{"id":"https://openalex.org/W7164962976","doi":"https://doi.org/10.48550/arxiv.2606.16139","title":"The Computational Complexity of Team Zero-Sum Games","display_name":"The Computational Complexity of Team Zero-Sum Games","publication_year":2026,"publication_date":"2026-06-15","ids":{"openalex":"https://openalex.org/W7164962976","doi":"https://doi.org/10.48550/arxiv.2606.16139"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.16139","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16139","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.16139","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136504240","display_name":"Ioannis Anagnostides","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anagnostides, Ioannis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083207837","display_name":"Ioannis Panageas","orcid":"https://orcid.org/0000-0003-0577-4147"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panageas, Ioannis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138709865","display_name":"Tuomas Sandholm","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sandholm, Tuomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111317389","display_name":"J.-B. Yan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Jingming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T11031","display_name":"Game Theory and Applications","score":0.6686999797821045,"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":0.6686999797821045,"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":0.060499999672174454,"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/T10142","display_name":"Formal Methods in Verification","score":0.03629999980330467,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6007999777793884},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.5684000253677368},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.542900025844574},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5184000134468079},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5131000280380249},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.47029998898506165},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.43700000643730164},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.43059998750686646},{"id":"https://openalex.org/keywords/coordination-game","display_name":"Coordination game","score":0.4174000024795532},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.3978999853134155}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6007999777793884},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.5684000253677368},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.542900025844574},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5184000134468079},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5131000280380249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5098000168800354},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.43700000643730164},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.43059998750686646},{"id":"https://openalex.org/C107257861","wikidata":"https://www.wikidata.org/wiki/Q656316","display_name":"Coordination game","level":2,"score":0.4174000024795532},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4138000011444092},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.400299996137619},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.3889000117778778},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3874000012874603},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37860000133514404},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.37229999899864197},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.3149999976158142},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.30219998955726624},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C56694532","wikidata":"https://www.wikidata.org/wiki/Q4421045","display_name":"Turns, rounds and time-keeping systems in games","level":4,"score":0.2879999876022339},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.2838999927043915},{"id":"https://openalex.org/C19754495","wikidata":"https://www.wikidata.org/wiki/Q3435924","display_name":"Computational problem","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C97399411","wikidata":"https://www.wikidata.org/wiki/Q825367","display_name":"Coin flipping","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.26030001044273376},{"id":"https://openalex.org/C11343654","wikidata":"https://www.wikidata.org/wiki/Q780008","display_name":"Solution concept","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.25940001010894775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.250900000333786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.16139","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16139","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.16139","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16139","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"celebrated":[1],"consequence":[2],"of":[3,51,65,78,134,143,154,168,212,225,242,253],"the":[4,60,76,94,114,140,152,165,222],"minimax":[5],"theorem":[6],"is":[7,88,116,145,197,252],"that":[8,84,188,217],"two-player":[9,53],"zero-sum":[10,46,54,80,99,156,214],"games":[11,55,58,66,81,100,144],"admit":[12],"a":[13,30,48,91,122,148,159,190,205,210,243],"tractable":[14],"equilibrium":[15],"characterization.":[16],"In":[17,71],"many":[18],"central":[19],"applications,":[20],"however,":[21],"each":[22,131],"side":[23],"comprises":[24],"multiple":[25],"independent":[26,254],"agents":[27],"who":[28],"share":[29],"common":[31],"objective":[32],"but":[33],"cannot":[34],"perfectly":[35],"coordinate":[36],"their":[37],"actions.":[38],"Such":[39],"settings":[40],"can":[41],"be":[42],"modeled":[43],"as":[44,102,104],"\\emph{team":[45],"games},":[47],"natural":[49],"generalization":[50],"both":[52],"and":[56,138,162,170,174,181,227],"potential":[57],"--":[59],"two":[61,136],"most":[62],"well-studied":[63],"classes":[64],"in":[67,164,194],"algorithmic":[68],"game":[69,215],"theory.":[70],"this":[72],"paper,":[73],"we":[74,150,186,208,239],"settle":[75],"complexity":[77,153],"team":[79,98,132,213],"by":[82,178],"establishing":[83],"computing":[85,189],"Nash":[86],"equilibria":[87],"\\PPAD-complete.":[89],"As":[90,147],"result,":[92],"despite":[93],"global":[95],"adversarial":[96],"structure,":[97],"are":[101],"hard":[103],"general-sum":[105],"games.":[106],"Our":[107],"hardness":[108,234],"result":[109],"holds":[110],"even":[111,199],"when":[112],"i)":[113],"precision":[115],"inverse":[117],"polynomial,":[118],"thereby":[119],"ruling":[120],"out":[121],"fully":[123],"polynomial-time":[124],"approximation":[125],"scheme":[126],"(unless":[127],"$\u00b6=":[128],"\\PPAD$);":[129],"ii)":[130],"consists":[133],"only":[135],"players;":[137],"iii)":[139],"underlying":[141],"class":[142,160],"polymatrix.":[146],"byproduct,":[149],"resolve":[151],"group-wise":[155],"polymatrix":[157],"games,":[158],"introduced":[161],"examined":[163],"seminal":[166],"work":[167],"Cai":[169],"Daskalakis":[171],"(SODA":[172],"'11),":[173],"more":[175],"recently":[176],"highlighted":[177],"Hollender,":[179],"Maystre,":[180],"Nagarajan":[182],"(ICLR":[183],"'25).":[184],"Moreover,":[185,231],"show":[187],"first-order":[191],"stationary":[192],"point":[193],"min-max":[195],"optimization":[196],"\\PPAD-complete":[198],"for":[200,236],"quadratic":[201,237],"(multilinear)":[202],"objectives.":[203],"From":[204],"technical":[206],"standpoint,":[207],"develop":[209],"series":[211],"gadgets":[216],"allow":[218],"us":[219],"to":[220,232],"simulate":[221],"breakthrough":[223],"reduction":[224],"Bernasconi":[226],"Castiglioni":[228],"(STOC":[229],"'26).":[230],"obtain":[233],"results":[235],"objectives,":[238],"make":[240],"use":[241],"general":[244],"technique":[245],"based":[246],"on":[247],"linear":[248],"local":[249],"approximation,":[250],"which":[251],"interest.":[255]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-17T00:00:00"}
