{"id":"https://openalex.org/W2921104972","doi":"https://doi.org/10.1007/s10107-020-01527-9","title":"Finding and verifying the nucleolus of cooperative games","display_name":"Finding and verifying the nucleolus of cooperative games","publication_year":2020,"publication_date":"2020-06-06","ids":{"openalex":"https://openalex.org/W2921104972","doi":"https://doi.org/10.1007/s10107-020-01527-9","mag":"2921104972"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01527-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01527-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01527-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01527-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019329502","display_name":"M\u00e1rton Benedek","orcid":"https://orcid.org/0000-0002-7492-1174"},"institutions":[{"id":"https://openalex.org/I163245316","display_name":"Corvinus University of Budapest","ror":"https://ror.org/01vxfm326","country_code":"HU","type":"education","lineage":["https://openalex.org/I163245316"]},{"id":"https://openalex.org/I4210155320","display_name":"ELTE Centre for Economic and Regional Studies","ror":"https://ror.org/051ea1411","country_code":"HU","type":"facility","lineage":["https://openalex.org/I106118109","https://openalex.org/I4210155320"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I4210147073","display_name":"Institute of Economics","ror":"https://ror.org/05ng8e884","country_code":"HU","type":"facility","lineage":["https://openalex.org/I106118109","https://openalex.org/I4210147073","https://openalex.org/I4210155320"]},{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"M\u00e1rton Benedek","raw_affiliation_strings":["Budapest University of Technology and Economics, Egry J\u00f3zsef u. 1., Budapest, 1111, Hungary","Corvinus University of Budapest, F\u0151v\u00e1m t\u00e9r 8., Budapest, 1093, Hungary","Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, T\u00f3th K\u00e1lm\u00e1n u. 4., Budapest, 1097, Hungary"],"affiliations":[{"raw_affiliation_string":"Budapest University of Technology and Economics, Egry J\u00f3zsef u. 1., Budapest, 1111, Hungary","institution_ids":["https://openalex.org/I29770179"]},{"raw_affiliation_string":"Corvinus University of Budapest, F\u0151v\u00e1m t\u00e9r 8., Budapest, 1093, Hungary","institution_ids":["https://openalex.org/I163245316"]},{"raw_affiliation_string":"Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences, T\u00f3th K\u00e1lm\u00e1n u. 4., Budapest, 1097, Hungary","institution_ids":["https://openalex.org/I4210155320","https://openalex.org/I4210147073","https://openalex.org/I7597260"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019337941","display_name":"J\u00f6rg Fliege","orcid":"https://orcid.org/0000-0002-4459-5419"},"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":"J\u00f6rg Fliege","raw_affiliation_strings":["Mathematical Sciences, University of Southampton, University Road, Southampton, SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences, University of Southampton, University Road, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","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":false,"raw_author_name":"Tri-Dung Nguyen","raw_affiliation_strings":["Mathematical Sciences, Business School and CORMSIS, University of Southampton, Southampton, SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences, Business School and CORMSIS, University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019329502"],"corresponding_institution_ids":["https://openalex.org/I163245316","https://openalex.org/I29770179","https://openalex.org/I4210147073","https://openalex.org/I4210155320","https://openalex.org/I7597260"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":3.3428,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94258258,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"190","issue":"1-2","first_page":"135","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9872999787330627,"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":0.9764000177383423,"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/computer-science","display_name":"Computer science","score":0.6534597873687744},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6117505431175232},{"id":"https://openalex.org/keywords/lawrence-kohlbergs-stages-of-moral-development","display_name":"Lawrence Kohlberg's stages of moral development","score":0.42932844161987305},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.410492479801178},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07728937268257141}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6534597873687744},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6117505431175232},{"id":"https://openalex.org/C4306678","wikidata":"https://www.wikidata.org/wiki/Q1194783","display_name":"Lawrence Kohlberg's stages of moral development","level":3,"score":0.42932844161987305},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.410492479801178},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07728937268257141},{"id":"https://openalex.org/C76247681","wikidata":"https://www.wikidata.org/wiki/Q6909101","display_name":"Moral development","level":2,"score":0.0},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10107-020-01527-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01527-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01527-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:426473","is_oa":false,"landing_page_url":"http://doi.org/10.1007/s10107-020-01527-9>).","pdf_url":null,"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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:kar.kent.ac.uk:93638","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01527-9>)","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:unipub.lib.uni-corvinus.hu:6106","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400280","display_name":"Corvinus Research Archive (Corvinus University of Budapest)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I163245316","host_organization_name":"Corvinus University of Budapest","host_organization_lineage":["https://openalex.org/I163245316"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10107-020-01527-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01527-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01527-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1361920374","display_name":"Cooperative Game Theory: New Mathematical and Algorithmic Approaches.","funder_award_id":"EP/P021042/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1934935867","display_name":null,"funder_award_id":"Engineering and Physical Sciences R","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3410465595","display_name":"DTA - University of Southampton","funder_award_id":"EP/M50662X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3505055956","display_name":null,"funder_award_id":"TUDFO/51757/2019-ITM, Thematic Excellence Program","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"id":"https://openalex.org/G4107333435","display_name":null,"funder_award_id":"TUDFO/51757/2019-ITM","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"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"},{"id":"https://openalex.org/G5266142934","display_name":null,"funder_award_id":"EP/M5","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8079175459","display_name":null,"funder_award_id":"TUDFO/51757/2019","funder_id":"https://openalex.org/F4320335908","funder_display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap"},{"id":"https://openalex.org/G8719353587","display_name":null,"funder_award_id":"EP/P0","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"},{"id":"https://openalex.org/F4320335908","display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2921104972.pdf","grobid_xml":"https://content.openalex.org/works/W2921104972.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W53596869","https://openalex.org/W1534528685","https://openalex.org/W1549171560","https://openalex.org/W1877528686","https://openalex.org/W1965547292","https://openalex.org/W1987344946","https://openalex.org/W2020121184","https://openalex.org/W2036615569","https://openalex.org/W2042923780","https://openalex.org/W2063810092","https://openalex.org/W2065788958","https://openalex.org/W2066311617","https://openalex.org/W2067219566","https://openalex.org/W2073544949","https://openalex.org/W2074062423","https://openalex.org/W2083218909","https://openalex.org/W2108959963","https://openalex.org/W2116198645","https://openalex.org/W2125363721","https://openalex.org/W2133953743","https://openalex.org/W2154435926","https://openalex.org/W2231698414","https://openalex.org/W2416389285","https://openalex.org/W2721250804","https://openalex.org/W2921104972","https://openalex.org/W3137934641","https://openalex.org/W4285719527","https://openalex.org/W6941464958"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2023084211","https://openalex.org/W2890005418","https://openalex.org/W4205175323","https://openalex.org/W2099929048","https://openalex.org/W4386507871","https://openalex.org/W1983454561","https://openalex.org/W2073500510"],"abstract_inverted_index":{"Abstract":[0],"The":[1,32,132],"nucleolus":[2,33,56,74,186,218],"offers":[3,63],"a":[4,64,70,114,178],"desirable":[5],"payoff-sharing":[6],"solution":[7,40,71],"in":[8,20,41,75],"cooperative":[9],"games,":[10],"thanks":[11],"to":[12,110,183],"its":[13],"attractive":[14],"properties\u2014it":[15],"always":[16],"exists":[17],"and":[18,28,112,176],"lies":[19],"the":[21,24,37,42,48,55,60,73,81,108,146,152,185,190,193,211,217],"core":[22,25],"(if":[23],"is":[26,30,34,57,72,137],"non-empty),":[27],"it":[29,45],"unique.":[31],"considered":[35],"as":[36],"most":[38,156],"\u2018stable\u2019":[39],"sense":[43],"that":[44,149],"lexicographically":[46],"minimizes":[47],"dissatisfactions":[49],"among":[50],"all":[51],"coalitions.":[52,170],"Although":[53],"computing":[54,216],"very":[58],"challenging,":[59],"Kohlberg":[61,147],"criterion":[62,115,148],"powerful":[65],"method":[66],"for":[67,103,215,219],"verifying":[68],"whether":[69],"relatively":[76],"small":[77],"games":[78,105,220],"(i.e.":[79],"with":[80,123,199],"number":[82],"of":[83,107,121,127,134,145,154,169,192,205,221],"players":[84],"$$n":[85],"\\le":[86],"15$$":[87],"<mml:math":[88,158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[89,159],"<mml:mrow>":[90,160],"<mml:mi>n</mml:mi>":[91,162],"<mml:mo>\u2264</mml:mo>":[92],"<mml:mn>15</mml:mn>":[93],"</mml:mrow>":[94,166],"</mml:math>":[95,167],").":[96],"This":[97],"approach,":[98],"however,":[99],"becomes":[100],"more":[101],"challenging":[102],"larger":[104],"because":[106],"need":[109],"form":[111],"check":[113],"involving":[116],"possibly":[117],"exponentially":[118,129],"large":[119,130,223],"collections":[120],"coalitions,":[122],"each":[124],"collection":[125],"potentially":[126],"an":[128,142],"size.":[131],"aim":[133],"this":[135],"work":[136],"twofold.":[138],"First,":[139],"we":[140,172],"develop":[141],"improved":[143],"version":[144],"involves":[150],"checking":[151],"\u2018balancedness\u2019":[153],"at":[155],"$$(n-1)$$":[157],"<mml:mo>(</mml:mo>":[161],"<mml:mo>-</mml:mo>":[163],"<mml:mn>1</mml:mn>":[164],"<mml:mo>)</mml:mo>":[165],"sets":[168],"Second,":[171],"exploit":[173],"these":[174],"results":[175],"introduce":[177],"novel":[179],"descent-based":[180],"constructive":[181],"algorithm":[182],"find":[184],"efficiently.":[187],"We":[188],"demonstrate":[189],"performance":[191],"new":[194],"algorithms":[195],"by":[196],"comparing":[197],"them":[198],"existing":[200],"methods":[201],"over":[202],"different":[203],"types":[204],"games.":[206],"Our":[207],"contribution":[208],"also":[209],"includes":[210],"first":[212],"open-source":[213],"code":[214],"moderately":[222],"sizes.":[224]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}