution","level":2,"score":0.5310623645782471},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.5305655002593994},{"id":"https://openalex.org/C158980903","wikidata":"https://www.wikidata.org/wiki/Q7899329","display_name":"Upstream and downstream (DNA)","level":3,"score":0.5176985263824463},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.5019989013671875},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.44877541065216064},{"id":"https://openalex.org/C175605778","wikidata":"https://www.wikidata.org/wiki/Q3299701","display_name":"Natural resource economics","level":1,"score":0.386050283908844},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.372546911239624},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3319167494773865},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.21255987882614136},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16893449425697327},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.10171005129814148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.0899716317653656},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08657380938529968},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.07933226227760315},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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},{"id":"https://openalex.org/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/6750805","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6750805","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6750805.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:6750805","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/6750805.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:dbea3dd3e438484985233a24f57b171a","is_oa":true,"landing_page_url":"https://doaj.org/article/dbea3dd3e438484985233a24f57b171a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/6750805","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/6750805","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/6750805.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1390345611","display_name":null,"funder_award_id":"CX20190784","funder_id":"https://openalex.org/F4320326217","funder_display_name":"Hunan Provincial Innovation Foundation for Postgraduate"},{"id":"https://openalex.org/G1449776604","display_name":null,"funder_award_id":"2018D020","funder_id":"https://openalex.org/F4320326217","funder_display_name":"Hunan Provincial Innovation Foundation for Postgraduate"},{"id":"https://openalex.org/G2017088330","display_name":null,"funder_award_id":"2018JJ2335","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G2932611137","display_name":null,"funder_award_id":"18YBA368","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G3438785633","display_name":null,"funder_award_id":"2018JJ2335","funder_id":"https://openalex.org/F4320326217","funder_display_name":"Hunan Provincial Innovation Foundation for Postgraduate"},{"id":"https://openalex.org/G3688449794","display_name":null,"funder_award_id":"CX20190784","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G3743390778","display_name":null,"funder_award_id":"18YBA368","funder_id":"https://openalex.org/F4320326217","funder_display_name":"Hunan Provincial Innovation Foundation for Postgraduate"},{"id":"https://openalex.org/G8228485880","display_name":null,"funder_award_id":"2018D020","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320326217","display_name":"Hunan Provincial Innovation Foundation for Postgraduate","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3006529361.pdf","grobid_xml":"https://content.openalex.org/works/W3006529361.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1419724723","https://openalex.org/W1964137943","https://openalex.org/W1987821789","https://openalex.org/W1988293563","https://openalex.org/W1998235498","https://openalex.org/W1998446429","https://openalex.org/W2001971892","https://openalex.org/W2010282961","https://openalex.org/W2018222783","https://openalex.org/W2028827284","https://openalex.org/W2041080829","https://openalex.org/W2071517368","https://openalex.org/W2075784261","https://openalex.org/W2092659423","https://openalex.org/W2098442768","https://openalex.org/W2116950002","https://openalex.org/W2117386630","https://openalex.org/W2153509701","https://openalex.org/W2160588450","https://openalex.org/W2260854174","https://openalex.org/W2569132109","https://openalex.org/W2743355387","https://openalex.org/W2800487597","https://openalex.org/W2804209738","https://openalex.org/W2911153710","https://openalex.org/W2948361239","https://openalex.org/W2951644981","https://openalex.org/W2969276875","https://openalex.org/W2972862430","https://openalex.org/W2975402681","https://openalex.org/W3022673580","https://openalex.org/W3122084255","https://openalex.org/W3122992687"],"related_works":["https://openalex.org/W3113528484","https://openalex.org/W3124485524","https://openalex.org/W2241146542","https://openalex.org/W3125376000","https://openalex.org/W4322775356","https://openalex.org/W2088945351","https://openalex.org/W2373560751","https://openalex.org/W2348356937","https://openalex.org/W2738872473","https://openalex.org/W2212782980"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"a":[3,12,24,111],"Stackelberg":[4],"differential":[5],"game":[6],"between":[7],"an":[8,41,103],"upstream":[9,47,57,133],"region":[10,14,31,58,130],"and":[11,19,40,79,108,138],"downstream":[13,30,129],"for":[15],"transboundary":[16],"pollution":[17,51],"control":[18,52],"ecological":[20,42,105,155],"compensation":[21,43,106,156],"(EC)":[22],"in":[23,49],"river":[25],"basin.":[26],"Among":[27],"them,":[28],"the":[29,33,56,60,75,98,128,132,153,162],"as":[32,59],"leader":[34],"chooses":[35],"its":[36,63],"abatement":[37,64,88,125,145,159],"investment":[38,65,89,126,146],"level":[39,66],"rate":[44,107],"to":[45,67],"encourage":[46],"investing":[48],"water":[50],"firstly.":[53],"After":[54],"then,":[55],"follower":[61],"determines":[62],"maximize":[68],"welfare.":[69,164],"FFurthermore,":[70],"we":[71],"take":[72],"into":[73,131],"consideration":[74],"effects":[76],"of":[77,91,148],"efficiency-improving":[78,137],"cost-reducing":[80,139],"learning":[81,140],"by":[82,141],"doing":[83,142],"which":[84,110],"are":[85],"originated":[86],"from":[87,127,144],"activity":[90,147],"both":[92,149],"regions":[93,150],"simultaneously.":[94],"The":[95,136],"results":[96],"show":[97],"following.":[99],"(i)":[100],"There":[101],"is":[102],"optimal":[104,154],"under":[109],"Pareto":[112],"improvement":[113],"result":[114],"can":[115,151],"be":[116],"obtained.":[117],"(ii)":[118],"Carrying":[119],"out":[120],"EC":[121],"will":[122],"shift":[123],"some":[124],"region.":[134],"(iii)":[135],"derived":[143],"decrease":[152],"rate,":[157],"increase":[158],"investment,and":[160],"improve":[161],"social":[163]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}