{"id":"https://openalex.org/W4225996305","doi":"https://doi.org/10.3390/g13010006","title":"Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions","display_name":"Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions","publication_year":2021,"publication_date":"2021-12-26","ids":{"openalex":"https://openalex.org/W4225996305","doi":"https://doi.org/10.3390/g13010006"},"language":"en","primary_location":{"id":"doi:10.3390/g13010006","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g13010006","pdf_url":"https://www.mdpi.com/2073-4336/13/1/6/pdf?version=1640601321","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-4336/13/1/6/pdf?version=1640601321","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020381550","display_name":"Jochen Staudacher","orcid":"https://orcid.org/0000-0002-0619-4606"},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jochen Staudacher","raw_affiliation_strings":["Fakult\u00e4t Informatik, Hochschule Kempten, 87435 Kempten, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0619-4606","affiliations":[{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102123890","display_name":"F\u00e9lix Wagner","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Wagner","raw_affiliation_strings":["Fakult\u00e4t Informatik, Hochschule Kempten, 87435 Kempten, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036997058","display_name":"Jan Filipp","orcid":null},"institutions":[{"id":"https://openalex.org/I2802623092","display_name":"Kempten University of Applied Sciences","ror":"https://ror.org/02m4p8096","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802623092"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Filipp","raw_affiliation_strings":["Fakult\u00e4t Informatik, Hochschule Kempten, 87435 Kempten, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t Informatik, Hochschule Kempten, 87435 Kempten, Germany","institution_ids":["https://openalex.org/I2802623092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020381550"],"corresponding_institution_ids":["https://openalex.org/I2802623092"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.6028,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.83657015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"1","first_page":"6","last_page":"6"},"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":0.9944000244140625,"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/T10646","display_name":"Experimental Behavioral Economics Studies","score":0.9760000109672546,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/voting","display_name":"Voting","score":0.6693793535232544},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6218363046646118},{"id":"https://openalex.org/keywords/weighted-voting","display_name":"Weighted voting","score":0.5961668491363525},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5408378839492798},{"id":"https://openalex.org/keywords/power-index","display_name":"Power index","score":0.4948412775993347},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.47888463735580444},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.477652907371521},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4314866364002228},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42262542247772217},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4090709686279297},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3650936484336853},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.270940363407135},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2517366409301758},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.08389836549758911}],"concepts":[{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.6693793535232544},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6218363046646118},{"id":"https://openalex.org/C132778050","wikidata":"https://www.wikidata.org/wiki/Q2065430","display_name":"Weighted voting","level":4,"score":0.5961668491363525},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5408378839492798},{"id":"https://openalex.org/C3018596841","wikidata":"https://www.wikidata.org/wiki/Q7236523","display_name":"Power index","level":2,"score":0.4948412775993347},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.47888463735580444},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.477652907371521},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4314866364002228},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42262542247772217},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4090709686279297},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3650936484336853},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.270940363407135},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2517366409301758},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.08389836549758911},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/g13010006","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g13010006","pdf_url":"https://www.mdpi.com/2073-4336/13/1/6/pdf?version=1640601321","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a3d6eaf64dac418cb9fa587cafdad54f","is_oa":true,"landing_page_url":"https://doaj.org/article/a3d6eaf64dac418cb9fa587cafdad54f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Games, Vol 13, Iss 1, p 6 (2021)","raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/257583","is_oa":true,"landing_page_url":"http://hdl.handle.net/10419/257583","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"},{"id":"pmh:oai:mdpi.com:/2073-4336/13/1/6/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/g13010006","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Games; Volume 13; Issue 1; Pages: 6","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/g13010006","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g13010006","pdf_url":"https://www.mdpi.com/2073-4336/13/1/6/pdf?version=1640601321","source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Games","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225996305.pdf","grobid_xml":"https://content.openalex.org/works/W4225996305.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W119581101","https://openalex.org/W204900244","https://openalex.org/W309690565","https://openalex.org/W1505028449","https://openalex.org/W1974327200","https://openalex.org/W1976399866","https://openalex.org/W1976402990","https://openalex.org/W1981022005","https://openalex.org/W1982912564","https://openalex.org/W1985941874","https://openalex.org/W1999646672","https://openalex.org/W2002616065","https://openalex.org/W2012023964","https://openalex.org/W2015247315","https://openalex.org/W2016424092","https://openalex.org/W2025176001","https://openalex.org/W2034631582","https://openalex.org/W2038127015","https://openalex.org/W2045122596","https://openalex.org/W2076786454","https://openalex.org/W2081183270","https://openalex.org/W2084225608","https://openalex.org/W2107192765","https://openalex.org/W2144872768","https://openalex.org/W2152039432","https://openalex.org/W2163787772","https://openalex.org/W2279799234","https://openalex.org/W2296415298","https://openalex.org/W2536000384","https://openalex.org/W2603943346","https://openalex.org/W2770417875","https://openalex.org/W2803826101","https://openalex.org/W3012471250","https://openalex.org/W3080236492","https://openalex.org/W3125880702","https://openalex.org/W3134840917","https://openalex.org/W3158277381","https://openalex.org/W3173574160","https://openalex.org/W3179877719","https://openalex.org/W4205799233","https://openalex.org/W4232841423","https://openalex.org/W6681471939","https://openalex.org/W6681572715","https://openalex.org/W6734488856","https://openalex.org/W6794321172","https://openalex.org/W6798285651"],"related_works":["https://openalex.org/W1497951756","https://openalex.org/W2149483255","https://openalex.org/W2010932316","https://openalex.org/W2327770525","https://openalex.org/W135982461","https://openalex.org/W1578486520","https://openalex.org/W2034971155","https://openalex.org/W2909050863","https://openalex.org/W1982707951","https://openalex.org/W3122534223"],"abstract_inverted_index":{"We":[0,87],"study":[1],"the":[2,23,30,35,52,61,64,68,94],"efficient":[3],"computation":[4],"of":[5,16,25,85,90],"power":[6,56,96],"indices":[7,39,57,97],"for":[8,33,40,48,51,82,93],"weighted":[9,41],"voting":[10,42],"games":[11],"with":[12,58,98],"precoalitions":[13,99],"amongst":[14],"subsets":[15],"players":[17],"(reflecting,":[18],"e.g.,":[19],"ideological":[20],"proximity)":[21],"using":[22],"paradigm":[24],"dynamic":[26],"programming.":[27],"Starting":[28],"from":[29],"state-of-the-art":[31],"algorithms":[32,50,79,92],"computing":[34,104],"Banzhaf":[36,71],"and":[37,67,73,102],"Shapley\u2013Shubik":[38],"games,":[43],"we":[44],"present":[45],"a":[46],"framework":[47],"fast":[49],"three":[53,95],"most":[54],"common":[55],"precoalitions,":[59],"i.e.,":[60],"Owen":[62],"index,":[63,72],"Banzhaf\u2013Owen":[65],"index":[66],"symmetric":[69],"coalitional":[70],"point":[74],"out":[75],"why":[76],"our":[77,91],"new":[78],"are":[80],"applicable":[81],"large":[83],"numbers":[84],"players.":[86],"discuss":[88],"implementations":[89],"in":[100],"C++":[101],"review":[103],"times,":[105],"as":[106,108],"well":[107],"storage":[109],"requirements.":[110]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
