{"id":"https://openalex.org/W4296616977","doi":"https://doi.org/10.3390/e24101333","title":"Complex Dynamics of a Cournot Quantum Duopoly Game with Memory and Heterogeneous Players","display_name":"Complex Dynamics of a Cournot Quantum Duopoly Game with Memory and Heterogeneous Players","publication_year":2022,"publication_date":"2022-09-22","ids":{"openalex":"https://openalex.org/W4296616977","doi":"https://doi.org/10.3390/e24101333","pmid":"https://pubmed.ncbi.nlm.nih.gov/37420353"},"language":"en","primary_location":{"id":"doi:10.3390/e24101333","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24101333","pdf_url":"https://www.mdpi.com/1099-4300/24/10/1333/pdf?version=1663833832","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/10/1333/pdf?version=1663833832","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047443563","display_name":"Luis Garc\u00eda-P\u00e9rez","orcid":"https://orcid.org/0000-0003-0087-881X"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Luis Garcia-Perez","raw_affiliation_strings":["Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103203052","display_name":"Juan Grau-Climent","orcid":"https://orcid.org/0000-0002-1018-7265"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan Grau-Climent","raw_affiliation_strings":["Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-1018-7265","affiliations":[{"raw_affiliation_string":"Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016689644","display_name":"Ram\u00f3n Alonso\u2010Sanz","orcid":"https://orcid.org/0000-0002-4668-2858"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ramon Alonso-Sanz","raw_affiliation_strings":["Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019337230","display_name":"Juan Carlos Losada","orcid":"https://orcid.org/0000-0002-4373-603X"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan C. Losada","raw_affiliation_strings":["Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-4373-603X","affiliations":[{"raw_affiliation_string":"Complex Systems Group, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103203052"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.904,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71573991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"10","first_page":"1333","last_page":"1333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cournot-competition","display_name":"Cournot competition","score":0.7183005809783936},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.6956936717033386},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5943357944488525},{"id":"https://openalex.org/keywords/duopoly","display_name":"Duopoly","score":0.5711715221405029},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5278831720352173},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4607686996459961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4348580539226532},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.41887450218200684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38513660430908203},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3488866686820984},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1848336160182953},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11651173233985901}],"concepts":[{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.7183005809783936},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.6956936717033386},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5943357944488525},{"id":"https://openalex.org/C180456769","wikidata":"https://www.wikidata.org/wiki/Q750207","display_name":"Duopoly","level":3,"score":0.5711715221405029},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5278831720352173},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4607686996459961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4348580539226532},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41887450218200684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38513660430908203},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3488866686820984},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1848336160182953},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11651173233985901},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24101333","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24101333","pdf_url":"https://www.mdpi.com/1099-4300/24/10/1333/pdf?version=1663833832","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:37420353","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37420353","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:d95f762079ab4e2e97fb34c30da87789","is_oa":true,"landing_page_url":"https://doaj.org/article/d95f762079ab4e2e97fb34c30da87789","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":"Entropy, Vol 24, Iss 10, p 1333 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/10/1333/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24101333","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 10; Pages: 1333","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9600972","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9600972","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24101333","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24101333","pdf_url":"https://www.mdpi.com/1099-4300/24/10/1333/pdf?version=1663833832","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4296616977.pdf"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1972591289","https://openalex.org/W2009825172","https://openalex.org/W2019112050","https://openalex.org/W2044057173","https://openalex.org/W2070505816","https://openalex.org/W2102892532","https://openalex.org/W2127017105","https://openalex.org/W2156439224","https://openalex.org/W2780769457","https://openalex.org/W2785640805","https://openalex.org/W2793829449","https://openalex.org/W2947435389","https://openalex.org/W3038125555","https://openalex.org/W3038430009","https://openalex.org/W3096928883","https://openalex.org/W3102034668","https://openalex.org/W4205290842","https://openalex.org/W4206557594","https://openalex.org/W4296616977","https://openalex.org/W6747991652"],"related_works":["https://openalex.org/W1494754662","https://openalex.org/W1815186740","https://openalex.org/W2075268106","https://openalex.org/W2057294517","https://openalex.org/W4401667060","https://openalex.org/W2996496936","https://openalex.org/W2013271236","https://openalex.org/W3140326999","https://openalex.org/W2969940344","https://openalex.org/W2026482387"],"abstract_inverted_index":{"Previous":[0],"authors":[1],"tend":[2],"to":[3],"consider":[4],"a":[5,15,27,48,168,180,204],"certain":[6,205],"range":[7],"of":[8,10,39,65,77,105,118,140,143,157,162,164,170,187,201,229,239,241],"values":[9,161,228],"the":[11,45,54,63,75,78,82,88,95,100,107,116,128,133,137,141,149,172,175,185,188,193,199,208,230,233,237,242],"parameters":[12],"involved":[13],"in":[14,84,99,132,136,152,179,207],"game,":[16],"not":[17],"taking":[18],"into":[19],"account":[20],"other":[21,46],"possible":[22],"values.":[23,86],"In":[24,70],"this":[25,71,211],"article,":[26,212],"quantum":[28,55,108,234],"dynamical":[29],"Cournot":[30],"duopoly":[31],"game":[32],"with":[33,102,190,222],"memory":[34,103,202,231],"and":[35,44,62,81,219,236],"heterogeneous":[36],"players":[37],"(one":[38],"them":[40],"is":[41,51,92,110,120,124,130,197],"boundedly":[42,243],"rational":[43,244],"one,":[47],"naive":[49],"player)":[50],"studied,":[52],"where":[53],"entanglement":[56,109],"can":[57,67],"be":[58,68],"greater":[59,111,131],"than":[60,112,135],"one":[61,113],"speed":[64,117,142,163,238],"adjustment":[66,119,144,165,240],"negative.":[69,121],"context,":[72],"we":[73],"analyzed":[74],"behavior":[76,186],"local":[79,89],"stability":[80,96,129,158,176],"profit":[83,189],"those":[85],"Considering":[87],"stability,":[90],"it":[91,123,147],"observed":[93],"that":[94,127,198],"region":[97],"increases":[98],"model":[101],"regardless":[104],"whether":[106,115],"or":[114],"However,":[122],"also":[125],"shown":[126,196],"negative":[134],"positive":[138],"zone":[139],"and,":[145,166],"therefore,":[146],"improves":[148],"results":[150],"obtained":[151],"previous":[153],"experiments.":[154],"This":[155],"increase":[156],"enables":[159],"higher":[160],"as":[167],"result":[169],"that,":[171],"system":[173],"reaches":[174],"faster,":[177],"resulting":[178],"remarkable":[181],"economic":[182],"advantage.":[183],"Regarding":[184],"these":[191,214],"parameters,":[192],"principal":[194],"effect":[195],"application":[200],"causes":[203],"delay":[206],"dynamics.":[209],"Through":[210],"all":[213],"statements":[215],"are":[216],"analytically":[217],"proved":[218],"widely":[220],"supported":[221],"several":[223],"numerical":[224],"simulations,":[225],"using":[226],"different":[227],"factor,":[232],"entanglement,":[235],"player.":[245]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
