Related papers: Solving Zero-Sum Games with Fewer Matrix-Vector Pr…
Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for…
Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial…
Recent developments in domains such as non-local games, quantum interactive proofs, and quantum generative adversarial networks have renewed interest in quantum game theory and, specifically, quantum zero-sum games. Central to classical…
We study $n$-agent Bayesian Games with $m$-dimensional vector types and linear payoffs, also called Linear Multidimensional Bayesian Games. This class of games is equivalent with $n$-agent, $m$-game Uniform Multigames. We distinguish…
Congestion games constitute an important class of games to model resource allocation by different users. As computing an exact or even an approximate pure Nash equilibrium is in general PLS-complete, Caragiannis et al. (2011) present a…
We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform…
This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an…
We initiate the study of how to perturb the reward in a zero-sum Markov game with two players to induce a desirable Nash equilibrium, namely arbitrating. Such a problem admits a bi-level optimization formulation. The lower level requires…
We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…
We focus on the design of algorithms for finding equilibria in 2-player zero-sum games. Although it is well known that such problems can be solved by a single linear program, there has been a surge of interest in recent years for simpler…
Recently, invariant risk minimization (IRM) (Arjovsky et al.) was proposed as a promising solution to address out-of-distribution (OOD) generalization. In Ahuja et al., it was shown that solving for the Nash equilibria of a new class of…
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…
We consider $\epsilon$-equilibria notions for constant value of $\epsilon$ in $n$-player $m$-actions games where $m$ is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that…
Motivated by the fact that in many game-theoretic settings, the game analyzed is only an approximation to the game being played, in this work we analyze equilibrium computation for the broad and natural class of bimatrix games that are…
We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in…
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 study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…
The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
We propose an efficient algorithm for finding first-order Nash equilibria in min-max problems of the form $\min_{x \in X}\max_{y\in Y} F(x,y)$, where the objective function is smooth in both variables and concave with respect to $y$; the…