{"id":"https://openalex.org/W2613443557","doi":"https://doi.org/10.1080/0952813x.2018.1456791","title":"Computing the Shapley value in allocation problems: approximations and bounds, with an application to the Italian VQR research assessment program","display_name":"Computing the Shapley value in allocation problems: approximations and bounds, with an application to the Italian VQR research assessment program","publication_year":2018,"publication_date":"2018-04-08","ids":{"openalex":"https://openalex.org/W2613443557","doi":"https://doi.org/10.1080/0952813x.2018.1456791","mag":"2613443557"},"language":"en","primary_location":{"id":"doi:10.1080/0952813x.2018.1456791","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0952813x.2018.1456791","pdf_url":null,"source":{"id":"https://openalex.org/S153467142","display_name":"Journal of Experimental & Theoretical Artificial Intelligence","issn_l":"0952-813X","issn":["0952-813X","1362-3079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Experimental & Theoretical Artificial Intelligence","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.04176","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074964672","display_name":"Francesco Lupia","orcid":"https://orcid.org/0000-0003-0775-6890"},"institutions":[{"id":"https://openalex.org/I45204951","display_name":"University of Calabria","ror":"https://ror.org/02rc97e94","country_code":"IT","type":"education","lineage":["https://openalex.org/I45204951"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Lupia","raw_affiliation_strings":["Department of Computer Science, Modeling, Electronics and Systems Engineering, University of Calabria , Rende, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0775-6890","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Modeling, Electronics and Systems Engineering, University of Calabria , Rende, Italy","institution_ids":["https://openalex.org/I45204951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056363536","display_name":"Angelo Mendicelli","orcid":null},"institutions":[{"id":"https://openalex.org/I45204951","display_name":"University of Calabria","ror":"https://ror.org/02rc97e94","country_code":"IT","type":"education","lineage":["https://openalex.org/I45204951"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Angelo Mendicelli","raw_affiliation_strings":["Department of Computer Science, Modeling, Electronics and Systems Engineering, University of Calabria , Rende, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Modeling, Electronics and Systems Engineering, University of Calabria , Rende, Italy","institution_ids":["https://openalex.org/I45204951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055684160","display_name":"Andrea Ribichini","orcid":"https://orcid.org/0000-0002-0281-4257"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Ribichini","raw_affiliation_strings":["Department of Physics, Sapienza University of Rome , Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Sapienza University of Rome , Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011519788","display_name":"Francesco Scarcello","orcid":"https://orcid.org/0000-0001-7765-1563"},"institutions":[{"id":"https://openalex.org/I45204951","display_name":"University of Calabria","ror":"https://ror.org/02rc97e94","country_code":"IT","type":"education","lineage":["https://openalex.org/I45204951"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Francesco Scarcello","raw_affiliation_strings":["Department of Computer Science, Modeling, Electronics and Systems Engineering, University of Calabria , Rende, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7765-1563","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Modeling, Electronics and Systems Engineering, University of Calabria , Rende, Italy","institution_ids":["https://openalex.org/I45204951"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040566508","display_name":"Marco Schaerf","orcid":"https://orcid.org/0000-0002-2016-1966"},"institutions":[{"id":"https://openalex.org/I210043505","display_name":"North-Caucasus Federal University","ror":"https://ror.org/05g1k4d79","country_code":"RU","type":"education","lineage":["https://openalex.org/I210043505"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT","RU"],"is_corresponding":false,"raw_author_name":"Marco Schaerf","raw_affiliation_strings":["Department of Computer, Control, and Management Engineering \u2018Antonio Ruberti\u2019, Sapienza University of Rome , Rome, Italy","Institute of Information Technologies and Telecommunications, North Caucasus Federal University , Stavropol, Russian Federation","North-Caucasus Federal University, Stavropol, Russia"],"raw_orcid":"https://orcid.org/0000-0002-2016-1966","affiliations":[{"raw_affiliation_string":"Department of Computer, Control, and Management Engineering \u2018Antonio Ruberti\u2019, Sapienza University of Rome , Rome, Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Institute of Information Technologies and Telecommunications, North Caucasus Federal University , Stavropol, Russian Federation","institution_ids":["https://openalex.org/I210043505"]},{"raw_affiliation_string":"North-Caucasus Federal University, Stavropol, Russia","institution_ids":["https://openalex.org/I210043505"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5011519788"],"corresponding_institution_ids":["https://openalex.org/I45204951"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00525619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"4","first_page":"505","last_page":"524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9839000105857849,"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":0.9519000053405762,"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":0.8554703593254089},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5857399702072144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5680269002914429},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5591593384742737},{"id":"https://openalex.org/keywords/cooperative-game-theory","display_name":"Cooperative game theory","score":0.524711012840271},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5135750770568848},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5026404857635498},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.2243511974811554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21375039219856262}],"concepts":[{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.8554703593254089},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5857399702072144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5680269002914429},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5591593384742737},{"id":"https://openalex.org/C2781416736","wikidata":"https://www.wikidata.org/wiki/Q105354050","display_name":"Cooperative game theory","level":3,"score":0.524711012840271},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5135750770568848},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5026404857635498},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.2243511974811554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21375039219856262},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1080/0952813x.2018.1456791","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0952813x.2018.1456791","pdf_url":null,"source":{"id":"https://openalex.org/S153467142","display_name":"Journal of Experimental & Theoretical Artificial Intelligence","issn_l":"0952-813X","issn":["0952-813X","1362-3079"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Experimental & Theoretical Artificial Intelligence","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.04176","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.04176","pdf_url":"https://arxiv.org/pdf/1709.04176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2613443557","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1709.04176v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:iris.uniroma1.it:11573/1102376","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/1102376","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/951636","is_oa":true,"landing_page_url":"http://hdl.handle.net/11573/951636","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1709.04176","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.04176","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2796589266","is_oa":false,"landing_page_url":"http://ceur-ws.org/Vol-1745/paper3.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.04176","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.04176","pdf_url":"https://arxiv.org/pdf/1709.04176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W935602133","https://openalex.org/W1277554001","https://openalex.org/W1660564827","https://openalex.org/W2002722727","https://openalex.org/W2005690414","https://openalex.org/W2031938875","https://openalex.org/W2032444001","https://openalex.org/W2032642145","https://openalex.org/W2046116913","https://openalex.org/W2073231946","https://openalex.org/W2085648025","https://openalex.org/W2157841626","https://openalex.org/W2168454385","https://openalex.org/W2170904976","https://openalex.org/W2222512263","https://openalex.org/W2487898712","https://openalex.org/W2962998749","https://openalex.org/W3123365255","https://openalex.org/W4233413206"],"related_works":["https://openalex.org/W2285990318","https://openalex.org/W2950617325","https://openalex.org/W622713660","https://openalex.org/W2181701992","https://openalex.org/W122841170","https://openalex.org/W2503919929","https://openalex.org/W2766085653","https://openalex.org/W2949121341","https://openalex.org/W2034685564","https://openalex.org/W2987025650","https://openalex.org/W1868887333","https://openalex.org/W1982124588","https://openalex.org/W2963036332","https://openalex.org/W2406013728","https://openalex.org/W3101463300","https://openalex.org/W2811121539","https://openalex.org/W633535488","https://openalex.org/W2736204762","https://openalex.org/W2064440236","https://openalex.org/W2950841572"],"abstract_inverted_index":{"In":[0],"allocation":[1,52,89],"problems":[2,53],"with":[3,73],"indivisible":[4],"goods,":[5],"money":[6],"compensation":[7],"is":[8,32],"used":[9,37],"to":[10,24,38,50],"distribute":[11],"worth":[12],"in":[13],"a":[14,20,33,40,85],"fair":[15,41],"way.":[16],"Coalitional":[17],"games":[18],"provide":[19],"formal":[21],"mathematical":[22],"framework":[23],"model":[25],"such":[26],"problems,":[27,90],"and":[28,54,62,82],"the":[29,66,92],"Shapley":[30,67],"value":[31,68],"solution":[34],"concept":[35],"widely":[36],"realise":[39],"distribution.":[42],"To":[43],"overcome":[44],"its":[45],"intractability,":[46],"we":[47,55],"describe":[48],"how":[49],"simplify":[51],"propose":[56],"algorithms":[57],"for":[58],"computing":[59],"lower":[60],"bounds":[61,64],"upper":[63],"of":[65,88],"that":[69],"can":[70],"be":[71],"combined":[72],"approximation":[74],"algorithms.":[75],"The":[76],"proposed":[77],"techniques":[78],"have":[79],"been":[80],"implemented":[81],"tested":[83],"on":[84],"real-world":[86],"application":[87],"namely,":[91],"Italian":[93],"research":[94],"assessment":[95],"program":[96],"known":[97],"as":[98],"VQR.":[99]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}