Related papers: On Synchronous, Asynchronous, and Randomized Best-…
This paper builds on the work of Degond, Herty and Liu by considering N-player stochastic differential games. The control corresponding to a Nash equilibrium of such a game is approximated through model predictive control (MPC) techniques.…
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…
This paper addresses the distributed Nash Equilibrium seeking problem for aggregative games, where legitimate players' decisions are affected by potential malicious players. To describe players' behavior, we introduce a novel heterogeneous…
We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is…
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…
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…
This paper addresses the problem of fair equilibrium selection in graphical games. Our approach is based on the data structure called the {\em best response policy}, which was proposed by Kearns et al. \cite{kls} as a way to represent all…
In a network game, players interact over a network and the utility of each player depends on his own action and on an aggregate of his neighbours' actions. Many real world networks of interest are asymmetric and involve a large number 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…
A class of nonzero-sum stochastic dynamic games with imperfect information structure is investigated. The game involves an arbitrary number of players, modeled as homogeneous Markov decision processes, aiming to find a sequential Nash…
This paper establishes the equivalence between synchronous and asynchronous coordination mechanisms in dynamic games with strategic complementarities and common interests. Synchronous coordination, characterized by simultaneous commitments,…
We derive Nash equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as a smooth…
In this paper, an aggregate game approach is proposed for the modeling and analysis of energy consumption control in smart grid. Since the electricity user's cost function depends on the aggregate load, which is unknown to the end users, an…
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…
The multi-cluster games are addressed in this paper, where all players team up with the players in the cluster that they belong to, and compete against the players in other clusters to minimize the cost function of their own cluster. The…
We leverage best response dynamics to solve monotone variational inequalities on compact and convex sets. Specialization of the method to variational inequalities in game theory recovers convergence results to Nash equilibria when agents…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…
This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…
We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power…