{"id":"https://openalex.org/W3049088669","doi":"https://doi.org/10.1109/tac.2020.3016903","title":"Heterogeneous Mixed Populations of Best-Responders and Imitators: Equilibrium Convergence and Stability","display_name":"Heterogeneous Mixed Populations of Best-Responders and Imitators: Equilibrium Convergence and Stability","publication_year":2020,"publication_date":"2020-08-14","ids":{"openalex":"https://openalex.org/W3049088669","doi":"https://doi.org/10.1109/tac.2020.3016903","mag":"3049088669"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.3016903","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3016903","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","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/A5065960203","display_name":"Hien Le","orcid":"https://orcid.org/0000-0003-2625-4853"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Hien Le","raw_affiliation_strings":["Faculty of Science, University of Alberta, Edmonton, AB, Canada"],"raw_orcid":"https://orcid.org/0000-0003-2625-4853","affiliations":[{"raw_affiliation_string":"Faculty of Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057708120","display_name":"Pouria Ramazi","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pouria Ramazi","raw_affiliation_strings":["Faculty of Science, University of Alberta, Edmonton, AB, Canada"],"raw_orcid":"https://orcid.org/0000-0003-4906-0090","affiliations":[{"raw_affiliation_string":"Faculty of Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065960203"],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":1.8655,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.85611333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"66","issue":"8","first_page":"3475","last_page":"3488"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9973000288009644,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6823755502700806},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.6658227443695068},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.5764306783676147},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.48130834102630615},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4421652853488922},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39394092559814453},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3900381028652191},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.3710874617099762}],"concepts":[{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6823755502700806},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.6658227443695068},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.5764306783676147},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.48130834102630615},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4421652853488922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39394092559814453},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3900381028652191},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.3710874617099762},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2020.3016903","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3016903","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320313335","display_name":"Alberta Environment and Parks","ror":null},{"id":"https://openalex.org/F4320319946","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W126122231","https://openalex.org/W1567210078","https://openalex.org/W1600803418","https://openalex.org/W1965519096","https://openalex.org/W1974667806","https://openalex.org/W1984697813","https://openalex.org/W1995158831","https://openalex.org/W2019542451","https://openalex.org/W2037865913","https://openalex.org/W2062873261","https://openalex.org/W2080683849","https://openalex.org/W2090595403","https://openalex.org/W2098040364","https://openalex.org/W2101091128","https://openalex.org/W2105973197","https://openalex.org/W2107549081","https://openalex.org/W2125326611","https://openalex.org/W2130200473","https://openalex.org/W2136945893","https://openalex.org/W2137307267","https://openalex.org/W2140553733","https://openalex.org/W2146180268","https://openalex.org/W2146812417","https://openalex.org/W2155717945","https://openalex.org/W2155796078","https://openalex.org/W2156413779","https://openalex.org/W2163300930","https://openalex.org/W2163389019","https://openalex.org/W2166799025","https://openalex.org/W2168939936","https://openalex.org/W2169801145","https://openalex.org/W2269677234","https://openalex.org/W2289521416","https://openalex.org/W2336556411","https://openalex.org/W2540486267","https://openalex.org/W2556464320","https://openalex.org/W2567923580","https://openalex.org/W2743410234","https://openalex.org/W2783269601","https://openalex.org/W2783307664","https://openalex.org/W2804086666","https://openalex.org/W2806261144","https://openalex.org/W2915158806","https://openalex.org/W3008566380","https://openalex.org/W3011732401","https://openalex.org/W3033723009","https://openalex.org/W3049088669","https://openalex.org/W3123352023","https://openalex.org/W3124409068","https://openalex.org/W6682716126","https://openalex.org/W6751925346"],"related_works":["https://openalex.org/W2803931294","https://openalex.org/W4389370903","https://openalex.org/W2282604764","https://openalex.org/W1554758635","https://openalex.org/W2500870930","https://openalex.org/W4302558842","https://openalex.org/W1721270588","https://openalex.org/W2010679956","https://openalex.org/W2955320052","https://openalex.org/W4248623114"],"abstract_inverted_index":{"In":[0],"anticoordination":[1,68,163],"social":[2,69],"contexts":[3],"such":[4,119],"as":[5,57],"stock":[6],"selection,":[7],"resource":[8],"allocation,":[9],"and":[10,28,38,59,98,112,144,160,170,172,211,227,245],"crowd":[11],"dispersion,":[12],"an":[13,76,115,123,141,236],"individual":[14,81,218],"earns":[15],"more":[16],"if":[17,143,146],"the":[18,41,136,202,209,214,217,220,225,231],"opponents":[19],"adopt":[20],"her":[21,85],"opposite":[22],"strategy.":[23],"Based":[24],"on":[25,40],"their":[26,193,198,206,243],"experience":[27],"available":[29,36,167],"information,":[30],"individuals":[31,191],"may":[32],"either":[33],"evaluate":[34],"all":[35,239],"options":[37],"decide":[39],"most":[42],"profitable":[43],"one,":[44],"or":[45],"simply":[46],"mimic":[47],"successful":[48],"others.":[49],"These":[50],"two":[51,166],"types":[52,109],"of":[53,73,90,107,110,157,216],"decision-makers":[54],"are":[55],"known":[56],"best-responders":[58,74,159,200],"imitators,":[60],"respectively.":[61],"Previous":[62],"studies":[63],"have":[64],"shown":[65],"that":[66,178,204],"in":[67,186],"contexts,":[70],"a":[71,88,128,154,187],"population":[72,89,137,156,210,232],"reaches":[75,140],"equilibrium":[77,124,142],"state,":[78],"where":[79],"every":[80],"is":[82,92],"satisfied":[83],"with":[84,165],"decision,":[86],"but":[87],"imitators":[91,161,212],"quite":[93],"likely":[94],"to":[95,133,175,182,197,234],"never":[96],"settle":[97],"undergo":[99],"perpetual":[100],"fluctuations.":[101],"Most":[102],"real-world":[103],"populations,":[104],"however,":[105],"consist":[106],"both":[108,158],"individuals,":[111],"it":[113,147],"remains":[114],"open":[116],"problem":[117],"whether":[118],"mixed-populations":[120],"eventually":[121],"reach":[122],"state.":[125],"We":[126,223],"provide":[127],"sharp,":[129],"yet":[130],"simple":[131],"answer":[132],"this":[134],"question:":[135],"almost":[138],"surely":[139],"only":[145],"admits":[148],"one.":[149],"More":[150],"specifically,":[151],"we":[152],"study":[153],"well-mixed":[155],"playing":[162],"games":[164],"strategies,":[168],"cooperation":[169],"defection,":[171],"earning":[173,219],"according":[174],"payoff":[176],"matrices":[177],"can":[179],"be":[180],"unique":[181],"each":[183],"player,":[184],"resulting":[185],"heterogeneous":[188],"population.":[189],"The":[190],"update":[192],"strategies":[194],"asynchronously":[195],"accordingly":[196],"types:":[199],"choose":[201],"strategy":[203,215],"maximizes":[205],"payoffs":[207],"against":[208],"copy":[213],"highest":[221],"payoff.":[222],"find":[224],"necessary":[226],"sufficient":[228],"condition":[229],"for":[230],"dynamics":[233],"admit":[235],"equilibrium,":[237],"identify":[238],"possible":[240],"equilibria,":[241],"investigate":[242],"stability":[244],"perform":[246],"convergence":[247],"analysis.":[248]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}