{"id":"https://openalex.org/W2992918303","doi":"https://doi.org/10.1007/s10458-019-09429-7","title":"Partition decision trees: representation for efficient computation of the Shapley value extended to games with externalities","display_name":"Partition decision trees: representation for efficient computation of the Shapley value extended to games with externalities","publication_year":2019,"publication_date":"2019-12-09","ids":{"openalex":"https://openalex.org/W2992918303","doi":"https://doi.org/10.1007/s10458-019-09429-7","mag":"2992918303"},"language":"en","primary_location":{"id":"doi:10.1007/s10458-019-09429-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10458-019-09429-7","pdf_url":null,"source":{"id":"https://openalex.org/S5405189","display_name":"Autonomous Agents and Multi-Agent Systems","issn_l":"1387-2532","issn":["1387-2532","1573-7454"],"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":"Autonomous Agents and Multi-Agent Systems","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/A5000212728","display_name":"Oskar Skibski","orcid":"https://orcid.org/0000-0002-3978-416X"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Oskar Skibski","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland","Institute of Informatics, University of Warsaw, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-3978-416X","affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025396810","display_name":"Tomasz Michalak","orcid":"https://orcid.org/0000-0002-5288-0324"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tomasz P. Michalak","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland","Institute of Informatics, University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037088437","display_name":"Yuko Sakurai","orcid":"https://orcid.org/0000-0002-0642-3878"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuko Sakurai","raw_affiliation_strings":["National Institute of Advanced Industrial Science and Technology, 1-3-1 Kasumigaseki, Chiyoda-ku, Tokyo, 100-8921, Japan","National Institute of Advanced Industrial Science and Technology, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Advanced Industrial Science and Technology, 1-3-1 Kasumigaseki, Chiyoda-ku, Tokyo, 100-8921, Japan","institution_ids":["https://openalex.org/I73613424"]},{"raw_affiliation_string":"National Institute of Advanced Industrial Science and Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I73613424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065393757","display_name":"Michael Wooldridge","orcid":"https://orcid.org/0000-0002-9329-8410"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michael Wooldridge","raw_affiliation_strings":["Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK","Department of Computer Science, University of Oxford, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Department of Computer Science, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048575057","display_name":"Makoto Yokoo","orcid":"https://orcid.org/0000-0003-4929-396X"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Makoto Yokoo","raw_affiliation_strings":["Faculty of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395, Japan","Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000212728"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.8423,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.94539144,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"34","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9988999962806702,"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":0.9988999962806702,"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":0.995199978351593,"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":0.989799976348877,"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/shapley-value","display_name":"Shapley value","score":0.9032245874404907},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.709901750087738},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6535534858703613},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6185839772224426},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5747938752174377},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4714333117008209},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4447590708732605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43820568919181824},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4052352011203766},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39260607957839966},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.3160106837749481},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22102344036102295},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12171980738639832}],"concepts":[{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.9032245874404907},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.709901750087738},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6535534858703613},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6185839772224426},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5747938752174377},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4714333117008209},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4447590708732605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43820568919181824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4052352011203766},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39260607957839966},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.3160106837749481},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22102344036102295},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12171980738639832},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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":1,"locations":[{"id":"doi:10.1007/s10458-019-09429-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10458-019-09429-7","pdf_url":null,"source":{"id":"https://openalex.org/S5405189","display_name":"Autonomous Agents and Multi-Agent Systems","issn_l":"1387-2532","issn":["1387-2532","1573-7454"],"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":"Autonomous Agents and Multi-Agent Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2492811296","display_name":null,"funder_award_id":"291528 (\u201cRACE\u201d)","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G2869855751","display_name":"Human Centric Mechanism Design for Sharing Society","funder_award_id":"17KK0008","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3050984150","display_name":"Human Centric Mechanism Design for Crowdsourcing","funder_award_id":"15H02751","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4146930921","display_name":"Establishing a Practical Theory of Market Design","funder_award_id":"17H00761","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5941046121","display_name":null,"funder_award_id":"DEC-2013/09/D/ST6/03920","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G7839616472","display_name":"Establishing Theory of Resource Allocation Mechanism Design for Sustainable Development","funder_award_id":"24220003","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":87,"referenced_works":["https://openalex.org/W48256706","https://openalex.org/W155540084","https://openalex.org/W179661928","https://openalex.org/W970540469","https://openalex.org/W1422351985","https://openalex.org/W1494851074","https://openalex.org/W1523207358","https://openalex.org/W1523568584","https://openalex.org/W1539346204","https://openalex.org/W1541475132","https://openalex.org/W1547467264","https://openalex.org/W1549171560","https://openalex.org/W1552671751","https://openalex.org/W1553692348","https://openalex.org/W1561843676","https://openalex.org/W1562353621","https://openalex.org/W1574410118","https://openalex.org/W1588483532","https://openalex.org/W1595459312","https://openalex.org/W1599103728","https://openalex.org/W1634954793","https://openalex.org/W1832793528","https://openalex.org/W1903683453","https://openalex.org/W1975264899","https://openalex.org/W1975794688","https://openalex.org/W1977203387","https://openalex.org/W1985862947","https://openalex.org/W1992083423","https://openalex.org/W2005690414","https://openalex.org/W2006377004","https://openalex.org/W2013069549","https://openalex.org/W2023581071","https://openalex.org/W2029140075","https://openalex.org/W2042413420","https://openalex.org/W2046116913","https://openalex.org/W2072385627","https://openalex.org/W2072665610","https://openalex.org/W2075385827","https://openalex.org/W2091208258","https://openalex.org/W2102099143","https://openalex.org/W2102152964","https://openalex.org/W2105197197","https://openalex.org/W2126233665","https://openalex.org/W2128546426","https://openalex.org/W2130520907","https://openalex.org/W2139634595","https://openalex.org/W2139742428","https://openalex.org/W2144910703","https://openalex.org/W2145790759","https://openalex.org/W2149422630","https://openalex.org/W2153166544","https://openalex.org/W2156887976","https://openalex.org/W2160099008","https://openalex.org/W2160138818","https://openalex.org/W2164244538","https://openalex.org/W2166830413","https://openalex.org/W2167073044","https://openalex.org/W2168001802","https://openalex.org/W2168150498","https://openalex.org/W2193638620","https://openalex.org/W2259808229","https://openalex.org/W2285990318","https://openalex.org/W2292224385","https://openalex.org/W2307833019","https://openalex.org/W2613252094","https://openalex.org/W2945364870","https://openalex.org/W2949557526","https://openalex.org/W2998378977","https://openalex.org/W3099451540","https://openalex.org/W3124760367","https://openalex.org/W3152304665","https://openalex.org/W4211220176","https://openalex.org/W4285719527","https://openalex.org/W4300337452","https://openalex.org/W4300576158","https://openalex.org/W6629277596","https://openalex.org/W6629855688","https://openalex.org/W6630022601","https://openalex.org/W6632513299","https://openalex.org/W6632743438","https://openalex.org/W6633251694","https://openalex.org/W6681603819","https://openalex.org/W6683637595","https://openalex.org/W6684395417","https://openalex.org/W6722226382","https://openalex.org/W7037776078","https://openalex.org/W7055933472"],"related_works":["https://openalex.org/W79233177","https://openalex.org/W3147268231","https://openalex.org/W1750845299","https://openalex.org/W3125424835","https://openalex.org/W2002181330","https://openalex.org/W2170170187","https://openalex.org/W3016558136","https://openalex.org/W2163633909","https://openalex.org/W2292224385","https://openalex.org/W4213175554"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}