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:2607. 17543v1 Announce Type: new Abstract: In two-player zero-sum games whose Nash equilibria form a convex set, regularized solvers such as Regularized Nash Dynamics (R-NaD) empirically select the maximum-entropy member: the information projection (I-projection) of a uniform reference onto the Nash set.
arXiv:2606. 29169v1 Announce Type: cross Abstract: Many important games have more than two players and imperfect information.
The paper investigates how a reference policy can be used to steer regularized self‑play toward a specific equilibrium in two‑player zero‑sum games. By anchoring the reference at a target equilibrium and refining the self‑play process, the authors achieve precise convergence to that target with very low exploitability and coordinate error. The study also explores the effects of off‑manifold references, mirror‑step sizing, and boundary saturation on selection accuracy.
arXiv:2608. 04149v1 Announce Type: cross Abstract: Swap regret governs the rate at which uncoupled learning dynamics converge to correlated equilibria in multiplayer general-sum games.
arXiv:2606. 01159v1 Announce Type: new Abstract: We study two-player zero-sum games (TPZSGs) with bandit feedback under fairness constraints requiring every action to be played with probability at least $\alpha/m$.
arXiv:2607. 19854v1 Announce Type: new Abstract: We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$.
arXiv:2608.24731v1 Announce Type: new Abstract: We settle the minimax-optimal alternating regret, a regret notion motivated by alternating learning dynamics in games, for both online linear optimizat...
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: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.
The paper introduces Regret-Weighted Payoff Sampling (RWPS), a budgeted estimator that selectively simulates only payoff-matrix cells relevant to a Nash equilibrium and uses a surrogate model for the remaining entries. RWPS provides an instance-dependent error bound weighted by the opponent’s equilibrium mixture and a coverage result guaranteeing that, once the deviation-relevant set is simulated, surrogate error does not affect either player’s regret. Experiments on three 21×21 general-sum games, including an asymmetric Colonel Blotto, show that RWPS achieves four to six times tighter bounds than previous methods and outperforms other sampling strategies on the CyGym and ANSG cyber simulators at low budgets.
arXiv:2607. 13402v1 Announce Type: cross Abstract: In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials.
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.