Fixed Sets and the Hardness of Computing Correlated Equilibria
We show that computing an approximate correlated equilibrium of a polytope game is PPAD-complete, and thus polynomial-time equivalent to finding a Nash equilibrium. This challenges the conventional view in game theory that correlated equilibria are more tractable objects than Nash equilibria. From a conceptual standpoint, we connect correlated equilibria to a natural generalization of fixed points, which we call fixed sets. A fixed set of a continuous function $f$ is a nonempty finite set $S$ such that $S \subseteq \operatorname{conv} f(S)$. Our main technical contribution is to prove that computing a fixed set is PPAD-hard even at inverse polynomial precision.
| Authors | Ioannis Anagnostides, Constantinos Daskalakis, Gabriele Farina et al. |
|---|---|
| Primary category | cs.GT |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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