{"id":"https://openalex.org/W2109332371","doi":"https://doi.org/10.1142/s0219198905000387","title":"CONVEXITY IN STOCHASTIC COOPERATIVE SITUATIONS","display_name":"CONVEXITY IN STOCHASTIC COOPERATIVE SITUATIONS","publication_year":2005,"publication_date":"2005-03-01","ids":{"openalex":"https://openalex.org/W2109332371","doi":"https://doi.org/10.1142/s0219198905000387","mag":"2109332371"},"language":"en","primary_location":{"id":"doi:10.1142/s0219198905000387","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219198905000387","pdf_url":null,"source":{"id":"https://openalex.org/S130757258","display_name":"International Game Theory Review","issn_l":"0219-1989","issn":["0219-1989","1793-6675"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Game Theory Review","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/A5022050117","display_name":"Judith Timmer","orcid":"https://orcid.org/0000-0001-9299-4775"},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"JUDITH TIMMER","raw_affiliation_strings":["Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077202688","display_name":"Peter Borm","orcid":"https://orcid.org/0000-0002-2710-1827"},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"PETER BORM","raw_affiliation_strings":["Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110737580","display_name":"S.H. Tijs","orcid":null},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"STEF TIJS","raw_affiliation_strings":["Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I193700539"],"apc_list":null,"apc_paid":null,"fwci":8.266,"has_fulltext":true,"cited_by_count":34,"citation_normalized_percentile":{"value":0.96873371,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"07","issue":"01","first_page":"25","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":1.0,"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/T11182","display_name":"Auction Theory and Applications","score":0.9912999868392944,"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/T11031","display_name":"Game Theory and Applications","score":0.986299991607666,"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/convexity","display_name":"Convexity","score":0.9055807590484619},{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.6945276856422424},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.6713970899581909},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.6701674461364746},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.6390728950500488},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6299806833267212},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5718041658401489},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.44117027521133423},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3675650954246521},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.34194400906562805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31284114718437195},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.18725037574768066}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.9055807590484619},{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.6945276856422424},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6713970899581909},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.6701674461364746},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.6390728950500488},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6299806833267212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5718041658401489},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.44117027521133423},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3675650954246521},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.34194400906562805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31284114718437195},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.18725037574768066},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0219198905000387","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219198905000387","pdf_url":null,"source":{"id":"https://openalex.org/S130757258","display_name":"International Game Theory Review","issn_l":"0219-1989","issn":["0219-1989","1793-6675"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Game Theory Review","raw_type":"journal-article"},{"id":"pmh:oai:ris.utwente.nl:openaire_cris_publications/a180b88f-f488-42d7-8d26-d7f1f575776f","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/a180b88f-f488-42d7-8d26-d7f1f575776f","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Timmer, J B, Borm, P & Tijs, S 2005, 'Convexity in stochastic cooperative situations', International game theory review, vol. 7, no. 1, pp. 25-42. https://doi.org/10.1142/S0219198905000387","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:wsi:igtrxx:v:07:y:2005:i:01:n:s0219198905000387","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219198905000387","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"},{"id":"pmh:oai:ris.utwente.nl:publications/a180b88f-f488-42d7-8d26-d7f1f575776f","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W964212441","https://openalex.org/W1562353621","https://openalex.org/W1567282288","https://openalex.org/W1966062834","https://openalex.org/W1989954001","https://openalex.org/W1994465572","https://openalex.org/W2059038847","https://openalex.org/W2061328785","https://openalex.org/W2085648025","https://openalex.org/W2087316155","https://openalex.org/W2089603165","https://openalex.org/W2103030588","https://openalex.org/W2112418544","https://openalex.org/W2161282633"],"related_works":["https://openalex.org/W4249226508","https://openalex.org/W1964872188","https://openalex.org/W2380202880","https://openalex.org/W2906499702","https://openalex.org/W4292447975","https://openalex.org/W2261574202","https://openalex.org/W1894585900","https://openalex.org/W2006581498","https://openalex.org/W2013832345","https://openalex.org/W1998066849"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,114],"new":[4],"model":[5],"concerning":[6],"cooperative":[7,25],"situations":[8,21],"in":[9,53],"which":[10],"the":[11,80,83,90,96,101,104,111],"payoffs":[12],"are":[13,50,72,92],"modeled":[14],"by":[15,22],"random":[16,28],"variables.":[17],"We":[18],"analyze":[19],"these":[20,48,67],"means":[23],"of":[24,37,70,82,103,110,113],"games":[26],"with":[27],"payoffs.":[29],"Special":[30],"attention":[31],"is":[32,85,107],"paid":[33],"to":[34,57],"three":[35,68],"types":[36,49,69,77],"convexity,":[38],"namely":[39],"coalitional-merge,":[40],"individual-merge":[41],"and":[42,52],"marginal":[43,105],"convexity.":[44],"The":[45],"relations":[46],"between":[47],"studied":[51],"particular,":[54],"as":[55,100],"opposed":[56],"their":[58],"deterministic":[59],"counterparts":[60],"for":[61],"TU":[62],"games,":[63],"we":[64],"show":[65],"that":[66,79,95],"convexity":[71],"not":[73],"equivalent.":[74],"However,":[75],"all":[76],"imply":[78],"core":[81,112],"game":[84],"nonempty.":[86],"Sufficient":[87],"conditions":[88],"on":[89],"preferences":[91],"derived":[93],"such":[94],"Shapley":[97],"value,":[98],"defined":[99],"average":[102],"vectors,":[106],"an":[108],"element":[109],"convex":[115],"game.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}