{"id":"https://openalex.org/W4288043190","doi":"https://doi.org/10.48550/arxiv.2207.10949","title":"Maximizing Nash Social Welfare in 2-Value Instances: Delineating Tractability","display_name":"Maximizing Nash Social Welfare in 2-Value Instances: Delineating Tractability","publication_year":2022,"publication_date":"2022-07-22","ids":{"openalex":"https://openalex.org/W4288043190","doi":"https://doi.org/10.48550/arxiv.2207.10949"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2207.10949","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.10949","pdf_url":"https://arxiv.org/pdf/2207.10949","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2207.10949","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087445362","display_name":"Hannaneh Akrami","orcid":"https://orcid.org/0000-0002-9935-5869"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Akrami, Hannaneh","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101472738","display_name":"Bhaskar Ray Chaudhury","orcid":"https://orcid.org/0000-0002-7808-1483"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chaudhury, Bhaskar Ray","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065332233","display_name":"Martin Hoefer","orcid":"https://orcid.org/0000-0003-0131-5605"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hoefer, Martin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010961023","display_name":"Kurt Mehlhorn","orcid":"https://orcid.org/0000-0003-4020-4334"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mehlhorn, Kurt","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055912205","display_name":"Marco Schmalhofer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmalhofer, Marco","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013411555","display_name":"Golnoosh Shahkarami","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shahkarami, Golnoosh","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075717840","display_name":"Giovanna Varricchio","orcid":"https://orcid.org/0000-0001-6839-8551"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Varricchio, Giovanna","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015210129","display_name":"Quentin Vermande","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vermande, Quentin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003496696","display_name":"Ernest van Wijland","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"van Wijland, Ernest","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5087445362"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9976999759674072,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9968000054359436,"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/T12137","display_name":"Economic theories and models","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/valuation","display_name":"Valuation (finance)","score":0.6938375234603882},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5842503309249878},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.577078104019165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5418920516967773},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.49156150221824646},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.47246527671813965},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.46798253059387207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.433694988489151},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4217374324798584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2960582375526428},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.2072974443435669},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10262447595596313}],"concepts":[{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.6938375234603882},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5842503309249878},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.577078104019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5418920516967773},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.49156150221824646},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.47246527671813965},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.46798253059387207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.433694988489151},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4217374324798584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2960582375526428},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.2072974443435669},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10262447595596313},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2207.10949","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.10949","pdf_url":"https://arxiv.org/pdf/2207.10949","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2207.10949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2207.10949","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2207.10949","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.10949","pdf_url":"https://arxiv.org/pdf/2207.10949","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6399999856948853}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4288043190.pdf","grobid_xml":"https://content.openalex.org/works/W4288043190.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2803931294","https://openalex.org/W2282604764","https://openalex.org/W2500870930","https://openalex.org/W2218535193","https://openalex.org/W4389370903","https://openalex.org/W2468739564","https://openalex.org/W1554758635","https://openalex.org/W4302558842","https://openalex.org/W2171981925","https://openalex.org/W2955320052"],"abstract_inverted_index":{"We":[0,89,113],"study":[1],"the":[2,52,58,62,65,85,105,129],"problem":[3],"of":[4,8,14,61,64,75,78,87],"allocating":[5],"a":[6,12,72,93,100,124],"set":[7,13],"indivisible":[9],"goods":[10],"among":[11],"agents":[15],"with":[16,145],"\\emph{2-value":[17],"additive":[18],"valuations}.":[19],"In":[20,67],"this":[21,68],"setting,":[22],"each":[23],"good":[24],"is":[25,46,139],"valued":[26],"either":[27],"$1$":[28],"or":[29],"$p/q$,":[30],"for":[31,128],"some":[32],"fixed":[33],"co-prime":[34],"numbers":[35],"$p,q\\in":[36],"\\mathbb{N}$":[37],"such":[38],"that":[39,81,110,132],"$1\\leq":[40],"q":[41],"<":[42],"p$.":[43],"Our":[44],"goal":[45],"to":[47,98,119,141],"find":[48,99],"an":[49,121,143],"allocation":[50,103,127,144],"maximizing":[51],"\\emph{Nash":[53],"social":[54],"welfare}":[55],"(\\NSW),":[56],"i.e.,":[57],"geometric":[59],"mean":[60],"valuations":[63],"agents.":[66],"work,":[69],"we":[70,136],"give":[71],"complete":[73],"characterization":[74],"polynomial-time":[76,96],"tractability":[77],"\\NSW\\":[79,102,126,147],"maximization":[80],"solely":[82],"depends":[83],"on":[84],"values":[86],"$q$.":[88],"start":[90],"by":[91],"providing":[92],"rather":[94],"simple":[95],"algorithm":[97,122],"maximum":[101,125,146],"when":[104],"valuation":[106],"functions":[107],"are":[108],"\\emph{integral},":[109],"is,":[111,133],"$q=1$.":[112],"then":[114],"exploit":[115],"more":[116],"involved":[117],"techniques":[118],"get":[120],"producing":[123],"\\emph{half-integral}":[130],"case,":[131],"$q=2$.":[134],"Finally,":[135],"show":[137],"it":[138],"\\classNP-hard":[140],"compute":[142],"whenever":[148],"$q\\geq3$.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-02-24T06:16:03.338239","created_date":"2022-07-27T00:00:00"}