{"id":"https://openalex.org/W1978032288","doi":"https://doi.org/10.1145/1148109.1148113","title":"The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions","display_name":"The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions","publication_year":2006,"publication_date":"2006-07-30","ids":{"openalex":"https://openalex.org/W1978032288","doi":"https://doi.org/10.1145/1148109.1148113","mag":"1978032288"},"language":"en","primary_location":{"id":"doi:10.1145/1148109.1148113","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1148109.1148113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030699433","display_name":"Alexis C. Kaporis","orcid":null},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"A.C. Kaporis","raw_affiliation_strings":["University of Patras, Patras, Greece"],"affiliations":[{"raw_affiliation_string":"University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011756177","display_name":"Paul G. Spirakis","orcid":"https://orcid.org/0000-0001-5396-3749"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"P.G. Spirakis","raw_affiliation_strings":["University of Patras, Patras, Greece"],"affiliations":[{"raw_affiliation_string":"University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030699433"],"corresponding_institution_ids":["https://openalex.org/I174878644"],"apc_list":null,"apc_paid":null,"fwci":7.8668,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.97313914,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"19","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9998000264167786,"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/T11031","display_name":"Game Theory and Applications","score":0.9998000264167786,"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":0.989300012588501,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.8859438896179199},{"id":"https://openalex.org/keywords/latency","display_name":"Latency (audio)","score":0.7413355112075806},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5880662202835083},{"id":"https://openalex.org/keywords/commodity","display_name":"Commodity","score":0.5188654661178589},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.46791818737983704},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.368367075920105},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.29407182335853577},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.11775234341621399}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.8859438896179199},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.7413355112075806},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5880662202835083},{"id":"https://openalex.org/C2779439359","wikidata":"https://www.wikidata.org/wiki/Q317088","display_name":"Commodity","level":2,"score":0.5188654661178589},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.46791818737983704},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.368367075920105},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.29407182335853577},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11775234341621399},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/1148109.1148113","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1148109.1148113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.109.3971","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.3971","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://students.ceid.upatras.gr/~kaporis/papers/kaporis-72456-init.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.484.4735","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.4735","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://students.ceid.upatras.gr/~kaporis/papers/KapSpi08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.877.3544","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.877.3544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Alexis_Kaporis/publication/223227483_The_price_of_optimum_in_Stackelberg_games_on_arbitrary_single_commodity_networks_and_latency_functions/links/00b495269788c2a3a9000000.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.880.3874","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.880.3874","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Alexis_Kaporis/publication/223227483_The_price_of_optimum_in_Stackelberg_games_on_arbitrary_single_commodity_networks_and_latency_functions/links/02bfe512dc3f9978ac000000.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.883.9818","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.883.9818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Alexis_Kaporis/publication/223227483_The_price_of_optimum_in_Stackelberg_games_on_arbitrary_single_commodity_networks_and_latency_functions/links/02bfe512dc3ff16a2f000000.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W40496385","https://openalex.org/W130824551","https://openalex.org/W169126583","https://openalex.org/W1526250527","https://openalex.org/W1562684525","https://openalex.org/W1578630563","https://openalex.org/W1579249907","https://openalex.org/W1753330597","https://openalex.org/W2006122291","https://openalex.org/W2012552037","https://openalex.org/W2012634103","https://openalex.org/W2029456721","https://openalex.org/W2030914480","https://openalex.org/W2039634593","https://openalex.org/W2039786295","https://openalex.org/W2053387401","https://openalex.org/W2068690208","https://openalex.org/W2070646375","https://openalex.org/W2075071286","https://openalex.org/W2088559962","https://openalex.org/W2097568888","https://openalex.org/W2098696428","https://openalex.org/W2109100253","https://openalex.org/W2110667918","https://openalex.org/W2118480861","https://openalex.org/W2123442845","https://openalex.org/W2125537511","https://openalex.org/W2129639820","https://openalex.org/W2132930161","https://openalex.org/W2143110141","https://openalex.org/W2144097899","https://openalex.org/W2145512846","https://openalex.org/W2147368141","https://openalex.org/W2149497768","https://openalex.org/W2151960821","https://openalex.org/W2155867373","https://openalex.org/W2158503783","https://openalex.org/W2164416056","https://openalex.org/W2406309358","https://openalex.org/W2585370079","https://openalex.org/W2914514011","https://openalex.org/W4302033101","https://openalex.org/W6634494593","https://openalex.org/W6651965038","https://openalex.org/W6676468133","https://openalex.org/W6676725597","https://openalex.org/W6713258388","https://openalex.org/W6817767538"],"related_works":["https://openalex.org/W2779562428","https://openalex.org/W1987753576","https://openalex.org/W3033499831","https://openalex.org/W2153002690","https://openalex.org/W2380362089","https://openalex.org/W1992162485","https://openalex.org/W2006248922","https://openalex.org/W2603701407","https://openalex.org/W2845623988","https://openalex.org/W1834011183"],"abstract_inverted_index":{"Let":[0],"M":[1,90],"be":[2,123],"a":[3,26,62,103,128,172],"single":[4],"s-t":[5,160],"network":[6,89],"of":[7,20,98,130,166],"parallel":[8],"links":[9],"with":[10,29],"load":[11],"dependent":[12],"latency":[13],"functions":[14],"shared":[15],"by":[16,42,102],"an":[17],"infinite":[18],"number":[19],"selfish":[21],"users.":[22],"This":[23,60],"may":[24],"yield":[25],"Nash":[27],"equilibrium":[28],"unbounded":[30],"Coordination":[31],"Ratio":[32],"[12,":[33],"26].":[34],"A":[35],"Leader":[36,104],"can":[37,122,141],"decrease":[38],"the":[39,54,83,94,146,167],"coordination":[40],"ratio":[41],"assigning":[43],"flow":[44,99,140],"\u03b1r":[45,139],"on":[46],"M,":[47],"and":[48],"then":[49],"all":[50],"Followers":[51],"assign":[52],"selfishly":[53],"(1":[55],"-":[56],"\u03b1)r":[57],"remaining":[58],"flow.":[59],"is":[61,78],"Stackelberg":[63,116],"Scheduling":[64],"Instance":[65],"(M,r,\u03b1),":[66],"0":[67],"\u2264":[68,70,143],"\u03b1":[69],"1.":[71],"It":[72],"was":[73],"shown":[74],"[23]":[75],"that":[76,135,152],"it":[77],"weakly":[79],"NP-hard":[80],"to":[81,105,158],"compute":[82,93],"optimal":[84,114],"Leader's":[85],"strategy.For":[86],"any":[87,159],"such":[88,134],"we":[91,150],"efficiently":[92],"minimum":[95],"portion":[96],"\u03b2M":[97],"r":[100],"needed":[101],"induce":[106,142],"M's":[107],"optimum":[108,147],"cost,":[109],"as":[110,112,171],"well":[111],"his":[113],"strategy.Unfortunately,":[115],"routing":[117],"in":[118],"more":[119],"general":[120],"nets":[121],"arbitrarily":[124],"hard.":[125],"Roughgarden":[126],"presented":[127],"modification":[129],"Braess's":[131,168],"Paradox":[132],"graph,":[133],"no":[136],"strategy":[137],"controlling":[138],"1<over>\u03b1":[144],"times":[145],"cost.":[148],"However,":[149],"show":[151],"our":[153],"main":[154],"result":[155],"also":[156],"applies":[157],"net":[161],"G.":[162],"We":[163],"take":[164],"care":[165],"graph":[169],"explicitly,":[170],"convincing":[173],"example.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
