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We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…
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…
Extensive-form games with imperfect recall are an important game-theoretic model that allows a compact representation of strategies in dynamic strategic interactions. Practical use of imperfect recall games is limited due to negative…
Zero-sum games are a fundamental setting for adversarial training and decision-making in multi-agent learning (MAL). Existing methods often ensure convergence to (approximate) Nash equilibria by introducing a form of regularization. Yet,…
We consider a class of nonsmooth aggregative games over networks in stochastic regimes, where each player is characterized by a composite cost function $f_i+r_i$, $f_i$ is a smooth expectation-valued function dependent on its own strategy…
This work investigates a problem of simultaneous global cost minimization and Nash equilibrium seeking, which commonly exists in $N$-cluster non-cooperative games. Specifically, the agents in the same cluster collaborate to minimize a…
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
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…
We study decentralized learning in two-player zero-sum discounted Markov games where the goal is to design a policy optimization algorithm for either agent satisfying two properties. First, the player does not need to know the policy of the…
Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
Distributed optimization and Nash equilibrium (NE) seeking problems have drawn much attention in the control community recently. This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative…
We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward…
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…
Designing efficient algorithms to compute Nash equilibria poses considerable challenges in Algorithmic Game Theory and Optimization. In this work, we employ integer programming techniques to compute Nash equilibria in Integer Programming…
This paper considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to…
The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of…
We study infinite-horizon discounted two-player zero-sum Markov games, and develop a decentralized algorithm that provably converges to the set of Nash equilibria under self-play. Our algorithm is based on running an Optimistic Gradient…
We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…