{"id":"https://openalex.org/W996368221","doi":"https://doi.org/10.1007/s00224-016-9701-5","title":"On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources","display_name":"On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources","publication_year":2016,"publication_date":"2016-08-25","ids":{"openalex":"https://openalex.org/W996368221","doi":"https://doi.org/10.1007/s00224-016-9701-5","mag":"996368221"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-016-9701-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-016-9701-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00224-016-9701-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","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%2Fs00224-016-9701-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054751334","display_name":"George Christodoulou","orcid":"https://orcid.org/0000-0002-9623-7461"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"George Christodoulou","raw_affiliation_strings":["University of Liverpool, Liverpool, UK","University of LIverpool, Liverpool, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"University of LIverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068565653","display_name":"Alkmini Sgouritsa","orcid":"https://orcid.org/0000-0003-3997-5131"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alkmini Sgouritsa","raw_affiliation_strings":["University of Liverpool, Liverpool, UK","University of LIverpool, Liverpool, UK"],"raw_orcid":"https://orcid.org/0000-0003-3997-5131","affiliations":[{"raw_affiliation_string":"University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"University of LIverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101455933","display_name":"Bo Tang","orcid":"https://orcid.org/0000-0003-0206-8271"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bo Tang","raw_affiliation_strings":["University of Liverpool, Liverpool, UK","University of LIverpool, Liverpool, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"University of LIverpool, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054751334"],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":2.9835,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.91152001,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"4","first_page":"600","last_page":"618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T12137","display_name":"Economic theories and models","score":0.9987999796867371,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9987000226974487,"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/price-of-anarchy","display_name":"Price of anarchy","score":0.8654764890670776},{"id":"https://openalex.org/keywords/subadditivity","display_name":"Subadditivity","score":0.8279595375061035},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7216290235519409},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6670847535133362},{"id":"https://openalex.org/keywords/inefficiency","display_name":"Inefficiency","score":0.6003203988075256},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.5991189479827881},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5648344159126282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5093363523483276},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.45913392305374146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3780197501182556},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3746309280395508},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3520938754081726},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3464687466621399},{"id":"https://openalex.org/keywords/price-of-stability","display_name":"Price of stability","score":0.3207666575908661},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.21175330877304077}],"concepts":[{"id":"https://openalex.org/C82149807","wikidata":"https://www.wikidata.org/wiki/Q7242623","display_name":"Price of anarchy","level":4,"score":0.8654764890670776},{"id":"https://openalex.org/C19220575","wikidata":"https://www.wikidata.org/wiki/Q1934099","display_name":"Subadditivity","level":2,"score":0.8279595375061035},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7216290235519409},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6670847535133362},{"id":"https://openalex.org/C2778869765","wikidata":"https://www.wikidata.org/wiki/Q6028363","display_name":"Inefficiency","level":2,"score":0.6003203988075256},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.5991189479827881},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5648344159126282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5093363523483276},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.45913392305374146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3780197501182556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3746309280395508},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3520938754081726},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3464687466621399},{"id":"https://openalex.org/C188466206","wikidata":"https://www.wikidata.org/wiki/Q7242626","display_name":"Price of stability","level":3,"score":0.3207666575908661},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.21175330877304077},{"id":"https://openalex.org/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","level":1,"score":0.0},{"id":"https://openalex.org/C126285488","wikidata":"https://www.wikidata.org/wiki/Q178476","display_name":"Monetary policy","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00224-016-9701-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-016-9701-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00224-016-9701-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00224-016-9701-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-016-9701-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00224-016-9701-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[{"id":"https://openalex.org/G1613467537","display_name":null,"funder_award_id":"EP/M008118/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7923599748","display_name":null,"funder_award_id":"M008118/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8025662718","display_name":null,"funder_award_id":"EP/K01000X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G828397419","display_name":null,"funder_award_id":"K01000X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G831499170","display_name":null,"funder_award_id":"LT140046","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W996368221.pdf","grobid_xml":"https://content.openalex.org/works/W996368221.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W155134184","https://openalex.org/W1487301434","https://openalex.org/W1489333206","https://openalex.org/W1526250527","https://openalex.org/W1568659650","https://openalex.org/W1582979652","https://openalex.org/W1757569435","https://openalex.org/W1976086105","https://openalex.org/W1987497363","https://openalex.org/W2005072840","https://openalex.org/W2030208840","https://openalex.org/W2052719152","https://openalex.org/W2058398491","https://openalex.org/W2060346604","https://openalex.org/W2093470907","https://openalex.org/W2095094403","https://openalex.org/W2104334470","https://openalex.org/W2108653052","https://openalex.org/W2112269231","https://openalex.org/W2115086848","https://openalex.org/W2115276154","https://openalex.org/W2136124238","https://openalex.org/W2144636928","https://openalex.org/W2162057799","https://openalex.org/W2167217653","https://openalex.org/W2170403527","https://openalex.org/W2513685331","https://openalex.org/W2627066480","https://openalex.org/W3017960000","https://openalex.org/W4251248798"],"related_works":["https://openalex.org/W2949813676","https://openalex.org/W1757569435","https://openalex.org/W2115276154","https://openalex.org/W2511754421","https://openalex.org/W2090874845","https://openalex.org/W1487301434","https://openalex.org/W2070394877","https://openalex.org/W2964281423","https://openalex.org/W2746352219","https://openalex.org/W1526250527","https://openalex.org/W1563327370","https://openalex.org/W1854960439","https://openalex.org/W2179146913","https://openalex.org/W2007583146","https://openalex.org/W3102653315","https://openalex.org/W3032760987","https://openalex.org/W2806555090","https://openalex.org/W1991307017","https://openalex.org/W2311526740","https://openalex.org/W2953392064"],"abstract_inverted_index":{"We":[0,34],"study":[1],"the":[2,5,36,43,49,65,76,96,151,160,169],"efficiency":[3],"of":[4,38,45,48],"proportional":[6,30],"allocation":[7],"mechanism":[8],"that":[9,64,120,159],"is":[10,123,162],"widely":[11],"used":[12],"to":[13,31,75,138],"allocate":[14],"divisible":[15,24],"resources.":[16],"Each":[17],"agent":[18],"submits":[19],"a":[20,28],"bid":[21],"for":[22,80,165],"each":[23],"resource":[25],"and":[26,54,84,109,125,143],"receives":[27],"fraction":[29],"her":[32],"bids.":[33],"quantify":[35],"inefficiency":[37],"Nash":[39,67],"equilibria":[40,68,82,100,167],"by":[41,101,129],"studying":[42],"Price":[44],"Anarchy":[46],"(PoA)":[47],"induced":[50],"game":[51],"under":[52],"complete":[53],"incomplete":[55],"information.":[56],"When":[57],"agents\u2019":[58,104],"valuations":[59,105],"are":[60,106],"concave,":[61],"we":[62,93,118,136,144,157],"show":[63,119,145],"Bayesian":[66,99],"can":[69],"be":[70,127],"arbitrarily":[71],"inefficient,":[72],"in":[73,168],"contrast":[74],"well-known":[77],"4/3":[78],"bound":[79,95,122,149],"pure":[81,166],"Johari":[83],"Tsitsiklis":[85],"(Math.":[86],"Oper.":[87],"Res.":[88],"29(3),":[89],"407\u2013435":[90],"2004).":[91],"Next,":[92],"upper":[94,148],"PoA":[97,152,161],"over":[98,153],"2":[102,164],"when":[103],"subadditive,":[107],"generalizing":[108],"strengthening":[110],"previous":[111],"bounds":[112],"on":[113,150],"lattice":[114],"submodular":[115],"valuations.":[116],"Furthermore,":[117],"this":[121],"tight":[124],"cannot":[126],"improved":[128,147],"any":[130],"simple":[131],"or":[132],"scale-free":[133],"mechanism.":[134],"Then":[135],"switch":[137],"settings":[139],"with":[140],"budget":[141],"constraints,":[142],"an":[146],"coarse-correlated":[154],"equilibria.":[155],"Finally,":[156],"prove":[158],"exactly":[163],"polyhedral":[170],"environment.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
