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We propose the first loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for…
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…
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…
In this paper, we address the challenge of Nash equilibrium (NE) seeking in non-cooperative convex games with partial-decision information. We propose a distributed algorithm, where each agent refines its strategy through projected-gradient…
We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…
This paper explores distributed aggregative games in multi-agent systems. Current methods for finding distributed Nash equilibrium require players to send original messages to their neighbors, leading to communication burden and privacy…
We study Nash equilibria learning of a general-sum stochastic game with an unknown transition probability density function. Agents take actions at the current environment state and their joint action influences the transition of the…
We study a distributed approach for seeking a Nash equilibrium in $n$-cluster games with strictly monotone mappings. Each player within each cluster has access to the current value of her own smooth local cost function estimated by a…
The approximation of mixed Nash equilibria (MNE) for zero-sum games with mean-field interacting players has recently raised much interest in machine learning. In this paper we propose a mean-field gradient descent dynamics for finding the…
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has…
We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…
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…
Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending…
This paper introduces a new method to achieve stable convergence to Nash equilibrium in duopoly noncooperative games. Inspired by the recent fixed-time Nash Equilibrium seeking (NES) as well as prescribed-time extremum seeking (ES) and…
Computing Nash equilibrium in multi-agent games is a longstanding challenge at the interface of game theory and computer science. It is well known that a general normal form game in N players and k strategies requires exponential space…
In stochastic Nash equilibrium problems (SNEPs), it is natural for players to be uncertain about their complex environments and have multi-dimensional unknown parameters in their models. Among various SNEPs, this paper focuses on locally…
We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is…
We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…