{"id":"https://openalex.org/W4297200215","doi":"https://doi.org/10.1016/j.chaos.2022.112645","title":"Expanding the duopoly Stackelberg game with marginal costs into a multipoly game with lowering the burden of mathematical calculations: a numerical analysis","display_name":"Expanding the duopoly Stackelberg game with marginal costs into a multipoly game with lowering the burden of mathematical calculations: a numerical analysis","publication_year":2022,"publication_date":"2022-09-10","ids":{"openalex":"https://openalex.org/W4297200215","doi":"https://doi.org/10.1016/j.chaos.2022.112645"},"language":"en","primary_location":{"id":"doi:10.1016/j.chaos.2022.112645","doi":"https://doi.org/10.1016/j.chaos.2022.112645","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.chaos.2022.112645","pdf_url":null,"source":{"id":"https://openalex.org/S70718007","display_name":"Chaos Solitons & Fractals","issn_l":"0960-0779","issn":["0960-0779","1873-2887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chaos, Solitons &amp; Fractals","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5101660965","display_name":"Bo Yan","orcid":"https://orcid.org/0000-0001-6498-5767","observed_orcids":["https://orcid.org/0000-0001-6498-5767"]},"institutions":[{"id":"https://openalex.org/I206324368","display_name":"Shaoyang University","ror":"https://ror.org/03fx09x73","country_code":"CN","type":"education","lineage":["https://openalex.org/I206324368"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Yan","raw_affiliation_strings":["School of Information Engineering, Shaoyang University, Shaoyang 422000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Shaoyang University, Shaoyang 422000, China","institution_ids":["https://openalex.org/I206324368"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074123381","display_name":"Atefeh Ahmadi","orcid":"https://orcid.org/0000-0002-4475-1426","observed_orcids":["https://orcid.org/0000-0002-4475-1426"]},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Atefeh Ahmadi","raw_affiliation_strings":["Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073013989","display_name":"Mahtab Mehrabbeik","orcid":"https://orcid.org/0000-0003-0336-6553","observed_orcids":["https://orcid.org/0000-0003-0336-6553"]},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mahtab Mehrabbeik","raw_affiliation_strings":["Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057487605","display_name":"Karthikeyan Rajagopal","orcid":"https://orcid.org/0000-0003-2993-7182","observed_orcids":["https://orcid.org/0000-0003-2993-7182"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karthikeyan Rajagopal","raw_affiliation_strings":["Centre for Nonlinear Systems, Chennai Institute of Technology, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Nonlinear Systems, Chennai Institute of Technology, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075708894","display_name":"Shaobo He","orcid":"https://orcid.org/0000-0001-5190-4841","observed_orcids":["https://orcid.org/0000-0001-5190-4841"]},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaobo He","raw_affiliation_strings":["School of Physics and Electronics, Central South University, Changsha 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Central South University, Changsha 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014962078","display_name":"Sajad Jafari","orcid":"https://orcid.org/0000-0002-6845-7539","observed_orcids":["https://orcid.org/0000-0002-6845-7539"]},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Sajad Jafari","raw_affiliation_strings":["Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran","Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]},{"raw_affiliation_string":"Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014962078"],"corresponding_institution_ids":["https://openalex.org/I158248296"],"apc_list":{"value":2580,"currency":"USD","value_usd":2580},"apc_paid":null,"fwci":1.3153,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78772521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"164","issue":null,"first_page":"112645","last_page":"112645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.6904000043869019,"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/T11031","display_name":"Game Theory and Applications","score":0.6904000043869019,"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/T11043","display_name":"Merger and Competition Analysis","score":0.2971000075340271,"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/T10328","display_name":"Supply Chain and Inventory Management","score":0.002899999963119626,"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/stackelberg-game","display_name":"Stackelberg game","score":0.9639999866485596},{"id":"https://openalex.org/keywords/duopoly","display_name":"duopoly","score":0.9150000214576721},{"id":"https://openalex.org/keywords/marginal-cost","display_name":"marginal cost","score":0.6880000233650208},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.9070000052452087},{"id":"https://openalex.org/keywords/sequential-parameter-optimization","display_name":"sequential parameter optimization","score":0.6740000247955322},{"id":"https://openalex.org/keywords/total-profit-maximization","display_name":"total profit maximization","score":0.7279999852180481},{"id":"https://openalex.org/keywords/leader-follower-competition","display_name":"leader-follower competition","score":0.6119999885559082},{"id":"https://openalex.org/keywords/computational-cost-reduction","display_name":"computational complexity reduction","score":0.6439999938011169},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"curse of dimensionality","score":0.8109999895095825}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.8854342103004456},{"id":"https://openalex.org/C180456769","wikidata":"https://www.wikidata.org/wiki/Q750207","display_name":"Duopoly","level":3,"score":0.7192973494529724},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6637462377548218},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6399545073509216},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.5559727549552917},{"id":"https://openalex.org/C160343169","wikidata":"https://www.wikidata.org/wiki/Q968642","display_name":"Backward induction","level":3,"score":0.548676073551178},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.524408221244812},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5162205696105957},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.4945065677165985},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4896131157875061},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4665151834487915},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.43154674768447876},{"id":"https://openalex.org/C66887028","wikidata":"https://www.wikidata.org/wiki/Q382444","display_name":"Marginal cost","level":2,"score":0.4259242117404938},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.4158886671066284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3438568711280823},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.30154722929000854},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.18199479579925537},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.chaos.2022.112645","doi":"https://doi.org/10.1016/j.chaos.2022.112645","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.chaos.2022.112645","pdf_url":null,"source":{"id":"https://openalex.org/S70718007","display_name":"Chaos Solitons & Fractals","issn_l":"0960-0779","issn":["0960-0779","1873-2887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chaos, Solitons &amp; Fractals","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008244","doi":null,"is_oa":false,"landing_page_url":"http://www.sciencedirect.com/science/article/pii/S0960077922008244","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,"listed_in":[],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4881329600","display_name":null,"funder_award_id":"2021JJ40516","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G491069176","display_name":null,"funder_award_id":"2020JJ5767","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7306501644","display_name":null,"funder_award_id":"61901530","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"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W128489831","https://openalex.org/W1497811343","https://openalex.org/W1779364053","https://openalex.org/W1890965854","https://openalex.org/W1967438932","https://openalex.org/W2004682554","https://openalex.org/W2009828583","https://openalex.org/W2012826487","https://openalex.org/W2015876446","https://openalex.org/W2029191936","https://openalex.org/W2030647919","https://openalex.org/W2066111511","https://openalex.org/W2069787633","https://openalex.org/W2102711942","https://openalex.org/W2150541615","https://openalex.org/W2161013542","https://openalex.org/W2167812033","https://openalex.org/W2283191420","https://openalex.org/W2499486700","https://openalex.org/W2542067956","https://openalex.org/W2773751033","https://openalex.org/W2789490124","https://openalex.org/W2792654902","https://openalex.org/W2825428470","https://openalex.org/W2936949191","https://openalex.org/W2996491693","https://openalex.org/W3004652661","https://openalex.org/W3033224839","https://openalex.org/W3036482170","https://openalex.org/W3090687309","https://openalex.org/W3093395053","https://openalex.org/W3101224460","https://openalex.org/W3110115967","https://openalex.org/W3128253106","https://openalex.org/W3134882872","https://openalex.org/W3188987401","https://openalex.org/W4221002030","https://openalex.org/W4226016658","https://openalex.org/W4233769195","https://openalex.org/W4294576339"],"related_works":["https://openalex.org/W2543186300","https://openalex.org/W4389471100","https://openalex.org/W2590361768","https://openalex.org/W2792654902","https://openalex.org/W74565447","https://openalex.org/W4362601075","https://openalex.org/W7168276945","https://openalex.org/W2320049973","https://openalex.org/W2054136157","https://openalex.org/W7004857288"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2022-09-27T00:00:00"}
