{"paper":{"title":"On the Complexity of Correlated Equilibria Beyond Normal-Form Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping.","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Brian Hu Zhang, Constantinos Daskalakis, Gabriele Farina, Ioannis Anagnostides, Noah Golowich, Tuomas Sandholm","submitted_at":"2026-05-17T21:50:52Z","abstract_excerpt":"Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly concave games -- has remained a major open problem, first highlighted by Papadimitriou and Roughgarden (JACM '08).\n  In this paper, we resolve several long-standing questions concerning the complexity of correlated equilibria and swap regret minimization. First, we show that computing a correlated equilibrium in concave quadratic games is as hard as computing t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping (Contr), providing the first strong evidence of intractability.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reduction establishing Contr-hardness for correlated equilibria holds specifically for the class of concave quadratic games and for the standard definition of correlated equilibrium; if the game class or equilibrium notion is altered, the hardness may not transfer (abstract statement on hardness for concave quadratic games).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper establishes Contr-hardness for correlated equilibria in concave quadratic games, an exponential lower bound on swap regret minimization, and FPTAS algorithms for poly-dimensional Φ-equilibria in concave games.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a8371c91302864c45c3016503e8164751762eb0dac4a6bb32e5cddb86fb51efc"},"source":{"id":"2605.17665","kind":"arxiv","version":1},"verdict":{"id":"4f70f890-4154-4794-93af-a7884fe0c7b8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:00:40.630042Z","strongest_claim":"computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping (Contr), providing the first strong evidence of intractability.","one_line_summary":"The paper establishes Contr-hardness for correlated equilibria in concave quadratic games, an exponential lower bound on swap regret minimization, and FPTAS algorithms for poly-dimensional Φ-equilibria in concave games.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reduction establishing Contr-hardness for correlated equilibria holds specifically for the class of concave quadratic games and for the standard definition of correlated equilibrium; 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