Related papers: On Tractable $\Phi$-Equilibria in Non-Concave Game…
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…
The computational study of equilibria involving constraints on players' strategies has been largely neglected. However, in real-world applications, players are usually subject to constraints ruling out the feasibility of some of their…
Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…
We know that the Nash equilibria of a game cannot be computed efficiently unless $P = PPAD$. But can they be learned? Are there dynamics that (1) can be computed efficiently by the players at each strategy profile and (2) are guaranteed to…
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…
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…
Correlated equilibria are a fundamental solution concept in game theory. However, despite decades of research, the complexity beyond games of polynomial type -- such as extensive-form games, congestion or routing games, and more broadly…
Learning and computation of equilibria are central problems in game theory, theory of computation, and artificial intelligence. In this work, we introduce proximal regret, a new notion of regret based on proximal operators that lies…
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…
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…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
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 unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and…
Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…
In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…
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…
Recent extensions to dynamic games of the well-known fictitious play learning procedure in static games were proved to globally converge to stationary Nash equilibria in two important classes of dynamic games (zero-sum and…
Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…
A wide array of modern machine learning applications - from adversarial models to multi-agent reinforcement learning - can be formulated as non-cooperative games whose Nash equilibria represent the system's desired operational states.…