{"id":"https://openalex.org/W7159602367","doi":"https://doi.org/10.48550/arxiv.2604.27942","title":"A Collective Variational Principle Unifying Bayesian Inference, Game Theory, and Thermodynamics","display_name":"A Collective Variational Principle Unifying Bayesian Inference, Game Theory, and Thermodynamics","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7159602367","doi":"https://doi.org/10.48550/arxiv.2604.27942"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.27942","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27942","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.27942","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012408243","display_name":"Djamel Bouchaffra","orcid":"https://orcid.org/0000-0002-9850-907X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bouchaffra, Djamel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036135070","display_name":"Fay\u00e7al Ykhlef","orcid":"https://orcid.org/0000-0002-5465-7046"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ykhlef, Faycal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023422312","display_name":"Mustapha Lebbah","orcid":"https://orcid.org/0000-0001-7245-6371"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lebbah, Mustapha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047336564","display_name":"Hanane Azzag","orcid":"https://orcid.org/0000-0001-6876-0688"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Azzag, Hanane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012408243"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.34220001101493835,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.34220001101493835,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.22190000116825104,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.07039999961853027,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/free-energy-principle","display_name":"Free energy principle","score":0.6097999811172485},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.45649999380111694},{"id":"https://openalex.org/keywords/bounded-rationality","display_name":"Bounded rationality","score":0.4537999927997589},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.43810001015663147},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4189000129699707},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.39989998936653137},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.3880999982357025},{"id":"https://openalex.org/keywords/solution-concept","display_name":"Solution concept","score":0.3822999894618988},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.3718000054359436}],"concepts":[{"id":"https://openalex.org/C33553690","wikidata":"https://www.wikidata.org/wiki/Q17014702","display_name":"Free energy principle","level":2,"score":0.6097999811172485},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.524399995803833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47110000252723694},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.45649999380111694},{"id":"https://openalex.org/C58694771","wikidata":"https://www.wikidata.org/wiki/Q814385","display_name":"Bounded rationality","level":2,"score":0.4537999927997589},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4189000129699707},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.39989998936653137},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C11343654","wikidata":"https://www.wikidata.org/wiki/Q780008","display_name":"Solution concept","level":3,"score":0.3822999894618988},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.3718000054359436},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3675999939441681},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33000001311302185},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C200594392","wikidata":"https://www.wikidata.org/wiki/Q812529","display_name":"Bayesian game","level":4,"score":0.32019999623298645},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3122999966144562},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2809999883174896},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2639000117778778},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C2777041938","wikidata":"https://www.wikidata.org/wiki/Q876695","display_name":"Indeterminism","level":3,"score":0.25589999556541443},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.27942","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27942","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.27942","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27942","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Collective":[0],"intelligence":[1],"emerges":[2],"across":[3,156],"biological,":[4,158],"physical,":[5],"and":[6,69,114,149,159,173],"artificial":[7,160],"systems":[8,53],"without":[9],"central":[10],"coordination,":[11],"yet":[12],"a":[13,47,60,89,96,109,123,136,142,166],"unifying":[14],"principle":[15,169],"governing":[16],"such":[17],"behaviour":[18],"remains":[19],"elusive.":[20],"The":[21],"Free":[22,44],"Energy":[23,45],"Principle":[24],"explains":[25],"how":[26],"individual":[27],"agents":[28],"adapt":[29],"through":[30],"variational":[31,97,168],"inference,":[32,171],"while":[33],"game":[34],"theory":[35,138],"formalises":[36],"strategic":[37,115],"interactions.":[38],"Here":[39],"we":[40,121],"introduce":[41,122],"the":[42,127],"Game-Theoretic":[43],"Principle,":[46],"unified":[48],"framework":[49],"showing":[50],"that":[51],"multi-agent":[52,132,161],"performing":[54],"local":[55,70],"free-energy":[56,124],"minimisation":[57],"implicitly":[58],"implement":[59],"stochastic":[61],"game.":[62,87],"We":[63,152],"prove":[64],"that,":[65],"under":[66],"bounded":[67],"rationality":[68],"information":[71],"constraints,":[72],"stationary":[73],"points":[74],"of":[75,84,92,126,139],"collective":[76],"free":[77],"energy":[78],"correspond":[79],"to":[80],"approximate":[81],"Nash":[82],"equilibria":[83,101],"an":[85],"induced":[86],"Conversely,":[88],"broad":[90],"class":[91],"cooperative":[93],"games":[94],"admits":[95],"representation":[98],"in":[99],"which":[100],"arise":[102],"as":[103],"Gibbs":[104],"distributions":[105],"over":[106],"coalitions,":[107],"establishing":[108],"bridge":[110],"between":[111,146],"Bayesian":[112],"inference":[113],"interaction.":[116],"To":[117],"characterise":[118],"higher-order":[119],"effects,":[120],"formulation":[125],"Harsanyi":[128],"dividend,":[129],"isolating":[130],"irreducible":[131],"synergy.":[133],"This":[134],"yields":[135],"predictive":[137],"cooperation,":[140],"including":[141],"falsifiable":[143],"non-monotonic":[144],"relationship":[145],"sensory":[147],"precision":[148],"agent":[150],"influence.":[151],"validate":[153],"this":[154],"prediction":[155],"neural,":[157],"systems.":[162],"These":[163],"results":[164],"identify":[165],"common":[167],"underlying":[170],"thermodynamics,":[172],"game-theoretic":[174],"equilibrium.":[175]},"counts_by_year":[],"updated_date":"2026-05-02T06:10:54.344120","created_date":"2026-05-02T00:00:00"}
