{"id":"https://openalex.org/W2101010482","doi":"https://doi.org/10.1109/tevc.2015.2490076","title":"Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games","display_name":"Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games","publication_year":2015,"publication_date":"2015-10-13","ids":{"openalex":"https://openalex.org/W2101010482","doi":"https://doi.org/10.1109/tevc.2015.2490076","mag":"2101010482"},"language":"en","primary_location":{"id":"doi:10.1109/tevc.2015.2490076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2015.2490076","pdf_url":null,"source":{"id":"https://openalex.org/S93787993","display_name":"IEEE Transactions on Evolutionary Computation","issn_l":"1089-778X","issn":["1089-778X","1941-0026"],"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 Evolutionary Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://nottingham-repository.worktribe.com/output/764047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058225357","display_name":"Jiawei Li","orcid":"https://orcid.org/0000-0003-4685-2615"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jiawei Li","raw_affiliation_strings":["Automated Scheduling, Optimization, and Planning Research Group, School of Computer Science, University of Nottingham, Nottingham, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automated Scheduling, Optimization, and Planning Research Group, School of Computer Science, University of Nottingham, Nottingham, U.K","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074319022","display_name":"Graham Kendall","orcid":"https://orcid.org/0000-0003-2006-5103"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]},{"id":"https://openalex.org/I155043079","display_name":"University of Nottingham Malaysia Campus","ror":"https://ror.org/04mz9mt17","country_code":"MY","type":"education","lineage":["https://openalex.org/I142263535","https://openalex.org/I155043079"]}],"countries":["GB","MY"],"is_corresponding":false,"raw_author_name":"Graham Kendall","raw_affiliation_strings":["Automated Scheduling, Optimization, and Planning Research Group, School of Computer Science, University of Nottingham, Nottingham, U.K","School of Computer Science, University of Nottingham, Malaysia Campus, Jalan Broga, Semenyih, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automated Scheduling, Optimization, and Planning Research Group, School of Computer Science, University of Nottingham, Nottingham, U.K","institution_ids":["https://openalex.org/I142263535"]},{"raw_affiliation_string":"School of Computer Science, University of Nottingham, Malaysia Campus, Jalan Broga, Semenyih, Malaysia","institution_ids":["https://openalex.org/I155043079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091177679","display_name":"Robert John","orcid":"https://orcid.org/0000-0002-2341-9993"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robert John","raw_affiliation_strings":["Automated Scheduling, Optimization, and Planning Research Group, School of Computer Science, University of Nottingham, Nottingham, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automated Scheduling, Optimization, and Planning Research Group, School of Computer Science, University of Nottingham, Nottingham, U.K","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.7739,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.97980979,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"3","first_page":"460","last_page":"469"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9994000196456909,"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":0.9994000196456909,"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/T11031","display_name":"Game Theory and Applications","score":0.9966999888420105,"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/T10646","display_name":"Experimental Behavioral Economics Studies","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"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/nash-equilibrium","display_name":"Nash equilibrium","score":0.8344286680221558},{"id":"https://openalex.org/keywords/folk-theorem","display_name":"Folk theorem","score":0.7314366102218628},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.6373023986816406},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.61305171251297},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6058698892593384},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.5870817303657532},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5720003247261047},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.5718501806259155},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.5686841607093811},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.564305305480957},{"id":"https://openalex.org/keywords/evolutionarily-stable-strategy","display_name":"Evolutionarily stable strategy","score":0.5116556286811829},{"id":"https://openalex.org/keywords/minimax-theorem","display_name":"Minimax theorem","score":0.5007038116455078},{"id":"https://openalex.org/keywords/normal-form-game","display_name":"Normal-form game","score":0.49480313062667847},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4756992757320404},{"id":"https://openalex.org/keywords/symmetric-equilibrium","display_name":"Symmetric equilibrium","score":0.4691635072231293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.460943341255188},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.4533325135707855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40120795369148254}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8344286680221558},{"id":"https://openalex.org/C21603316","wikidata":"https://www.wikidata.org/wiki/Q650738","display_name":"Folk theorem","level":5,"score":0.7314366102218628},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.6373023986816406},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.61305171251297},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6058698892593384},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.5870817303657532},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5720003247261047},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.5718501806259155},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.5686841607093811},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.564305305480957},{"id":"https://openalex.org/C2519700","wikidata":"https://www.wikidata.org/wiki/Q1069992","display_name":"Evolutionarily stable strategy","level":3,"score":0.5116556286811829},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.5007038116455078},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.49480313062667847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4756992757320404},{"id":"https://openalex.org/C93979843","wikidata":"https://www.wikidata.org/wiki/Q7661306","display_name":"Symmetric equilibrium","level":5,"score":0.4691635072231293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.460943341255188},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.4533325135707855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40120795369148254},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tevc.2015.2490076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tevc.2015.2490076","pdf_url":null,"source":{"id":"https://openalex.org/S93787993","display_name":"IEEE Transactions on Evolutionary Computation","issn_l":"1089-778X","issn":["1089-778X","1941-0026"],"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 Evolutionary Computation","raw_type":"journal-article"},{"id":"pmh:oai:dspace.stir.ac.uk:1893/23314","is_oa":false,"landing_page_url":"http://hdl.handle.net/1893/23314","pdf_url":null,"source":{"id":"https://openalex.org/S4306400268","display_name":"Stirling Online Research Repository (University of Stirling)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12093191","host_organization_name":"University of Stirling","host_organization_lineage":["https://openalex.org/I12093191"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:eprints.nottingham.ac.uk:30423","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7296643","pdf_url":null,"source":{"id":"https://openalex.org/S4306402014","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:764047","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/764047","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"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":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:nottingham-repository.worktribe.com:764047","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/764047","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"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":"","raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6414137052","display_name":null,"funder_award_id":"EP/H000968/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7122244894","display_name":"Towards More Effective Computational Search","funder_award_id":"EP/H000968/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W40063797","https://openalex.org/W1415442047","https://openalex.org/W1499339896","https://openalex.org/W1600069961","https://openalex.org/W1960351623","https://openalex.org/W1967829443","https://openalex.org/W1970404295","https://openalex.org/W1972512895","https://openalex.org/W1976450472","https://openalex.org/W1979025384","https://openalex.org/W1979505449","https://openalex.org/W1988769349","https://openalex.org/W1990870166","https://openalex.org/W1997323965","https://openalex.org/W1997897041","https://openalex.org/W2000705537","https://openalex.org/W2023176958","https://openalex.org/W2026177035","https://openalex.org/W2051773680","https://openalex.org/W2053845340","https://openalex.org/W2056837943","https://openalex.org/W2060855831","https://openalex.org/W2061371531","https://openalex.org/W2062663664","https://openalex.org/W2063928388","https://openalex.org/W2068167410","https://openalex.org/W2071047902","https://openalex.org/W2078097723","https://openalex.org/W2080286264","https://openalex.org/W2083639782","https://openalex.org/W2097374210","https://openalex.org/W2102759796","https://openalex.org/W2103315867","https://openalex.org/W2105834378","https://openalex.org/W2108238158","https://openalex.org/W2119458064","https://openalex.org/W2120593719","https://openalex.org/W2121180068","https://openalex.org/W2124191651","https://openalex.org/W2126580421","https://openalex.org/W2127268174","https://openalex.org/W2127808790","https://openalex.org/W2132099021","https://openalex.org/W2139774323","https://openalex.org/W2140790422","https://openalex.org/W2153029769","https://openalex.org/W2171779188","https://openalex.org/W2292587149","https://openalex.org/W2330024298","https://openalex.org/W2331296304","https://openalex.org/W2490944349","https://openalex.org/W2493238591","https://openalex.org/W3122516856","https://openalex.org/W4234761190","https://openalex.org/W4250744658","https://openalex.org/W4251841679","https://openalex.org/W6635605672","https://openalex.org/W6675509861"],"related_works":["https://openalex.org/W1833660299","https://openalex.org/W2166366941","https://openalex.org/W2092374696","https://openalex.org/W1554758635","https://openalex.org/W282191634","https://openalex.org/W1988732867","https://openalex.org/W4301347782","https://openalex.org/W1667857601","https://openalex.org/W1853631319","https://openalex.org/W2101010482"],"abstract_inverted_index":{"Stability":[0],"analysis":[1],"is":[2,56,90,116],"an":[3,57,128],"important":[4],"research":[5],"direction":[6],"in":[7,46,84],"evolutionary":[8,70],"game":[9,45],"theory.":[10],"Evolutionarily":[11],"stable":[12,71,140],"states":[13,72,141],"have":[14,103],"a":[15,65,78,93,133],"close":[16],"relationship":[17],"with":[18],"Nash":[19,50,82],"equilibria":[20,115],"of":[21,43,81,95,146,161],"repeated":[22,85],"games,":[23,151],"which":[24],"are":[25,124,157],"characterized":[26],"by":[27,92,159],"the":[28,33,40,44,53,75,113,119,138,143,153,162],"folk":[29,34],"theorem.":[30],"When":[31],"applying":[32],"theorem,":[35],"one":[36],"needs":[37],"to":[38,48,68,106,136],"compute":[39,69,137],"minimax":[41,54,120],"profile":[42,55],"order":[47],"find":[49],"equilibria.":[51],"Computing":[52,112],"NP-hard":[58],"problem.":[59],"In":[60],"this":[61,130],"paper,":[62],"we":[63],"investigate":[64],"new":[66,79],"methodology":[67],"based":[73],"on":[74],"level-k":[76,88,114],"equilibrium,":[77],"refinement":[80],"equilibrium":[83,89],"games.":[86,149],"A":[87],"implemented":[91],"group":[94],"players":[96],"who":[97,102],"adopt":[98],"reactive":[99],"strategies":[100,110,123],"and":[101,122,142],"no":[104],"incentive":[105],"deviate":[107],"from":[108],"their":[109],"simultaneously.":[111],"tractable":[117,134],"because":[118],"payoffs":[121],"not":[125],"needed.":[126],"As":[127],"application,":[129],"paper":[131],"develops":[132],"algorithm":[135],"evolutionarily":[139],"Pareto":[144],"front":[145],"n-player":[147],"symmetric":[148],"Three":[150],"including":[152],"iterated":[154],"prisoner's":[155],"dilemma,":[156],"analyzed":[158],"means":[160],"proposed":[163],"methodology.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}