{"id":"https://openalex.org/W2290123495","doi":"https://doi.org/10.1109/cdc.2015.7402816","title":"Random time delays in evolutionary game dynamics","display_name":"Random time delays in evolutionary game dynamics","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2290123495","doi":"https://doi.org/10.1109/cdc.2015.7402816","mag":"2290123495"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7402816","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7402816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5015728051","display_name":"Nesrine Ben-Khalifa","orcid":null},"institutions":[{"id":"https://openalex.org/I198415970","display_name":"Universit\u00e9 d'Avignon et des Pays de Vaucluse","ror":"https://ror.org/00mfpxb84","country_code":"FR","type":"education","lineage":["https://openalex.org/I198415970"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Nesrine Ben-Khalifa","raw_affiliation_strings":["CER/LIA, University of Avignon, France"],"affiliations":[{"raw_affiliation_string":"CER/LIA, University of Avignon, France","institution_ids":["https://openalex.org/I198415970"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078537181","display_name":"Rachid El-Azouzi","orcid":"https://orcid.org/0000-0002-4756-0887"},"institutions":[{"id":"https://openalex.org/I198415970","display_name":"Universit\u00e9 d'Avignon et des Pays de Vaucluse","ror":"https://ror.org/00mfpxb84","country_code":"FR","type":"education","lineage":["https://openalex.org/I198415970"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rachid El-Azouzi","raw_affiliation_strings":["CER/LIA, University of Avignon, France"],"affiliations":[{"raw_affiliation_string":"CER/LIA, University of Avignon, France","institution_ids":["https://openalex.org/I198415970"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006338234","display_name":"Y\u00e9z\u00e9ka\u00ebl Hayel","orcid":"https://orcid.org/0000-0003-3891-3916"},"institutions":[{"id":"https://openalex.org/I198415970","display_name":"Universit\u00e9 d'Avignon et des Pays de Vaucluse","ror":"https://ror.org/00mfpxb84","country_code":"FR","type":"education","lineage":["https://openalex.org/I198415970"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yezekael Hayel","raw_affiliation_strings":["CER/LIA, University of Avignon, France"],"affiliations":[{"raw_affiliation_string":"CER/LIA, University of Avignon, France","institution_ids":["https://openalex.org/I198415970"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015728051"],"corresponding_institution_ids":["https://openalex.org/I198415970"],"apc_list":null,"apc_paid":null,"fwci":3.0739,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.93178326,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3840","last_page":"3845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/replicator-equation","display_name":"Replicator equation","score":0.7516680955886841},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.6546192169189453},{"id":"https://openalex.org/keywords/evolutionarily-stable-strategy","display_name":"Evolutionarily stable strategy","score":0.5907372236251831},{"id":"https://openalex.org/keywords/erlang","display_name":"Erlang (programming language)","score":0.5408587455749512},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5332778096199036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4672083258628845},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45972344279289246},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.45929592847824097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4403625726699829},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4384782910346985},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.43703755736351013},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4212532639503479},{"id":"https://openalex.org/keywords/evolutionary-dynamics","display_name":"Evolutionary dynamics","score":0.4118230938911438},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.37024009227752686},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33973801136016846},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.1697620451450348},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.11221513152122498},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10055536031723022},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07671099901199341},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06929594278335571}],"concepts":[{"id":"https://openalex.org/C50318809","wikidata":"https://www.wikidata.org/wiki/Q2145081","display_name":"Replicator equation","level":3,"score":0.7516680955886841},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6546192169189453},{"id":"https://openalex.org/C2519700","wikidata":"https://www.wikidata.org/wiki/Q1069992","display_name":"Evolutionarily stable strategy","level":3,"score":0.5907372236251831},{"id":"https://openalex.org/C82484044","wikidata":"https://www.wikidata.org/wiki/Q334879","display_name":"Erlang (programming language)","level":3,"score":0.5408587455749512},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5332778096199036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4672083258628845},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45972344279289246},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.45929592847824097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4403625726699829},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4384782910346985},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.43703755736351013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4212532639503479},{"id":"https://openalex.org/C171578705","wikidata":"https://www.wikidata.org/wiki/Q5418700","display_name":"Evolutionary dynamics","level":3,"score":0.4118230938911438},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.37024009227752686},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33973801136016846},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.1697620451450348},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.11221513152122498},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10055536031723022},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07671099901199341},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06929594278335571},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C42383842","wikidata":"https://www.wikidata.org/wiki/Q193076","display_name":"Functional programming","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2015.7402816","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7402816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1415442047","https://openalex.org/W1534391781","https://openalex.org/W1589370926","https://openalex.org/W1600821972","https://openalex.org/W1960351623","https://openalex.org/W1965818884","https://openalex.org/W1978497094","https://openalex.org/W1982843671","https://openalex.org/W2009465547","https://openalex.org/W2014172170","https://openalex.org/W2028798910","https://openalex.org/W2039346667","https://openalex.org/W2065643755","https://openalex.org/W2081827062","https://openalex.org/W2084015854","https://openalex.org/W2085728653","https://openalex.org/W2093187348","https://openalex.org/W2125904738","https://openalex.org/W4233991420","https://openalex.org/W4301046466"],"related_works":["https://openalex.org/W4206213492","https://openalex.org/W4241847945","https://openalex.org/W2007729092","https://openalex.org/W2786288004","https://openalex.org/W1973788147","https://openalex.org/W2079705272","https://openalex.org/W1593767881","https://openalex.org/W657685289","https://openalex.org/W2031837421","https://openalex.org/W3108987668"],"abstract_inverted_index":{"In":[0,27,54],"this":[1,55],"paper,":[2],"we":[3,8,57,96],"study":[4,58,111],"evolutionary":[5],"games":[6],"and":[7,43,93,99],"examine":[9],"the":[10,13,19,30,59,67,74,78,87,91,103,107,112],"stability":[11,105],"of":[12,48,61,86,106,114],"Evolutionarily":[14],"Stable":[15],"Strategy":[16],"(ESS)":[17],"in":[18,66],"continuous-time":[20],"replicator":[21,68],"dynamics":[22],"with":[23],"random":[24],"time":[25,64],"delays.":[26],"many":[28],"examples":[29],"interactions":[31],"between":[32],"individuals":[33],"take":[34,44],"place":[35],"instantaneously":[36],"but":[37],"their":[38],"impacts":[39],"are":[40],"not":[41],"immediate":[42],"a":[45],"certain":[46],"amount":[47],"time,":[49],"which":[50],"is":[51,80],"usually":[52],"random.":[53],"paper":[56],"effect":[60],"randomly":[62],"distributed":[63],"delays":[65],"dynamics.":[69],"We":[70,109],"show":[71],"that,":[72],"under":[73],"exponential":[75],"delay":[76],"distribution,":[77],"ESS":[79],"asymptotically":[81],"stable":[82],"for":[83,102],"any":[84],"value":[85],"rate":[88],"parameter.":[89],"For":[90],"uniform":[92],"Erlang":[94],"distributions,":[95],"derive":[97],"necessary":[98],"sufficient":[100],"conditions":[101],"asymptotic":[104],"ESS.":[108],"also":[110],"case":[113],"one":[115],"delayed":[116],"strategy.":[117]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}