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We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy…

We study generalized Nash equilibrium (GNE) problems in games with quadratic costs and individual linear equality constraints. Departing from approaches that require strong monotonicity and/or shared constraints, we reformulate the KKT…

Privacy preservation has served as a key metric in designing Nash equilibrium (NE) computation algorithms. Although differential privacy (DP) has been widely employed for privacy guarantees, it does not exploit prior distributional…

We study distributionally robust Markov games (DR-MGs) with the average-reward criterion, a framework for multi-agent decision-making under uncertainty over extended horizons. In average reward DR-MGs, agents aim to maximize their…

We design a distributed algorithm for learning Nash equilibria over time-varying communication networks in a partial-decision information scenario, where each agent can access its own cost function and local feasible set, but can only…

We consider the problem of finding a Nash equilibrium (NE) in a general-sum game, where player $i$'s objective is $f_i(x)=f_i(x_1,...,x_n)$, with $x_j\in\mathbb{R}^{d_j}$ denoting the strategy variables of player $j$. Our focus is on…

This paper presents a novel distributed formulation of the min-max optimization problem. Such a formulation enables enhanced flexibility among agents when optimizing their maximization variables. To address the problem, we propose two…

Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash…

This paper considers the privacy-preserving Nash equilibrium seeking strategy design for a class of networked aggregative games, in which the players' objective functions are considered to be sensitive information to be protected. In…

The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…

We prove input-to-state stability (ISS) of perturbed Newton-type methods for generalized equations arising from Nash equilibrium (NE) and generalized NE (GNE) problems. This ISS property allows the use of inexact computations in…

The Nash equilibrium problem is a widely used tool to model non-cooperative games. Many solution methods have been proposed in the literature to compute solutions of Nash equilibrium problems with continuous strategy sets, but, besides some…

We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…

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…

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…

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…

This paper considers the design of fully distributed Nash equilibrium seeking strategies for multi-agent games. To develop fully distributed seeking strategies, two adaptive control laws, including a node-based control law and an edge-based…

In stochastic Nash equilibrium problems (SNEPs), it is natural for players to be uncertain about their complex environments and have multi-dimensional unknown parameters in their models. Among various SNEPs, this paper focuses on locally…

In this paper, we study the problem of consensus-based distributed Nash equilibrium (NE) seeking where a network of players, abstracted as a directed graph, aim to minimize their own local cost functions non-cooperatively. Considering the…