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We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the…
Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving…
This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system.…
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.…
A key feature of wireless communications is the spatial reuse. However, the spatial aspect is not yet well understood for the purpose of designing efficient spectrum sharing mechanisms. In this paper, we propose a framework of spatial…
We explore the power of semidefinite programming (SDP) for finding additive $epsilon$-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the…
We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query…
We study natural improvement dynamics in weighted congestion games with polynomial latencies of maximum degree $d\geq 1$. We focus on two problems regarding the existence and efficiency of approximate pure Nash equilibria, with a reasonable…
This paper aims at investigating the problem of fast convergence to the Nash equilibrium (NE) for N-Player noncooperative differential games. The proposed method is such that the players attain their NE point without steady-state…
We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative convex games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate to her neighbors in…
Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given…
In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm…
We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…
We consider the problem of decentralized multi-agent reinforcement learning in Markov games. A fundamental question is whether there exist algorithms that, when adopted by all agents and run independently in a decentralized fashion, lead to…
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…
We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black…
We consider generalized Nash equilibrium (GNE) problems in games with strongly monotone pseudo-gradients and jointly linear coupling constraints. We establish the convergence rate of a payoff-based approach intended to learn a variational…
Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…