{"id":"https://openalex.org/W2808514714","doi":"https://doi.org/10.1134/s0005117918060139","title":"Equilibrium Trajectories in Dynamical Bimatrix Games with Average Integral Payoff Functionals","display_name":"Equilibrium Trajectories in Dynamical Bimatrix Games with Average Integral Payoff Functionals","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2808514714","doi":"https://doi.org/10.1134/s0005117918060139","mag":"2808514714"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117918060139","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117918060139","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote 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/A5080331211","display_name":"Nikolay A. Krasovskii","orcid":"https://orcid.org/0000-0003-4313-0799"},"institutions":[{"id":"https://openalex.org/I4210104969","display_name":"Ural State Agrarian University","ror":"https://ror.org/01kn8x502","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210104969"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"N. A. Krasovskii","raw_affiliation_strings":["Ural State Agrarian University, Yekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Ural State Agrarian University, Yekaterinburg, Russia","institution_ids":["https://openalex.org/I4210104969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057355901","display_name":"A.M. T\u00e4rasyev","orcid":"https://orcid.org/0000-0002-8366-9628"},"institutions":[{"id":"https://openalex.org/I4210105350","display_name":"N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/029fhmb28","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210105350","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I4210119369","display_name":"Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/02s4h3z39","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210119369"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. M. Tarasyev","raw_affiliation_strings":["Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia","institution_ids":["https://openalex.org/I4210105350","https://openalex.org/I4210119369"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080331211"],"corresponding_institution_ids":["https://openalex.org/I4210104969"],"apc_list":null,"apc_paid":null,"fwci":0.4235,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67694473,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"79","issue":"6","first_page":"1148","last_page":"1167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9975000023841858,"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":0.9975000023841858,"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":0.9952999949455261,"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/T12137","display_name":"Economic theories and models","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7674347758293152},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7001103162765503},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.6867576837539673},{"id":"https://openalex.org/keywords/replicator-equation","display_name":"Replicator equation","score":0.6756024360656738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.59577876329422},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5630471706390381},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.5626625418663025},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.5589162707328796},{"id":"https://openalex.org/keywords/risk-dominance","display_name":"Risk dominance","score":0.5429309606552124},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.5375307202339172},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.5270410180091858},{"id":"https://openalex.org/keywords/travelers-dilemma","display_name":"Traveler's dilemma","score":0.4723915755748749},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.4475826621055603},{"id":"https://openalex.org/keywords/evolutionary-game-theory","display_name":"Evolutionary game theory","score":0.4116831421852112},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3958754539489746},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.3948117196559906},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.3782121539115906}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7674347758293152},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7001103162765503},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.6867576837539673},{"id":"https://openalex.org/C50318809","wikidata":"https://www.wikidata.org/wiki/Q2145081","display_name":"Replicator equation","level":3,"score":0.6756024360656738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.59577876329422},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5630471706390381},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.5626625418663025},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.5589162707328796},{"id":"https://openalex.org/C22349654","wikidata":"https://www.wikidata.org/wiki/Q2039354","display_name":"Risk dominance","level":5,"score":0.5429309606552124},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.5375307202339172},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.5270410180091858},{"id":"https://openalex.org/C47993264","wikidata":"https://www.wikidata.org/wiki/Q1518456","display_name":"Traveler's dilemma","level":5,"score":0.4723915755748749},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.4475826621055603},{"id":"https://openalex.org/C20249471","wikidata":"https://www.wikidata.org/wiki/Q2298789","display_name":"Evolutionary game theory","level":3,"score":0.4116831421852112},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3958754539489746},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.3948117196559906},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.3782121539115906},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117918060139","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117918060139","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W257442556","https://openalex.org/W1552612980","https://openalex.org/W1578630563","https://openalex.org/W1590824230","https://openalex.org/W1968243381","https://openalex.org/W1970031354","https://openalex.org/W2005609532","https://openalex.org/W2086162313","https://openalex.org/W2109150831","https://openalex.org/W2264212190","https://openalex.org/W2299208487","https://openalex.org/W2749408143","https://openalex.org/W2913152358","https://openalex.org/W3046687426","https://openalex.org/W3144674976"],"related_works":["https://openalex.org/W1554758635","https://openalex.org/W4301347782","https://openalex.org/W1667857601","https://openalex.org/W3192122086","https://openalex.org/W1489279485","https://openalex.org/W1989380950","https://openalex.org/W3007764521","https://openalex.org/W2144905124","https://openalex.org/W3018272572","https://openalex.org/W2921671016"],"abstract_inverted_index":{"This":[0],"paper":[1,99],"considers":[2],"models":[3,166],"of":[4,14,23,29,48,65,80,89,106,116,142,176],"evolutionary":[5,72,107,165,183,195],"non-zero-sum":[6,81],"games":[7,83,184,196],"on":[8,56,113,203],"the":[9,21,43,57,62,71,87,90,101,114,117,126,132,137,143,168,177,186,192,198,204],"infinite":[10,58,205],"time":[11],"interval.":[12],"Methods":[13],"differential":[15,82],"game":[16,24,73],"theory":[17],"are":[18,38,50,84],"used":[19],"for":[20,42,70,86,146,182,194],"analysis":[22],"interactions":[25],"between":[26],"two":[27],"groups":[28,37],"participants.":[30],"We":[31,60],"assume":[32],"that":[33,124],"participants":[34],"in":[35,97,159],"these":[36],"controlled":[39],"by":[40],"signals":[41],"behavior":[44],"change.":[45],"The":[46,76,94],"payoffs":[47],"coalitions":[49],"defined":[51],"as":[52],"average":[53,187],"integral":[54,188],"functionals":[55,190,202],"horizon.":[59,206],"pose":[61],"design":[63],"problem":[64],"a":[66,174],"dynamical":[67,118,152,178],"Nash":[68,91,119,153,179],"equilibrium":[69,92,120,154,180],"under":[74],"consideration.":[75],"ideas":[77],"and":[78,104,130,164,191],"approaches":[79],"employed":[85],"determination":[88],"solutions.":[93],"results":[95,158],"derived":[96],"this":[98],"involve":[100],"dynamic":[102],"constructions":[103],"methods":[105],"games.":[108],"Much":[109],"attention":[110],"is":[111],"focused":[112],"formation":[115],"with":[121,167,185,197],"players":[122],"strategies":[123,150],"maximize":[125],"corresponding":[127],"payoff":[128,189,201],"functions":[129],"have":[131],"guaranteed":[133],"properties":[134],"according":[135],"to":[136,161],"minimax":[138,144],"approach.":[139],"An":[140],"application":[141],"approach":[145],"constructing":[147],"optimal":[148],"control":[149],"generates":[151],"trajectories":[155,181,193],"yielding":[156],"better":[157],"comparison":[160,175],"static":[162],"solutions":[163],"replicator":[169],"dynamics.":[170],"Finally,":[171],"we":[172],"make":[173],"global":[199],"terminal":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}