{"id":"https://openalex.org/W3176430832","doi":"https://doi.org/10.1007/978-3-030-79416-3_1","title":"Computational Complexity of Multi-player Evolutionarily Stable Strategies","display_name":"Computational Complexity of Multi-player Evolutionarily Stable Strategies","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3176430832","doi":"https://doi.org/10.1007/978-3-030-79416-3_1","mag":"3176430832"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-79416-3_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-79416-3_1","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://pure.au.dk/portal/en/publications/9d3bcba6-a688-40f0-91c5-b17a876141de","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013751546","display_name":"Manon Blanc","orcid":null},"institutions":[{"id":"https://openalex.org/I11559806","display_name":"\u00c9cole Normale Sup\u00e9rieure Paris-Saclay","ror":"https://ror.org/00hx6zz33","country_code":"FR","type":"education","lineage":["https://openalex.org/I11559806","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]},{"id":"https://openalex.org/I4210150317","display_name":"Laboratoire de Biologie et Pharmacologie Appliqu\u00e9e","ror":"https://ror.org/03njrcx45","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210096427","https://openalex.org/I4210150317"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Manon Blanc","raw_affiliation_strings":["ENS Paris-Saclay, Gif-Sur-Yvette, France","ENS Paris Saclay - Ecole Normale Sup\u00e9rieure  Paris-Saclay (4 avenue des Sciences, 91190 Gif-sur-Yvette - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENS Paris-Saclay, Gif-Sur-Yvette, France","institution_ids":["https://openalex.org/I4210128565"]},{"raw_affiliation_string":"ENS Paris Saclay - Ecole Normale Sup\u00e9rieure  Paris-Saclay (4 avenue des Sciences, 91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4210150317","https://openalex.org/I29607241","https://openalex.org/I11559806"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055834958","display_name":"Kristoffer Arnsfelt Hansen","orcid":"https://orcid.org/0000-0002-1155-8072"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Kristoffer Arnsfelt Hansen","raw_affiliation_strings":["Aarhus University, Aarhus, Denmark","Aarhus University [Aarhus] (Nordre Ringgade 1 DK-8000 Aarhus C - Denmark)"],"raw_orcid":"https://orcid.org/0000-0002-1155-8072","affiliations":[{"raw_affiliation_string":"Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]},{"raw_affiliation_string":"Aarhus University [Aarhus] (Nordre Ringgade 1 DK-8000 Aarhus C - Denmark)","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013751546"],"corresponding_institution_ids":["https://openalex.org/I11559806","https://openalex.org/I29607241","https://openalex.org/I4210128565","https://openalex.org/I4210150317"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.7181,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69884031,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9984999895095825,"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/T11031","display_name":"Game Theory and Applications","score":0.9970999956130981,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9670000076293945,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.7088085412979126},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6329646110534668},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.6152960062026978},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.515403151512146},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.49618038535118103},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4932343363761902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4899229407310486},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.481740266084671},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4422631561756134},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.4327358603477478},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40124964714050293},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3805687427520752},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20578956604003906},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13257989287376404},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0578477680683136}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.7088085412979126},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6329646110534668},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.6152960062026978},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.515403151512146},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.49618038535118103},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4932343363761902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4899229407310486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.481740266084671},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4422631561756134},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.4327358603477478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40124964714050293},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3805687427520752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20578956604003906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13257989287376404},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0578477680683136},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-030-79416-3_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-79416-3_1","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:pure.atira.dk:openaire/9d3bcba6-a688-40f0-91c5-b17a876141de","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/9d3bcba6-a688-40f0-91c5-b17a876141de","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Blanc, M & Hansen, K A 2021, Computational Complexity of Multi-player Evolutionarily Stable Strategies. in R Santhanam & D Musatov (eds), Computer Science \u2013 Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings : 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28\u2013July 2, 2021, Proceedings. Springer, Lecture Notes in Computer Science, vol. 12730, pp. 1-17, 16th International Computer Science Symposium in Russia , Sochi, Russian Federation, 28/06/2021. https://doi.org/10.1007/978-3-030-79416-31","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-04259372v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04259372","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CSR 2021, Jun 2021, Sochi, Russia. pp.1-17, ⟨10.1007/978-3-030-79416-3_1⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/9d3bcba6-a688-40f0-91c5-b17a876141de","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/9d3bcba6-a688-40f0-91c5-b17a876141de","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Blanc, M & Hansen, K A 2021, Computational Complexity of Multi-player Evolutionarily Stable Strategies. in R Santhanam & D Musatov (eds), Computer Science \u2013 Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings : 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russia, June 28\u2013July 2, 2021, Proceedings. Springer, Lecture Notes in Computer Science, vol. 12730, pp. 1-17, 16th International Computer Science Symposium in Russia , Sochi, Russian Federation, 28/06/2021. https://doi.org/10.1007/978-3-030-79416-31","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W41260695","https://openalex.org/W94985437","https://openalex.org/W144370434","https://openalex.org/W592569499","https://openalex.org/W1483023182","https://openalex.org/W1547662725","https://openalex.org/W1560512928","https://openalex.org/W1967829443","https://openalex.org/W1968620083","https://openalex.org/W2013815105","https://openalex.org/W2028798910","https://openalex.org/W2033259331","https://openalex.org/W2040721698","https://openalex.org/W2067754486","https://openalex.org/W2071846104","https://openalex.org/W2077856214","https://openalex.org/W2080928066","https://openalex.org/W2101230787","https://openalex.org/W2105973197","https://openalex.org/W2111235650","https://openalex.org/W2130164058","https://openalex.org/W2131662609","https://openalex.org/W2292587149","https://openalex.org/W2296078827","https://openalex.org/W2301555989","https://openalex.org/W2330024298","https://openalex.org/W2604467574","https://openalex.org/W2609177694","https://openalex.org/W2612212426","https://openalex.org/W2790462119","https://openalex.org/W2891099160","https://openalex.org/W2914643490","https://openalex.org/W2936093783","https://openalex.org/W2946395282","https://openalex.org/W2963575622","https://openalex.org/W2972563375","https://openalex.org/W3037386776","https://openalex.org/W4234761190","https://openalex.org/W4246714063","https://openalex.org/W4301168154"],"related_works":["https://openalex.org/W266537895","https://openalex.org/W1589381382","https://openalex.org/W270168689","https://openalex.org/W2086025566","https://openalex.org/W2461808546","https://openalex.org/W2082636129","https://openalex.org/W2000805093","https://openalex.org/W2075449032","https://openalex.org/W1702487489","https://openalex.org/W2132910148"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,69,80],"study":[4],"the":[5,35,39,59,63,72,100,104,108],"computational":[6],"complexity":[7,78],"of":[8,24,38,48,51,62,93,121],"computing":[9],"an":[10,25,49,133],"evolutionary":[11],"stable":[12],"strategy":[13,131],"(ESS)":[14],"in":[15],"multi-player":[16,53],"symmetric":[17],"games.":[18],"For":[19],"two-player":[20],"games,":[21],"deciding":[22,46,127],"existence":[23,47],"ESS":[26,50,134],"is":[27,55,74,90,132,135],"complete":[28,136],"for":[29,76,137],"$$\\mathrm":[30],"{\\Sigma":[31],"}^\\mathrm":[32],"{p}_2$$":[33],",":[34,98],"second":[36,60],"level":[37,61],"polynomial":[40,65],"time":[41,66],"hierarchy.":[42,67],"We":[43],"show":[44,70],"that":[45,71,126],"a":[52,77,91,118,129],"game":[54],"closely":[56],"connected":[57],"to":[58],"real":[64],"Namely,":[68],"problem":[73],"hard":[75],"class":[79,102],"denote":[81],"as":[82],"$$\\exists":[83,94],"^\\mathrm":[84],"{D}\\cdot":[85],"\\forall":[86,95],"\\mathbb":[87,96,139],"{R}$$":[88,97,140],"and":[89],"member":[92],"where":[99],"former":[101],"restrict":[103],"latter":[105],"by":[106],"having":[107],"existentially":[109],"quantified":[110],"variables":[111],"be":[112],"Boolean":[113],"rather":[114],"then":[115],"real-valued.":[116],"As":[117],"special":[119],"case":[120],"our":[122],"results":[123],"it":[124],"follows":[125],"whether":[128],"given":[130],"$$\\forall":[138],".":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-07-05T00:00:00"}