{"id":"https://openalex.org/W2101522887","doi":"https://doi.org/10.1145/1329125.1329433","title":"Computing the Banzhaf power index in network flow games","display_name":"Computing the Banzhaf power index in network flow games","publication_year":2007,"publication_date":"2007-05-14","ids":{"openalex":"https://openalex.org/W2101522887","doi":"https://doi.org/10.1145/1329125.1329433","mag":"2101522887"},"language":"en","primary_location":{"id":"doi:10.1145/1329125.1329433","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1329125.1329433","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems","raw_type":"proceedings-article"},"type":"conference-paper","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/A5062949033","display_name":"Yoram Bachrach","orcid":"https://orcid.org/0000-0002-4382-7636"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yoram Bachrach","raw_affiliation_strings":["The Hebrew University of Jerusalem, Israel","The Hebrew University of Jerusalem, , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University of Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University of Jerusalem, , Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091010876","display_name":"Jeffrey S. Rosenschein","orcid":"https://orcid.org/0000-0002-4042-9739"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Jeffrey S. Rosenschein","raw_affiliation_strings":["The Hebrew University of Jerusalem, Israel","The Hebrew University of Jerusalem, , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University of Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University of Jerusalem, , Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"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":0.9998000264167786,"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":0.9987000226974487,"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/voting","display_name":"Voting","score":0.770314633846283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6712226867675781},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.6302769780158997},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.6219607591629028},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5975058078765869},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5691287517547607},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5679284334182739},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.5517303347587585},{"id":"https://openalex.org/keywords/power-index","display_name":"Power index","score":0.531836986541748},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5186366438865662},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3447835445404053},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34107545018196106},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3353665769100189},{"id":"https://openalex.org/keywords/politics","display_name":"Politics","score":0.2539258599281311},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.24914970993995667},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.23507529497146606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18742051720619202},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.08469539880752563},{"id":"https://openalex.org/keywords/world-wide-web","display_name":"World Wide Web","score":0.07031804323196411}],"concepts":[{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.770314633846283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6712226867675781},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.6302769780158997},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.6219607591629028},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5975058078765869},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5691287517547607},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5679284334182739},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5517303347587585},{"id":"https://openalex.org/C3018596841","wikidata":"https://www.wikidata.org/wiki/Q7236523","display_name":"Power index","level":2,"score":0.531836986541748},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5186366438865662},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3447835445404053},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34107545018196106},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3353665769100189},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.2539258599281311},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.24914970993995667},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.23507529497146606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18742051720619202},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.08469539880752563},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.07031804323196411},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1329125.1329433","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1329125.1329433","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.5530","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.5530","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.huji.ac.il/%7Eyori/aamas07bachrach.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.4000000059604645,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3012705863","display_name":null,"funder_award_id":"898/05","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W59059920","https://openalex.org/W70412040","https://openalex.org/W1562353621","https://openalex.org/W1579245706","https://openalex.org/W1889721679","https://openalex.org/W1970663091","https://openalex.org/W1977911709","https://openalex.org/W1999983866","https://openalex.org/W2002616065","https://openalex.org/W2012634103","https://openalex.org/W2025604370","https://openalex.org/W2030710637","https://openalex.org/W2038127015","https://openalex.org/W2046116913","https://openalex.org/W2064699170","https://openalex.org/W2073197094","https://openalex.org/W2111154829","https://openalex.org/W2127145580","https://openalex.org/W2144872768","https://openalex.org/W2146980819","https://openalex.org/W2626618164","https://openalex.org/W3124653719","https://openalex.org/W3200814081"],"related_works":["https://openalex.org/W2058693177","https://openalex.org/W3142887577","https://openalex.org/W2074516001","https://openalex.org/W4233142526","https://openalex.org/W1485092126","https://openalex.org/W2149483255","https://openalex.org/W1497951756","https://openalex.org/W3020945092","https://openalex.org/W1982707951","https://openalex.org/W2327770525"],"abstract_inverted_index":{"Preference":[0],"aggregation":[1],"is":[2,62,69],"used":[3],"in":[4,21,37,53],"a":[5,12,34,38],"variety":[6],"of":[7,64],"multiagent":[8,22],"applications,":[9],"and":[10,56],"as":[11],"result,":[13],"voting":[14,40],"theory":[15],"has":[16,36],"become":[17],"an":[18],"important":[19],"topic":[20],"system":[23],"research.":[24],"However,":[25],"power":[26,60],"indices":[27],"(which":[28],"reflect":[29],"how":[30],"much":[31],"\"real":[32],"power\"":[33],"voter":[35],"weighted":[39],"system)":[41],"have":[42,49],"received":[43],"relatively":[44],"little":[45],"attention,":[46],"although":[47],"they":[48],"long":[50],"been":[51],"studied":[52],"political":[54],"science":[55],"economics.":[57],"The":[58],"Banzhaf":[59],"index":[61],"one":[63],"the":[65],"most":[66],"popular;":[67],"it":[68],"also":[70],"well-defined":[71],"for":[72],"any":[73],"simple":[74],"coalitional":[75],"game.":[76]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}