Related papers: Smooth Nash Equilibria: Algorithms and Complexity
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…
We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval…
Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…
Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…
We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the…
In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm…
We introduce Cut-and-Play, a practically-efficient algorithm for computing Nash equilibria in simultaneous non-cooperative games where players decide via nonconvex and possibly unbounded optimization problems with separable payoff…
Nash equilibrium is often heralded as a guiding principle for rational decision-making in strategic interactions. However, it is well-known that Nash equilibrium sometimes fails as a reliable predictor of outcomes, with two of the most…
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due…
In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…
We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…
We study the problem of computing stationary Nash equilibria in discounted perfect information stochastic games from the viewpoint of computational complexity. For two-player games we prove the problem to be in PPAD, which together with a…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any $n$-player anonymous game with a bounded number of strategies and any constant $\delta>0$, an…
Finding Nash equilibria in two-player zero-sum imperfect-information games remains a central challenge in multi-agent reinforcement learning. Recent multi-round regularization methods offer a promising direction, yet existing approaches…
We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…