Related papers: Coupled Wasserstein Gradient Flows for Min-Max and…
In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow…
We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not…
We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games. It is well-known that such dynamics converge locally when $S \succ 0$ and may diverge when $S=0$, where $S\succeq 0$ is the…
We present a novel notion of $\lambda$-monotonicity for an $n$-species system of partial differential equations governed by mass-preserving flow dynamics, extending monotonicity in Banach spaces to the Wasserstein-2 metric space. We show…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
This paper studies an $N$-coalition non-cooperative game problem, where the players in the same coalition cooperatively minimize the sum of their local cost functions under a directed communication graph, while collectively acting as a…
We study the existence and computation of Nash equilibria in concave games where the players' admissible strategies are subject to shared coupling constraints. Under playerwise concavity of constraints, we prove existence of Nash…
We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our…
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…
Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…
We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected…
We provide a distributed algorithm to learn a Nash equilibrium in a class of non-cooperative games with strongly monotone mappings and unconstrained action sets. Each player has access to her own smooth local cost function and can…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
Cooperative games are those in which both agents share the same payoff structure. Value-based reinforcement-learning algorithms, such as variants of Q-learning, have been applied to learning cooperative games, but they only apply when the…
Cooperative games are those in which both agents share the same payoff structure. Value-based reinforcement-learning algorithms, such as variants of Q-learning, have been applied to learning cooperative games, but they only apply when the…