{"id":"https://openalex.org/W2406977383","doi":"https://doi.org/10.1109/tac.2015.2477975","title":"On the Convergence of Piecewise Linear Strategic Interaction Dynamics on Networks","display_name":"On the Convergence of Piecewise Linear Strategic Interaction Dynamics on Networks","publication_year":2015,"publication_date":"2015-09-11","ids":{"openalex":"https://openalex.org/W2406977383","doi":"https://doi.org/10.1109/tac.2015.2477975","mag":"2406977383"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2015.2477975","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2477975","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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/A5022064746","display_name":"Bahman Gharesifard","orcid":"https://orcid.org/0000-0003-1495-3489"},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bahman Gharesifard","raw_affiliation_strings":["Queen's University, Kingston, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Queen's University, Kingston, ON, Canada","institution_ids":["https://openalex.org/I204722609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036105299","display_name":"Behrouz Touri","orcid":"https://orcid.org/0000-0003-4724-7329"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Behrouz Touri","raw_affiliation_strings":["University of Colorado Boulder, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado Boulder, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019604570","display_name":"Tamer Ba\u015far","orcid":"https://orcid.org/0000-0003-4406-7875"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamer Basar","raw_affiliation_strings":["University of Illinoisat Urbana-Champaign, Urbana-Champaign, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinoisat Urbana-Champaign, Urbana-Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028973855","display_name":"Jeff S. Shamma","orcid":"https://orcid.org/0000-0001-5638-9551"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeff Shamma","raw_affiliation_strings":["King Abdullah University of Science and Technology (KAUST), Georgia Institute of Technology, Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"King Abdullah University of Science and Technology (KAUST), Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2884,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80577593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"61","issue":"6","first_page":"1682","last_page":"1687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9991999864578247,"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/T11031","display_name":"Game Theory and Applications","score":0.9986000061035156,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6981421709060669},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.6641404628753662},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5024025440216064},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48076173663139343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40457338094711304},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4001968502998352},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37603557109832764},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37590447068214417},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15521472692489624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15143203735351562},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12435230612754822},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12036922574043274},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0704704225063324}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6981421709060669},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.6641404628753662},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5024025440216064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48076173663139343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40457338094711304},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4001968502998352},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37603557109832764},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37590447068214417},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15521472692489624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15143203735351562},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12435230612754822},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12036922574043274},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0704704225063324},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2015.2477975","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2477975","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/584223","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/584223","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1560897552","display_name":null,"funder_award_id":"FA9550-09-1-0538","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4603001257","display_name":null,"funder_award_id":"FA9550-10-1-0573","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G463051470","display_name":null,"funder_award_id":"#FA9550-10-1-0573","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6904062931","display_name":null,"funder_award_id":"FA9550-09-1-0538","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"}],"funders":[{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1519314965","https://openalex.org/W1578630563","https://openalex.org/W1788292158","https://openalex.org/W1964757264","https://openalex.org/W1970704004","https://openalex.org/W1972807647","https://openalex.org/W1974144061","https://openalex.org/W1994872192","https://openalex.org/W2041157860","https://openalex.org/W2060602676","https://openalex.org/W2102622811","https://openalex.org/W2105837036","https://openalex.org/W2124172444","https://openalex.org/W2126479355","https://openalex.org/W2129492921","https://openalex.org/W2130518506","https://openalex.org/W2132499788","https://openalex.org/W2159715570","https://openalex.org/W2165565577","https://openalex.org/W2166127999","https://openalex.org/W2170451139","https://openalex.org/W3022321359","https://openalex.org/W3090497192","https://openalex.org/W3122244605","https://openalex.org/W3123808662","https://openalex.org/W3124203484","https://openalex.org/W3148958427","https://openalex.org/W4230134995","https://openalex.org/W4238591275","https://openalex.org/W4240896209","https://openalex.org/W4255896881","https://openalex.org/W4285719527","https://openalex.org/W4298404569"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W2724817865","https://openalex.org/W2400992695","https://openalex.org/W2281834912","https://openalex.org/W2382944939","https://openalex.org/W1489941249","https://openalex.org/W3123492739","https://openalex.org/W4320486059","https://openalex.org/W2494168571","https://openalex.org/W3121191496"],"abstract_inverted_index":{"We":[0,25,50],"prove":[1],"that":[2],"the":[3,34,40,45,53],"piecewise":[4],"linear":[5],"best-response":[6],"dynamical":[7,31],"systems":[8],"of":[9,18,29,39,42,47,56,68,80],"strategic":[10],"interactions":[11],"are":[12],"asymptotically":[13],"convergent":[14],"to":[15,75],"their":[16,69,73],"set":[17,41],"equilibria":[19,43],"on":[20,62],"any":[21],"weighted":[22],"undirected":[23],"graph.":[24],"study":[26],"various":[27],"features":[28],"these":[30],"systems,":[32],"including":[33,72],"uniqueness":[35],"and":[36,44,59,65,77],"abundance":[37],"properties":[38],"emergence":[46],"unstable":[48],"equilibria.":[49],"also":[51],"introduce":[52],"novel":[54],"notions":[55],"social":[57,60],"equivalence":[58],"dominance":[61],"directed":[63],"graphs,":[64],"demonstrate":[66],"some":[67],"interesting":[70],"implications,":[71],"correspondence":[74],"consensus":[76],"chromatic":[78],"number":[79],"partite":[81],"graphs.":[82],"Examples":[83],"illustrate":[84],"our":[85],"results.":[86]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}