{"id":"https://openalex.org/W4399806302","doi":"https://doi.org/10.1007/s13235-024-00568-5","title":"Some Remarks on Linear-Quadratic Closed-Loop Games with Many Players","display_name":"Some Remarks on Linear-Quadratic Closed-Loop Games with Many Players","publication_year":2024,"publication_date":"2024-06-19","ids":{"openalex":"https://openalex.org/W4399806302","doi":"https://doi.org/10.1007/s13235-024-00568-5"},"language":"en","primary_location":{"id":"doi:10.1007/s13235-024-00568-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13235-024-00568-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13235-024-00568-5.pdf","source":{"id":"https://openalex.org/S2502731256","display_name":"Dynamic Games and Applications","issn_l":"2153-0785","issn":["2153-0785","2153-0793"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dynamic Games and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s13235-024-00568-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091271759","display_name":"Marco Cirant","orcid":"https://orcid.org/0000-0002-7114-1818"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marco Cirant","raw_affiliation_strings":["Dipartimento di Matematica \u201cT. Levi-Civita\u201d, Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy","Dipartimento di Matematica \"T. Levi-Civita\", Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cT. Levi-Civita\u201d, Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica \"T. Levi-Civita\", Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031074914","display_name":"Davide Francesco Redaelli","orcid":"https://orcid.org/0009-0004-9125-9022"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Davide Francesco Redaelli","raw_affiliation_strings":["Dipartimento di Matematica \u201cT. Levi-Civita\u201d, Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy","Dipartimento di Matematica \"T. Levi-Civita\", Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cT. Levi-Civita\u201d, Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica \"T. Levi-Civita\", Universit\u00e0 degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091271759"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.5647,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82936085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"15","issue":"2","first_page":"558","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T12137","display_name":"Economic theories and models","score":0.9937999844551086,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9745000004768372,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/nash-equilibrium","display_name":"Nash equilibrium","score":0.7027233242988586},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6057972311973572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6046715974807739},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5962795615196228},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5507612228393555},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5169134140014648},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4717313349246979},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4225609600543976},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.41998291015625},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.41445836424827576},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34677132964134216},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27802109718322754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1494700014591217}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7027233242988586},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6057972311973572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6046715974807739},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5962795615196228},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5507612228393555},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5169134140014648},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4717313349246979},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4225609600543976},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.41998291015625},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.41445836424827576},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34677132964134216},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27802109718322754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1494700014591217},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s13235-024-00568-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13235-024-00568-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13235-024-00568-5.pdf","source":{"id":"https://openalex.org/S2502731256","display_name":"Dynamic Games and Applications","issn_l":"2153-0785","issn":["2153-0785","2153-0793"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dynamic Games and Applications","raw_type":"journal-article"},{"id":"pmh:oai:www.research.unipd.it:11577/3515966","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3515966","pdf_url":"https://www.research.unipd.it/bitstream/11577/3515966/2/unpaywall-bitstream--1400767440.pdf","source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00568-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s13235-024-00568-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":{"id":"doi:10.1007/s13235-024-00568-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13235-024-00568-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13235-024-00568-5.pdf","source":{"id":"https://openalex.org/S2502731256","display_name":"Dynamic Games and Applications","issn_l":"2153-0785","issn":["2153-0785","2153-0793"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Dynamic Games and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4821329654","display_name":null,"funder_award_id":"GNAMPA","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G6870276786","display_name":null,"funder_award_id":"GNAMPA","funder_id":"https://openalex.org/F4320333369","funder_display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni"}],"funders":[{"id":"https://openalex.org/F4320309832","display_name":"Fondazione Cassa di Risparmio di Padova e Rovigo","ror":"https://ror.org/02jecj653"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399806302.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1821455959","https://openalex.org/W2005303193","https://openalex.org/W2011000015","https://openalex.org/W2011435133","https://openalex.org/W2038686546","https://openalex.org/W2119707575","https://openalex.org/W2149953340","https://openalex.org/W2468041409","https://openalex.org/W2592169312","https://openalex.org/W2618428225","https://openalex.org/W2889330615","https://openalex.org/W3023486662","https://openalex.org/W3047552776","https://openalex.org/W3112984646","https://openalex.org/W3125484093","https://openalex.org/W3137837840","https://openalex.org/W3165467868","https://openalex.org/W3181437949","https://openalex.org/W3209096915","https://openalex.org/W3214559626","https://openalex.org/W4230008158","https://openalex.org/W4282033747","https://openalex.org/W4307279931","https://openalex.org/W4315781372","https://openalex.org/W4376286405","https://openalex.org/W4389389278","https://openalex.org/W4402097554","https://openalex.org/W6600310979","https://openalex.org/W6602163396","https://openalex.org/W6830136761"],"related_works":["https://openalex.org/W2952621539","https://openalex.org/W2236801283","https://openalex.org/W4389760972","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"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"identify":[2],"structural":[3],"assumptions":[4],"which":[5,140],"provide":[6,87],"solvability":[7],"of":[8,26,31,43,105,112],"the":[9,24,48,63,66,71,81,98,110,122,129,143],"Nash":[10,49,125],"system":[11,50,126],"arising":[12],"from":[13,121],"a":[14,29,35,44,103,146],"linear-quadratic":[15],"closed-loop":[16,95],"game,":[17],"with":[18,21],"stable":[19],"properties":[20],"respect":[22],"to":[23,62,65,75,86,152],"number":[25,111],"players.":[27],"In":[28,102],"setting":[30,104],"interactions":[32,113],"governed":[33],"by":[34],"sparse":[36],"graph,":[37],"both":[38],"short-time":[39],"and":[40],"long-time":[41],"existence":[42],"classical":[45],"solution":[46,64],"for":[47,80,97,145],"set":[51],"in":[52,77],"infinitely":[53],"many":[54],"dimensions":[55],"are":[56,84,132],"addressed,":[57],"as":[58,60,70,149],"well":[59],"convergence":[61,147],"respective":[67],"ergodic":[68],"problem":[69],"time":[72,138],"horizon":[73],"goes":[74,151],"infinity;":[76],"addition,":[78],"equilibria":[79,96],"infinite-dimensional":[82],"game":[83],"shown":[85],"$$\\epsilon":[88],"$$":[89],"<mml:math":[90],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[91],"<mml:mi>\u03f5</mml:mi>":[92],"</mml:math>":[93],"-Nash":[94],"N":[99,123,150],"-player":[100,124],"game.":[101],"generalized":[106],"mean-field":[107],"type":[108],"(where":[109],"is":[114],"large":[115,137],"but":[116],"not":[117],"necessarily":[118],"symmetric),":[119],"directly":[120],"estimates":[127],"on":[128,134],"value":[130],"functions":[131],"deduced":[133],"an":[135],"arbitrary":[136],"horizon,":[139],"should":[141],"pave":[142],"way":[144],"result":[148],"infinity.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}