{"id":"https://openalex.org/W2013869930","doi":"https://doi.org/10.1103/physreve.64.056138","title":"Continuum time limit and stationary states of the minority game","display_name":"Continuum time limit and stationary states of the minority game","publication_year":2001,"publication_date":"2001-10-30","ids":{"openalex":"https://openalex.org/W2013869930","doi":"https://doi.org/10.1103/physreve.64.056138","mag":"2013869930","pmid":"https://pubmed.ncbi.nlm.nih.gov/11736045"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.64.056138","doi":"https://doi.org/10.1103/physreve.64.056138","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.64.056138","pdf_url":null,"source":{"id":"https://openalex.org/S4210224030","display_name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","issn_l":"1063-651X","issn":["1063-651X","1095-3787","1538-4519"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cond-mat/0102257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051471901","display_name":"Matteo Marsili A","orcid":"https://orcid.org/0000-0001-9437-6989","observed_orcids":["https://orcid.org/0000-0001-9437-6989"]},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I4210163092","display_name":"Istituto Nazionale per la Fisica della Materia","ror":"https://ror.org/02kswma64","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210155236","https://openalex.org/I4210163092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Matteo Marsili","raw_affiliation_strings":["Istituto Nazionale per la Fisica della Materia (INFM), Trieste-SISSA Unit, Via Beirut 2-4, Trieste 34014, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto Nazionale per la Fisica della Materia (INFM), Trieste-SISSA Unit, Via Beirut 2-4, Trieste 34014, Italy","institution_ids":["https://openalex.org/I138549579","https://openalex.org/I4210163092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063789606","display_name":"Damien Challet","orcid":"https://orcid.org/0000-0001-5457-1077","observed_orcids":["https://orcid.org/0000-0001-5457-1077"]},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210163092","display_name":"Istituto Nazionale per la Fisica della Materia","ror":"https://ror.org/02kswma64","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210155236","https://openalex.org/I4210163092"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Damien Challet","raw_affiliation_strings":["Istituto Nazionale per la Fisica della Materia (INFM), Trieste-SISSA Unit, Via Beirut 2-4, Trieste 34014, Italy","Theoretical Physics, Oxford University, 1, Keble Road, Oxford OX1 3NP, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto Nazionale per la Fisica della Materia (INFM), Trieste-SISSA Unit, Via Beirut 2-4, Trieste 34014, Italy","institution_ids":["https://openalex.org/I138549579","https://openalex.org/I4210163092"]},{"raw_affiliation_string":"Theoretical Physics, Oxford University, 1, Keble Road, Oxford OX1 3NP, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.5945,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.98286929,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"64","issue":"5","first_page":"056138","last_page":"056138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9940999746322632,"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"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9940999746322632,"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"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.0031999999191612005,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/minority-game","display_name":"minority game","score":0.9980000257492065},{"id":"https://openalex.org/keywords/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.9800000190734863},{"id":"https://openalex.org/keywords/stationary-states","display_name":"stationary states","score":0.8820000290870667},{"id":"https://openalex.org/keywords/disordered-spin-systems","display_name":"disordered spin systems","score":0.8920000195503235},{"id":"https://openalex.org/keywords/ground-state-configuration","display_name":"ground state configuration","score":0.7549999952316284},{"id":"https://openalex.org/keywords/learning-rate","display_name":"learning rate","score":0.6869999766349792},{"id":"https://openalex.org/keywords/collective-behavior","display_name":"collective behavior","score":0.6809999942779541},{"id":"https://openalex.org/keywords/agent-based-modeling","display_name":"agent-based modeling","score":0.5899999737739563},{"id":"https://openalex.org/keywords/symmetric-phase","display_name":"symmetric phase","score":0.6970000267028809}],"concepts":[{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.7014585137367249},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6457255482673645},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5873489379882812},{"id":"https://openalex.org/C100339178","wikidata":"https://www.wikidata.org/wiki/Q2548752","display_name":"Collective behavior","level":2,"score":0.5619792938232422},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.4661352038383484},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46496301889419556},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4173591434955597},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41734081506729126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2635727524757385},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.182865709066391},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0934474766254425},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.08045637607574463},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","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":5,"locations":[{"id":"doi:10.1103/physreve.64.056138","doi":"https://doi.org/10.1103/physreve.64.056138","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.64.056138","pdf_url":null,"source":{"id":"https://openalex.org/S4210224030","display_name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","issn_l":"1063-651X","issn":["1063-651X","1095-3787","1538-4519"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:11736045","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11736045","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter physics","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:cond-mat/0102257","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0102257","pdf_url":"https://arxiv.org/pdf/cond-mat/0102257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.310.6903","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.6903","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cond-mat/0102257v1.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.cond-mat/0102257","doi":"https://doi.org/10.48550/arxiv.cond-mat/0102257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cond-mat/0102257","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cond-mat/0102257","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cond-mat/0102257","pdf_url":"https://arxiv.org/pdf/cond-mat/0102257","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W584634945","https://openalex.org/W1967508279","https://openalex.org/W1972740153","https://openalex.org/W1987655776","https://openalex.org/W1998718137","https://openalex.org/W2012835785","https://openalex.org/W2015663875","https://openalex.org/W2019322277","https://openalex.org/W2037014352","https://openalex.org/W2072387357","https://openalex.org/W2078919031","https://openalex.org/W2091653681","https://openalex.org/W2096348520","https://openalex.org/W2107379449","https://openalex.org/W2109382217","https://openalex.org/W2155545397","https://openalex.org/W2952876803","https://openalex.org/W3099545960","https://openalex.org/W3100643943","https://openalex.org/W3102551942","https://openalex.org/W4206502013","https://openalex.org/W4250121003"],"related_works":["https://openalex.org/W2107379449","https://openalex.org/W1640784407","https://openalex.org/W1135405693","https://openalex.org/W3034340860","https://openalex.org/W2062638545","https://openalex.org/W2021198656","https://openalex.org/W2287541906","https://openalex.org/W2065284440","https://openalex.org/W2061523235","https://openalex.org/W2055213436"],"abstract_inverted_index":{"We":[0,19],"discuss":[1],"in":[2,78,125],"detail":[3],"the":[4,11,16,25,45,52,65,73,79,86,89,95,108,112,119,126,136,139,143],"derivation":[5],"of":[6,15,24,36,56,88,94,107,111,129,142,145],"stochastic":[7],"differential":[8],"equations":[9],"for":[10],"continuum":[12],"time":[13],"limit":[14],"minority":[17,26,113],"game.":[18,114],"show":[20],"that":[21,44,118],"all":[22],"properties":[23,48],"game":[27],"can":[28],"be":[29],"understood":[30],"by":[31,51],"a":[32,57,92,102,146],"careful":[33],"theoretical":[34],"analysis":[35],"such":[37],"equations.":[38],"In":[39],"particular,":[40],"(i)":[41],"we":[42,63,71,84,116],"confirm":[43],"stationary":[46,67],"state":[47,54,68],"are":[49],"given":[50],"ground":[53],"configurations":[55],"disordered":[58],"(soft)":[59],"spin":[60],"system,":[61],"(ii)":[62],"derive":[64],"full":[66],"distribution,":[69],"(iii)":[70],"characterize":[72],"dependence":[74],"on":[75],"initial":[76],"conditions":[77],"symmetric":[80],"phase,":[81],"and":[82,104],"(iv)":[83],"clarify":[85],"behavior":[87,110,128],"system":[90],"as":[91],"function":[93],"learning":[96],"rate.":[97],"This":[98],"leaves":[99],"us":[100],"with":[101],"complete":[103],"coherent":[105],"picture":[106],"collective":[109,140],"Strikingly":[115],"find":[117],"temperaturelike":[120],"parameter,":[121],"which":[122],"is":[123],"introduced":[124],"choice":[127],"individual":[130],"agents":[131],"turns":[132],"out":[133],"to":[134],"play":[135],"role,":[137],"at":[138],"level,":[141],"inverse":[144],"thermodynamic":[147],"temperature.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}