{"id":"https://openalex.org/W4388600314","doi":"https://doi.org/10.1145/3632525","title":"Stochastic Approximation for Estimating the Price of Stability in Stochastic Nash Games","display_name":"Stochastic Approximation for Estimating the Price of Stability in Stochastic Nash Games","publication_year":2023,"publication_date":"2023-11-11","ids":{"openalex":"https://openalex.org/W4388600314","doi":"https://doi.org/10.1145/3632525"},"language":"en","primary_location":{"id":"doi:10.1145/3632525","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3632525","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3632525","source":{"id":"https://openalex.org/S38703467","display_name":"ACM Transactions on Modeling and Computer Simulation","issn_l":"1049-3301","issn":["1049-3301","1558-1195"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Computer Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3632525","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010113200","display_name":"Afrooz Jalilzadeh","orcid":"https://orcid.org/0000-0002-3734-1082"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Afrooz Jalilzadeh","raw_affiliation_strings":["University of Arizona, Tucson, USA"],"raw_orcid":"https://orcid.org/0000-0002-3734-1082","affiliations":[{"raw_affiliation_string":"University of Arizona, Tucson, USA","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003164670","display_name":"Farzad Yousefian","orcid":"https://orcid.org/0000-0003-2628-741X"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Farzad Yousefian","raw_affiliation_strings":["Rutgers University New Brunswick, New Brunswick, USA"],"raw_orcid":"https://orcid.org/0000-0003-2628-741X","affiliations":[{"raw_affiliation_string":"Rutgers University New Brunswick, New Brunswick, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100654252","display_name":"Mohammadjavad Ebrahimi","orcid":"https://orcid.org/0000-0003-1042-8118"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohammadjavad Ebrahimi","raw_affiliation_strings":["Rutgers University New Brunswick, New Brunswick, USA"],"raw_orcid":"https://orcid.org/0000-0003-1042-8118","affiliations":[{"raw_affiliation_string":"Rutgers University New Brunswick, New Brunswick, USA","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010113200"],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":null,"apc_paid":null,"fwci":0.497,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72019161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"34","issue":"2","first_page":"1","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6308321952819824},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.5672496557235718},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.5607286095619202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49496930837631226},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.46309542655944824},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.46117982268333435},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4314877986907959},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42468899488449097},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4203202724456787},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.4116882085800171},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39038029313087463}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6308321952819824},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.5672496557235718},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.5607286095619202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49496930837631226},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.46309542655944824},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.46117982268333435},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4314877986907959},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42468899488449097},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4203202724456787},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.4116882085800171},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39038029313087463},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3632525","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3632525","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3632525","source":{"id":"https://openalex.org/S38703467","display_name":"ACM Transactions on Modeling and Computer Simulation","issn_l":"1049-3301","issn":["1049-3301","1558-1195"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Computer Simulation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3632525","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3632525","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3632525","source":{"id":"https://openalex.org/S38703467","display_name":"ACM Transactions on Modeling and Computer Simulation","issn_l":"1049-3301","issn":["1049-3301","1558-1195"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Modeling and Computer Simulation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2373497080","display_name":null,"funder_award_id":"ECCS-1944500","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2916031245","display_name":null,"funder_award_id":"ECCS-2231863","funder_id":"https://openalex.org/F4320337392","funder_display_name":"Division of Electrical, Communications and Cyber Systems"},{"id":"https://openalex.org/G4416318167","display_name":"Generalized Stochastic Nash Equilibrium Framework: Theory, Computation, and Application","funder_award_id":"2231863","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4720003262","display_name":null,"funder_award_id":"N00014-22","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G811776586","display_name":null,"funder_award_id":"N00014-22-1-2757","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8584136913","display_name":"CAREER: Advancing Mathematical Models and Algorithms for Decentralized Optimization in Complex Multi-agent Networks","funder_award_id":"1944500","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388600314.pdf","grobid_xml":"https://content.openalex.org/works/W4388600314.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1487404723","https://openalex.org/W1519983590","https://openalex.org/W1583497301","https://openalex.org/W1822292100","https://openalex.org/W1981276685","https://openalex.org/W1991765628","https://openalex.org/W1992208280","https://openalex.org/W1994616650","https://openalex.org/W2008796819","https://openalex.org/W2020123437","https://openalex.org/W2026355589","https://openalex.org/W2049895746","https://openalex.org/W2049966847","https://openalex.org/W2055828890","https://openalex.org/W2057226027","https://openalex.org/W2075567596","https://openalex.org/W2080335539","https://openalex.org/W2086161653","https://openalex.org/W2089559088","https://openalex.org/W2095094403","https://openalex.org/W2099681657","https://openalex.org/W2124181538","https://openalex.org/W2559655401","https://openalex.org/W2593248927","https://openalex.org/W2752009570","https://openalex.org/W2940300781","https://openalex.org/W2962823973","https://openalex.org/W2963155955","https://openalex.org/W2963290659","https://openalex.org/W2969951231","https://openalex.org/W2993285063","https://openalex.org/W3018617837","https://openalex.org/W3100033291","https://openalex.org/W3156816032","https://openalex.org/W3198165553","https://openalex.org/W4238093859","https://openalex.org/W4241368925","https://openalex.org/W4241705128","https://openalex.org/W4249200845","https://openalex.org/W4294576339","https://openalex.org/W4300515374","https://openalex.org/W4388600314"],"related_works":["https://openalex.org/W2236801283","https://openalex.org/W2728657731","https://openalex.org/W1853631319","https://openalex.org/W2092374696","https://openalex.org/W2481143976","https://openalex.org/W2803932348","https://openalex.org/W3207342620","https://openalex.org/W2607684552","https://openalex.org/W2013767790","https://openalex.org/W4315489088"],"abstract_inverted_index":{"The":[0],"goal":[1],"in":[2,13,29,99,130],"this":[3,158],"article":[4],"is":[5,23],"to":[6,122,152],"approximate":[7],"the":[8,25,38,46,64,71,100,103,125,128,133,138,146,186,195,200],"Price":[9],"of":[10,40,66,102,127,132,137,145,160],"Stability":[11],"(PoS)":[12],"stochastic":[14,18,76,91,111,162,211],"Nash":[15,41,212],"games":[16],"using":[17],"approximation":[19,196],"(SA)":[20],"schemes.":[21],"PoS":[22,47,104,187],"among":[24],"most":[26],"popular":[27],"metrics":[28],"game":[30],"theory":[31],"and":[32,58,82,87,175,188,191],"provides":[33],"an":[34,142,168,181],"avenue":[35],"for":[36,69,124,157,184],"estimating":[37],"efficiency":[39],"games.":[42],"In":[43],"particular,":[44],"evaluating":[45],"can":[48],"help":[49],"with":[50,79],"designing":[51],"efficient":[52,67],"networked":[53,210],"systems,":[54],"including":[55],"communication":[56],"networks":[57],"power":[59],"market":[60],"mechanisms.":[61],"Motivated":[62],"by":[63],"absence":[65],"methods":[68],"computing":[70],"PoS,":[72],"first":[73],"we":[74,115,179,203],"consider":[75],"optimization":[77,163],"problems":[78],"a":[80,88,108,117,209],"nonsmooth":[81],"merely":[83,89],"convex":[84],"objective":[85],"function":[86],"monotone":[90],"variational":[92],"inequality":[93],"(SVI)":[94],"constraint.":[95],"This":[96],"problem":[97],"appears":[98,151],"numerator":[101],"ratio.":[105],"We":[106,140],"develop":[107,180],"randomized":[109],"block-coordinate":[110],"extra-(sub)gradient":[112],"method":[113],"where":[114,165],"employ":[116],"novel":[118],"iterative":[119],"penalization":[120],"scheme":[121,183],"account":[123],"mapping":[126],"SVI":[129],"each":[131],"two":[134],"gradient":[135],"updates":[136],"algorithm.":[139],"obtain":[141],"iteration":[143],"complexity":[144],"order":[147],"\u03f5":[148,166],"-4":[149],"that":[150],"be":[153],"best":[154],"known":[155],"result":[156],"class":[159],"constrained":[161],"problems,":[164],"denotes":[167],"arbitrary":[169],"bound":[170],"on":[171,194,208],"suitably":[172],"defined":[173],"infeasibility":[174],"suboptimality":[176],"metrics.":[177],"Second,":[178],"SA-based":[182],"approximating":[185],"derive":[189],"lower":[190],"upper":[192],"bounds":[193],"error.":[197],"To":[198],"validate":[199],"theoretical":[201],"findings,":[202],"provide":[204],"preliminary":[205],"simulation":[206],"results":[207],"Cournot":[213],"competition.":[214]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}