{"id":"https://openalex.org/W2509713345","doi":"https://doi.org/10.1007/s11590-016-1077-6","title":"Distributionally robust chance-constrained games: existence and characterization of Nash equilibrium","display_name":"Distributionally robust chance-constrained games: existence and characterization of Nash equilibrium","publication_year":2016,"publication_date":"2016-09-09","ids":{"openalex":"https://openalex.org/W2509713345","doi":"https://doi.org/10.1007/s11590-016-1077-6","mag":"2509713345"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-016-1077-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-016-1077-6","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","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/A5113710666","display_name":"Vikas Vikram Singh","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Vikas Vikram Singh","raw_affiliation_strings":["Laboratoire de Recherche en Informatique, Universit\u00e9 Paris Sud XI, B\u00e2t 650, 91405, Orsay Cedex, France","LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Recherche en Informatique, Universit\u00e9 Paris Sud XI, B\u00e2t 650, 91405, Orsay Cedex, France","institution_ids":["https://openalex.org/I4210144804","https://openalex.org/I102197404"]},{"raw_affiliation_string":"LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046267369","display_name":"Oualid Jouini","orcid":"https://orcid.org/0000-0002-9498-165X"},"institutions":[{"id":"https://openalex.org/I216852786","display_name":"\u00c9cole Centrale Paris","ror":"https://ror.org/00v0y5771","country_code":"FR","type":"education","lineage":["https://openalex.org/I216852786"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I280199911","display_name":"Bouygues (France)","ror":"https://ror.org/056185y51","country_code":"FR","type":"company","lineage":["https://openalex.org/I280199911"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210134356","display_name":"Laboratoire G\u00e9nie Industriel","ror":"https://ror.org/0455wwj08","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210134356"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Oualid Jouini","raw_affiliation_strings":["Laboratoire G\u00e9nie Industriel, CentraleSup\u00e9lec, Universit\u00e9 Paris-Saclay, Grande Voie des Vignes, 92 290, Ch\u00e2tenay-Malabry, France","LGI - Laboratoire G\u00e9nie Industriel - EA 2606 (CentraleSup\u00e9lec - B\u00e2timent Bouygues\r\n3 rue Joliot Curie\r\n91190 GIF-SUR-YVETTE - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire G\u00e9nie Industriel, CentraleSup\u00e9lec, Universit\u00e9 Paris-Saclay, Grande Voie des Vignes, 92 290, Ch\u00e2tenay-Malabry, France","institution_ids":["https://openalex.org/I4210107720","https://openalex.org/I277688954","https://openalex.org/I216852786"]},{"raw_affiliation_string":"LGI - Laboratoire G\u00e9nie Industriel - EA 2606 (CentraleSup\u00e9lec - B\u00e2timent Bouygues\r\n3 rue Joliot Curie\r\n91190 GIF-SUR-YVETTE - France)","institution_ids":["https://openalex.org/I4210134356","https://openalex.org/I4210107720","https://openalex.org/I280199911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076935029","display_name":"Abdel Lisser","orcid":"https://orcid.org/0000-0003-1318-6679"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Abdel Lisser","raw_affiliation_strings":["Laboratoire de Recherche en Informatique, Universit\u00e9 Paris Sud XI, B\u00e2t 650, 91405, Orsay Cedex, France","LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Recherche en Informatique, Universit\u00e9 Paris Sud XI, B\u00e2t 650, 91405, Orsay Cedex, France","institution_ids":["https://openalex.org/I4210144804","https://openalex.org/I102197404"]},{"raw_affiliation_string":"LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5113710666"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.529,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90254535,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"7","first_page":"1385","last_page":"1405"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9980000257492065,"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/T10315","display_name":"Decision-Making and Behavioral Economics","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1800","display_name":"General Decision Sciences"},"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/T12137","display_name":"Economic theories and models","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7347389459609985},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.681976854801178},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.6119774580001831},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.5671590566635132},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5599121451377869},{"id":"https://openalex.org/keywords/strategy","display_name":"Strategy","score":0.5159359574317932},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5066528916358948},{"id":"https://openalex.org/keywords/symmetric-game","display_name":"Symmetric game","score":0.4939606785774231},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4840323328971863},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.4657972753047943},{"id":"https://openalex.org/keywords/normal-form-game","display_name":"Normal-form game","score":0.454490602016449},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.4483097493648529},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.44385913014411926},{"id":"https://openalex.org/keywords/solution-concept","display_name":"Solution concept","score":0.4365195333957672},{"id":"https://openalex.org/keywords/risk-dominance","display_name":"Risk dominance","score":0.43240275979042053},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.39831823110580444},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.39129599928855896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3542812168598175}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7347389459609985},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.681976854801178},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.6119774580001831},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.5671590566635132},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5599121451377869},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.5159359574317932},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5066528916358948},{"id":"https://openalex.org/C93733245","wikidata":"https://www.wikidata.org/wiki/Q3770642","display_name":"Symmetric game","level":5,"score":0.4939606785774231},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4840323328971863},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.4657972753047943},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.454490602016449},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.4483097493648529},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.44385913014411926},{"id":"https://openalex.org/C11343654","wikidata":"https://www.wikidata.org/wiki/Q780008","display_name":"Solution concept","level":3,"score":0.4365195333957672},{"id":"https://openalex.org/C22349654","wikidata":"https://www.wikidata.org/wiki/Q2039354","display_name":"Risk dominance","level":5,"score":0.43240275979042053},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.39831823110580444},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.39129599928855896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3542812168598175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-016-1077-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-016-1077-6","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01728722v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01728722","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Optimization Letters, 2017, 11 (7), pp.1385 - 1405. &#x27E8;10.1007/s11590-016-1077-6&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W116972955","https://openalex.org/W1516105317","https://openalex.org/W1518992076","https://openalex.org/W1965069249","https://openalex.org/W1987420866","https://openalex.org/W1993402578","https://openalex.org/W1994737592","https://openalex.org/W1997944939","https://openalex.org/W2011696174","https://openalex.org/W2021472931","https://openalex.org/W2039355449","https://openalex.org/W2040503200","https://openalex.org/W2050607668","https://openalex.org/W2059670050","https://openalex.org/W2061627126","https://openalex.org/W2067050450","https://openalex.org/W2067796483","https://openalex.org/W2075567596","https://openalex.org/W2077954281","https://openalex.org/W2084312524","https://openalex.org/W2086681812","https://openalex.org/W2089649903","https://openalex.org/W2093258787","https://openalex.org/W2120177315","https://openalex.org/W2122770475","https://openalex.org/W2126952111","https://openalex.org/W2140214428","https://openalex.org/W2140259584","https://openalex.org/W2159230854","https://openalex.org/W2167356658","https://openalex.org/W2188009703","https://openalex.org/W2215997563","https://openalex.org/W2322316662","https://openalex.org/W2787523326","https://openalex.org/W2798344481","https://openalex.org/W4234534407","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W1853631319","https://openalex.org/W4365460918","https://openalex.org/W2355770865","https://openalex.org/W2131967794","https://openalex.org/W2187345782","https://openalex.org/W2188009703","https://openalex.org/W2770888554","https://openalex.org/W2621228214","https://openalex.org/W2896274930","https://openalex.org/W2097540415"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
