{"id":"https://openalex.org/W2893539232","doi":"https://doi.org/10.1007/s10957-018-1403-5","title":"Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values","display_name":"Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values","publication_year":2018,"publication_date":"2018-09-29","ids":{"openalex":"https://openalex.org/W2893539232","doi":"https://doi.org/10.1007/s10957-018-1403-5","mag":"2893539232"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-018-1403-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-018-1403-5","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","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/A5088057393","display_name":"J. M. Alonso-Meijide","orcid":"https://orcid.org/0000-0002-8723-1404"},"institutions":[{"id":"https://openalex.org/I200284239","display_name":"Universidade de Santiago de Compostela","ror":"https://ror.org/030eybx10","country_code":"ES","type":"education","lineage":["https://openalex.org/I200284239"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 M. Alonso-Meijide","raw_affiliation_strings":["Grupo MODESTYA, Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Universidade de Santiago de Compostela, Santiago de Compostela, Spain"],"affiliations":[{"raw_affiliation_string":"Grupo MODESTYA, Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Universidade de Santiago de Compostela, Santiago de Compostela, Spain","institution_ids":["https://openalex.org/I200284239"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025241344","display_name":"Juli\u00e1n Costa","orcid":"https://orcid.org/0000-0001-9760-9581"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juli\u00e1n Costa","raw_affiliation_strings":["Grupo MODES, Departamento de Matem\u00e1ticas, Universidade da Coru\u00f1a, A Coru\u00f1a, Spain"],"affiliations":[{"raw_affiliation_string":"Grupo MODES, Departamento de Matem\u00e1ticas, Universidade da Coru\u00f1a, A Coru\u00f1a, Spain","institution_ids":["https://openalex.org/I11019714"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071506658","display_name":"Ignacio Garc\u0131\u0301a-Jurado","orcid":"https://orcid.org/0000-0002-6681-1629"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ignacio Garc\u00eda-Jurado","raw_affiliation_strings":["Grupo MODES, Departamento de Matem\u00e1ticas, Universidade da Coru\u00f1a, A Coru\u00f1a, Spain"],"affiliations":[{"raw_affiliation_string":"Grupo MODES, Departamento de Matem\u00e1ticas, Universidade da Coru\u00f1a, A Coru\u00f1a, Spain","institution_ids":["https://openalex.org/I11019714"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088057393"],"corresponding_institution_ids":["https://openalex.org/I200284239"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.3339,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94786694,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"180","issue":"3","first_page":"1027","last_page":"1035"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9966999888420105,"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":0.9732000231742859,"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/null","display_name":"Null (SQL)","score":0.8290848135948181},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.7624998688697815},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.655668318271637},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.569113552570343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5161365270614624},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4989755153656006},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.47020870447158813},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.46946966648101807},{"id":"https://openalex.org/keywords/null-hypothesis","display_name":"Null hypothesis","score":0.4420608580112457},{"id":"https://openalex.org/keywords/additive-function","display_name":"Additive function","score":0.4177218973636627},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34347981214523315},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11195892095565796},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.09524312615394592}],"concepts":[{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.8290848135948181},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.7624998688697815},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.655668318271637},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.569113552570343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5161365270614624},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4989755153656006},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.47020870447158813},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.46946966648101807},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.4420608580112457},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.4177218973636627},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34347981214523315},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11195892095565796},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.09524312615394592},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-018-1403-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-018-1403-5","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1403-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-018-1403-5","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":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W85180509","https://openalex.org/W204900244","https://openalex.org/W1981022005","https://openalex.org/W1983688774","https://openalex.org/W1985862947","https://openalex.org/W2033704240","https://openalex.org/W2071232943","https://openalex.org/W2076492340","https://openalex.org/W2090854437","https://openalex.org/W2102099143","https://openalex.org/W2130443667","https://openalex.org/W2153675089","https://openalex.org/W2157896294","https://openalex.org/W2790542255","https://openalex.org/W3103482818","https://openalex.org/W3148887536","https://openalex.org/W4248321094"],"related_works":["https://openalex.org/W2042012404","https://openalex.org/W4299308707","https://openalex.org/W2921570851","https://openalex.org/W1503292914","https://openalex.org/W2266550105","https://openalex.org/W1995117839","https://openalex.org/W3160699011","https://openalex.org/W3149597039","https://openalex.org/W2791171867","https://openalex.org/W3165895314"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}