{"id":"https://openalex.org/W2892353438","doi":"https://doi.org/10.1007/s10479-018-3047-0","title":"Efficient computation of the Shapley value for large-scale linear production games","display_name":"Efficient computation of the Shapley value for large-scale linear production games","publication_year":2018,"publication_date":"2018-09-20","ids":{"openalex":"https://openalex.org/W2892353438","doi":"https://doi.org/10.1007/s10479-018-3047-0","mag":"2892353438"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-018-3047-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-018-3047-0","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.soton.ac.uk/425036/1/LPGames.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039495491","display_name":"Phuoc Hoang Le","orcid":"https://orcid.org/0000-0002-3554-4206"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Phuoc Hoang Le","raw_affiliation_strings":["Southampton Business School and Centre for Operational Research, Management Science and Information Systems (CORMSIS), University of Southampton, Southampton, SO17 1BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southampton Business School and Centre for Operational Research, Management Science and Information Systems (CORMSIS), University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082841553","display_name":"Tri-Dung Nguyen","orcid":"https://orcid.org/0000-0002-4158-9099"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Tri-Dung Nguyen","raw_affiliation_strings":["Southampton Mathematical Sciences and Business School, University of Southampton, Southampton, SO17 1BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southampton Mathematical Sciences and Business School, University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021959924","display_name":"Tolga Bekta\u015f","orcid":"https://orcid.org/0000-0003-0634-144X"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tolga Bekta\u015f","raw_affiliation_strings":["Southampton Business School and Centre for Operational Research, Management Science and Information Systems (CORMSIS), University of Southampton, Southampton, SO17 1BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southampton Business School and Centre for Operational Research, Management Science and Information Systems (CORMSIS), University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082841553"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.4237,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.9132144,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"287","issue":"2","first_page":"761","last_page":"781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9918000102043152,"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":0.9904999732971191,"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":0.9569742679595947},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.8073021173477173},{"id":"https://openalex.org/keywords/cooperative-game-theory","display_name":"Cooperative game theory","score":0.7180697321891785},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6169053912162781},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5985528230667114},{"id":"https://openalex.org/keywords/production","display_name":"Production (economics)","score":0.5969435572624207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5729719996452332},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.5705872178077698},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5300835371017456},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5076354742050171},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.46339064836502075},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4490375220775604},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4343099296092987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3176409900188446},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18198129534721375},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.14660266041755676},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.12378597259521484}],"concepts":[{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.9569742679595947},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.8073021173477173},{"id":"https://openalex.org/C2781416736","wikidata":"https://www.wikidata.org/wiki/Q105354050","display_name":"Cooperative game theory","level":3,"score":0.7180697321891785},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6169053912162781},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5985528230667114},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.5969435572624207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5729719996452332},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.5705872178077698},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5300835371017456},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5076354742050171},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.46339064836502075},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4490375220775604},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4343099296092987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3176409900188446},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18198129534721375},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.14660266041755676},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.12378597259521484},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10479-018-3047-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10479-018-3047-0","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:425036","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s10479-018-3047-0>).","pdf_url":"https://eprints.soton.ac.uk/425036/1/LPGames.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"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:RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-3047-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10479-018-3047-0","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:kar.kent.ac.uk:92913","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/92913/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:eprints.soton.ac.uk:425036","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s10479-018-3047-0>).","pdf_url":"https://eprints.soton.ac.uk/425036/1/LPGames.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"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"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.5600000023841858}],"awards":[{"id":"https://openalex.org/G4469099560","display_name":null,"funder_award_id":"EP/P021042/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2892353438.pdf","grobid_xml":"https://content.openalex.org/works/W2892353438.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1593575857","https://openalex.org/W1762430620","https://openalex.org/W1920545862","https://openalex.org/W1966848756","https://openalex.org/W1968143987","https://openalex.org/W1982104453","https://openalex.org/W1999587457","https://openalex.org/W1999646672","https://openalex.org/W2002430844","https://openalex.org/W2002616065","https://openalex.org/W2026745519","https://openalex.org/W2030400787","https://openalex.org/W2035507135","https://openalex.org/W2044298016","https://openalex.org/W2046116913","https://openalex.org/W2060444450","https://openalex.org/W2073231946","https://openalex.org/W2081334386","https://openalex.org/W2101895569","https://openalex.org/W2102099143","https://openalex.org/W2103012681","https://openalex.org/W2109296605","https://openalex.org/W2276615843","https://openalex.org/W2294445636","https://openalex.org/W2487898712","https://openalex.org/W2583836055","https://openalex.org/W2798566347","https://openalex.org/W3036159281","https://openalex.org/W3102501663","https://openalex.org/W4233413206","https://openalex.org/W6637924259"],"related_works":["https://openalex.org/W3204498529","https://openalex.org/W2187416006","https://openalex.org/W1981630704","https://openalex.org/W2134138723","https://openalex.org/W1894585900","https://openalex.org/W2006581498","https://openalex.org/W1538386239","https://openalex.org/W3176033544","https://openalex.org/W2012494228","https://openalex.org/W2002199716"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}