{"id":"https://openalex.org/W2107637077","doi":"https://doi.org/10.1109/gamenets.2009.5137391","title":"From competition to coopetition: Stackelberg equilibrium in multi-user power control games","display_name":"From competition to coopetition: Stackelberg equilibrium in multi-user power control games","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2107637077","doi":"https://doi.org/10.1109/gamenets.2009.5137391","mag":"2107637077"},"language":"en","primary_location":{"id":"doi:10.1109/gamenets.2009.5137391","is_oa":false,"landing_page_url":"https://doi.org/10.1109/gamenets.2009.5137391","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 International Conference on Game Theory for Networks","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/A5074724507","display_name":"Yi Su","orcid":"https://orcid.org/0000-0002-5834-8240"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yi Su","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles, USA","Department of Electrical Engineering, UCLA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Electrical Engineering, UCLA, USA#TAB#","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012339002","display_name":"Mihaela van der Schaar","orcid":"https://orcid.org/0000-0003-3933-6049"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mihaela van der Schaar","raw_affiliation_strings":["Department of Electrical Engineering, University of California, Los Angeles, USA","Department of Electrical Engineering, UCLA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, Los Angeles, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Electrical Engineering, UCLA, USA#TAB#","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074724507"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":0.2991,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.63490758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"107","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12146","display_name":"Power Line Communications and Noise","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11499","display_name":"ICT Impact and Policies","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.9149388074874878},{"id":"https://openalex.org/keywords/coopetition","display_name":"Coopetition","score":0.8113902807235718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7576508522033691},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5763135552406311},{"id":"https://openalex.org/keywords/competition","display_name":"Competition (biology)","score":0.509718120098114},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.4995718002319336},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4991719722747803},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.47365602850914},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.4599667191505432},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37086647748947144},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.16325396299362183},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.15439608693122864},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.14706450700759888},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.12654781341552734},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11200034618377686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.08224409818649292}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.9149388074874878},{"id":"https://openalex.org/C2777216475","wikidata":"https://www.wikidata.org/wiki/Q615782","display_name":"Coopetition","level":3,"score":0.8113902807235718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7576508522033691},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5763135552406311},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.509718120098114},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.4995718002319336},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4991719722747803},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.47365602850914},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.4599667191505432},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37086647748947144},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.16325396299362183},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.15439608693122864},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.14706450700759888},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.12654781341552734},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11200034618377686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.08224409818649292},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/gamenets.2009.5137391","is_oa":false,"landing_page_url":"https://doi.org/10.1109/gamenets.2009.5137391","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 International Conference on Game Theory for Networks","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Partnerships for the goals","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/17"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1975320652","https://openalex.org/W2002937495","https://openalex.org/W2004224914","https://openalex.org/W2071707134","https://openalex.org/W2104929522","https://openalex.org/W2107413438","https://openalex.org/W2110391887","https://openalex.org/W2111933819","https://openalex.org/W2124409123","https://openalex.org/W2139083802","https://openalex.org/W2139306630","https://openalex.org/W2143046241","https://openalex.org/W2145771620","https://openalex.org/W2156194062","https://openalex.org/W2158291106","https://openalex.org/W2161272050","https://openalex.org/W2202450854","https://openalex.org/W2296319761","https://openalex.org/W2610335499","https://openalex.org/W3146387078","https://openalex.org/W4236584668","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W2026907359","https://openalex.org/W1981800580","https://openalex.org/W2994124117","https://openalex.org/W2618752689","https://openalex.org/W2971526008","https://openalex.org/W4289422123","https://openalex.org/W3025389440","https://openalex.org/W2991761232","https://openalex.org/W4292703869","https://openalex.org/W3107507524"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,21,39,61,77,97,103,115,121,125,150,156,167,173],"problem":[4],"of":[5,46],"how":[6,33],"to":[7,94,165,171,175],"allocate":[8],"power":[9],"among":[10,105],"competing":[11,48],"users":[12,26,106,179],"sharing":[13],"a":[14,28,34,72,88,110,133,146],"frequency-":[15],"selective":[16],"interference":[17],"channel.":[18],"We":[19,31,66],"model":[20],"interaction":[22],"between":[23],"these":[24],"selfish":[25],"as":[27],"non-cooperative":[29],"game.":[30],"study":[32],"foresighted":[35,78,116,147],"user,":[36],"who":[37],"knows":[38],"channel":[40],"state":[41],"information":[42,152,169],"and":[43,170],"response":[44,100],"strategies":[45],"its":[47,52,82,154],"users,":[49],"should":[50],"optimize":[51],"own":[53],"transmission":[54,84],"strategy.":[55],"To":[56],"characterize":[57],"this":[58],"multiuser":[59],"interaction,":[60],"Stackelberg":[62],"equilibrium":[63],"is":[64,107,128],"introduced.":[65],"start":[67],"by":[68,86],"analyzing":[69],"in":[70],"detail":[71],"simple":[73],"two-user":[74],"scenario,":[75],"where":[76],"user":[79,117,148],"can":[80],"determine":[81],"optimal":[83,126],"strategy":[85],"solving":[87],"bi-level":[89],"program":[90],"which":[91],"allows":[92],"him":[93],"account":[95],"for":[96],"myopic":[98,122],"user's":[99],"strategies.":[101],"Therefore,":[102],"competition":[104,112],"transformed":[108],"into":[109],"cooperative":[111],"(coopetition)":[113],"since":[114],"will":[118,159],"avoid":[119],"interfering":[120],"user.":[123],"Since":[124],"solution":[127],"computationally":[129],"prohibitive,":[130],"we":[131],"propose":[132],"low-complexity":[134],"algorithm":[135],"based":[136],"on":[137],"Lagrangian":[138],"duality":[139],"theory.":[140],"Numerical":[141],"simulations":[142],"illustrate":[143],"that,":[144],"if":[145],"has":[149],"necessary":[151],"about":[153],"competitor,":[155],"resulting":[157],"coopetition":[158],"benefit":[160],"both":[161],"users.":[162],"Possible":[163],"methods":[164],"acquire":[166],"required":[168],"extend":[172],"formulation":[174],"more":[176],"than":[177],"two":[178],"are":[180],"also":[181],"discussed.":[182]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}