The paper proves that computing an approximate correlated equilibrium for a polytope game is PPAD‑complete, showing it is polynomial‑time equivalent to finding a Nash equilibrium. It introduces the notion of a fixed set—a finite set contained in the convex hull of its image under a continuous function—and demonstrates that computing such a fixed set is PPAD‑hard even at inverse polynomial precision.
arXiv:2609.22757v1 Announce Type: cross Abstract: A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing t...
arXiv:2610.03621v1 Announce Type: cross Abstract: There has been a surge of recent work on correlated equilibrium concepts in Markov games. However, existing results focus on concepts weaker than nor...
arXiv:2607. 11752v1 Announce Type: cross Abstract: For decades, static solution concepts (Nash, Correlated, and Coarse Correlated Equilibria) and the Price of Anarchy (PoA) have formed the bedrock of algorithmic game theory, with no-regret learning proving fast convergence to such game-theoretic equilibria.
For decades, static solution concepts (Nash, Correlated, and Coarse Correlated Equilibria) and the Price of Anarchy (PoA) have formed the bedrock of algorithmic game theory, with no-regret learning proving fast convergence to such game-theoretic equilibria. We show that reducing multi-agent learning to static equilibrium and black-box regret analysis obscures underlying dynamic disequilibrium and game theoretic bounds.
arXiv:2606. 28308v1 Announce Type: cross Abstract: Many two-player zero-sum games admit not a unique Nash equilibrium but a convex set of them: a polytope of profiles that all share the minimax value V* yet prescribe different behaviour.
arXiv:2606. 17000v1 Announce Type: cross Abstract: We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials.
arXiv:2504. 03432v4 Announce Type: replace-cross Abstract: Solving (Stampacchia) variational inequalities (SVIs) is a foundational problem at the heart of optimization.
We prove that computing a complete contiguous $\varepsilon$-envy-free cake allocation is PPAD-complete for normalized rational piecewise-constant additive valuations. The hardness holds even when $\va...
arXiv:2609.00504v1 Announce Type: cross Abstract: In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show t...
arXiv:2606. 29169v1 Announce Type: cross Abstract: Many important games have more than two players and imperfect information.
The paper presents a quasipolynomial-time algorithm for finding an ε-approximate fixed point of any d-dimensional nonexpansion under the λ∞ norm, running in time −log(1/ε)^{O(log^2 d)}. The method relies on a boosting argument that geometrically shrinks the search region. As a consequence, the algorithm shows that simple stochastic games can be solved in quasipolynomial time.
The paper presents the first PAC learning framework for general-sum concurrent stochastic games with uncertain transitions, addressing the challenge of Nash equilibrium existence. It introduces data‑driven L¹ confidence sets over transition kernels and a robust CSG solver that computes a social‑welfare optimal ε‑NE, or provides a certificate that no exact NE exists. The algorithm achieves polynomial sample complexity under a minimum reachability condition and is validated on benchmark CSGs with near‑optimal performance.