{"id":"https://openalex.org/W4391021311","doi":"https://doi.org/10.1109/cdc49753.2023.10383591","title":"Markov Games with Decoupled Dynamics: Price of Anarchy and Sample Complexity","display_name":"Markov Games with Decoupled Dynamics: Price of Anarchy and Sample Complexity","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391021311","doi":"https://doi.org/10.1109/cdc49753.2023.10383591"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383591","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383591","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5102025389","display_name":"Runyu Zhang","orcid":"https://orcid.org/0000-0002-9333-3554"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Runyu Zhang","raw_affiliation_strings":["John A. Paulson School of Engineering and Applied Sciences, Harvard University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"John A. Paulson School of Engineering and Applied Sciences, Harvard University","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115592030","display_name":"Yuyang Zhang","orcid":"https://orcid.org/0009-0004-5699-4144"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuyang Zhang","raw_affiliation_strings":["John A. Paulson School of Engineering and Applied Sciences, Harvard University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"John A. Paulson School of Engineering and Applied Sciences, Harvard University","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036187447","display_name":"Rohit Konda","orcid":"https://orcid.org/0000-0002-0423-5531"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rohit Konda","raw_affiliation_strings":["University of California,Department of Electrical and Computer Engineering,Santa,Barbara","Department of Electrical and Computer Engineering, University of California, Santa, Barbara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California,Department of Electrical and Computer Engineering,Santa,Barbara","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa, Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012022449","display_name":"Bryce L. Ferguson","orcid":"https://orcid.org/0000-0003-4373-7363"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bryce Ferguson","raw_affiliation_strings":["University of California,Department of Electrical and Computer Engineering,Santa,Barbara","Department of Electrical and Computer Engineering, University of California, Santa, Barbara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California,Department of Electrical and Computer Engineering,Santa,Barbara","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa, Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003146330","display_name":"Jason R. Marden","orcid":"https://orcid.org/0000-0003-3260-8574"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jason Marden","raw_affiliation_strings":["University of California,Department of Electrical and Computer Engineering,Santa,Barbara","Department of Electrical and Computer Engineering, University of California, Santa, Barbara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California,Department of Electrical and Computer Engineering,Santa,Barbara","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Santa, Barbara","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100368048","display_name":"Na Li","orcid":"https://orcid.org/0000-0001-9545-3050"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Na Li","raw_affiliation_strings":["John A. Paulson School of Engineering and Applied Sciences, Harvard University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"John A. Paulson School of Engineering and Applied Sciences, Harvard University","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3173,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65269632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"8100","last_page":"8107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9995999932289124,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9995999932289124,"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":0.9994000196456909,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.7337138652801514},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6966476440429688},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6386411786079407},{"id":"https://openalex.org/keywords/markov-perfect-equilibrium","display_name":"Markov perfect equilibrium","score":0.5946333408355713},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5816242694854736},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5752958059310913},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5609604716300964},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5350450277328491},{"id":"https://openalex.org/keywords/price-of-anarchy","display_name":"Price of anarchy","score":0.526267409324646},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5225498080253601},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.45863401889801025},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.4464327394962311},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.432881236076355},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4158124625682831},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.40185192227363586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3413294553756714},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.2426903247833252},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15428388118743896},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.13000881671905518},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08771160244941711},{"id":"https://openalex.org/keywords/price-of-stability","display_name":"Price of stability","score":0.08498400449752808}],"concepts":[{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.7337138652801514},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6966476440429688},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6386411786079407},{"id":"https://openalex.org/C67091656","wikidata":"https://www.wikidata.org/wiki/Q6771328","display_name":"Markov perfect equilibrium","level":3,"score":0.5946333408355713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5816242694854736},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5752958059310913},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5609604716300964},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5350450277328491},{"id":"https://openalex.org/C82149807","wikidata":"https://www.wikidata.org/wiki/Q7242623","display_name":"Price of anarchy","level":4,"score":0.526267409324646},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5225498080253601},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.45863401889801025},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.4464327394962311},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.432881236076355},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4158124625682831},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.40185192227363586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3413294553756714},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.2426903247833252},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15428388118743896},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.13000881671905518},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08771160244941711},{"id":"https://openalex.org/C188466206","wikidata":"https://www.wikidata.org/wiki/Q7242626","display_name":"Price of stability","level":3,"score":0.08498400449752808},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C126285488","wikidata":"https://www.wikidata.org/wiki/Q178476","display_name":"Monetary policy","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383591","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383591","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G2893851641","display_name":null,"funder_award_id":"FA95550-20-1-0054,FA9550-21-1-0203","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8612939657","display_name":null,"funder_award_id":"N00014-20-1-2359","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1526250527","https://openalex.org/W1808619423","https://openalex.org/W2044667552","https://openalex.org/W2057913812","https://openalex.org/W2122858720","https://openalex.org/W2159759087","https://openalex.org/W2172195920","https://openalex.org/W2183587304","https://openalex.org/W2294025081","https://openalex.org/W2481762555","https://openalex.org/W2552120320","https://openalex.org/W2791729947","https://openalex.org/W2793759590","https://openalex.org/W2883532348","https://openalex.org/W2963625099","https://openalex.org/W2968359733","https://openalex.org/W3010780098","https://openalex.org/W3041382148","https://openalex.org/W3099868047","https://openalex.org/W3169011731","https://openalex.org/W3171210634","https://openalex.org/W3172288035","https://openalex.org/W3204286672","https://openalex.org/W3205487934","https://openalex.org/W3209101326","https://openalex.org/W3210375408","https://openalex.org/W4283033454","https://openalex.org/W4283372584","https://openalex.org/W4285215989","https://openalex.org/W4300015991","https://openalex.org/W4391021311","https://openalex.org/W6748721451","https://openalex.org/W6759115203","https://openalex.org/W6762234667","https://openalex.org/W6780486084","https://openalex.org/W6796527454","https://openalex.org/W6797200228","https://openalex.org/W6802440018","https://openalex.org/W6802528643","https://openalex.org/W6803084572","https://openalex.org/W6838943866","https://openalex.org/W6852311862"],"related_works":["https://openalex.org/W2472051997","https://openalex.org/W4297209929","https://openalex.org/W3122286720","https://openalex.org/W3124951190","https://openalex.org/W3121902238","https://openalex.org/W2560823894","https://openalex.org/W4301139417","https://openalex.org/W2770991434","https://openalex.org/W2016588739","https://openalex.org/W1774502531"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,9,15,42,50,64,69,74,85,111],"finite-time":[4],"horizon":[5],"Markov":[6,46,75,82,86],"games":[7,47,56],"where":[8,31],"agents'":[10],"dynamics":[11],"are":[12,119],"decoupled":[13],"but":[14],"rewards":[16],"can":[17],"possibly":[18],"be":[19],"coupled":[20],"across":[21],"agents.":[22],"The":[23],"policy":[24,98],"class":[25],"is":[26,113],"restricted":[27],"to":[28,59,67,104],"local":[29,37],"policies":[30],"agents":[32],"make":[33],"decisions":[34],"using":[35,121],"their":[36],"state.":[38],"We":[39],"first":[40],"introduce":[41],"notion":[43],"of":[44,71,73,81,110],"smooth":[45],"which":[48,101],"extends":[49],"smoothness":[51,65],"argument":[52],"for":[53],"normal":[54],"form":[55],"([1],":[57],"[2])":[58],"our":[60,117],"setting,":[61],"and":[62],"leverage":[63],"property":[66],"bound":[68],"price":[70],"anarchy":[72],"game.":[76,125],"For":[77],"a":[78,92,105,122],"specific":[79],"type":[80],"game":[83],"called":[84],"potential":[87],"game,":[88],"we":[89],"also":[90,114],"develop":[91],"distributed":[93],"learning":[94],"algorithm,":[95],"multi-agent":[96],"soft":[97],"iteration":[99],"(MA-SPI),":[100],"provably":[102],"converges":[103],"Nash":[106],"equilibrium.":[107],"Sample":[108],"complexity":[109],"algorithm":[112],"provided.":[115],"Lastly,":[116],"results":[118],"validated":[120],"dynamic":[123],"covering":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
