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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…

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Existing settings of decentralized learning either require players to have full information or the system to have certain special structure that may be hard to check and hinder their applicability to practical systems. To overcome this, we…

This paper tackles the problem of solving stochastic optimization problems with a decision-dependent distribution in the setting of stochastic strongly-monotone games and when the distributional dependence is unknown. A two-stage approach…

The computational characterization of game-theoretic solution concepts is a central topic in artificial intelligence, with the aim of developing computationally efficient tools for finding optimal ways to behave in strategic interactions.…

In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are…

The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past…

A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the…

Noncooperative game-theoretic tools have been increasingly used to study many important resource allocation problems in communications, networking, smart grids, and portfolio optimization. In this paper, we consider a general class of…

In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…

In this paper, we consider a large class of constrained non-cooperative stochastic Markov games with countable state spaces and discounted cost criteria. In one-player case, i.e., constrained discounted Markov decision models, it is…

Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…

We study the robust Nash equilibrium (RNE) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies. Each user measures this impact, which may be…

Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement…

Designing optimal interdependent networks is important for the robustness and efficiency of national critical infrastructures. Here, we establish a two-person game-theoretic model in which two network designers choose to maximize the global…

The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex…

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…

Motivated by Cournot models, this paper proposes novel models of the noncooperative and cooperative differential games with density constraints in infinite dimensions, where markets consist of infinite firms and demand dynamics are governed…

To facilitate effective, safe deployment in the real world, individual robots must reason about interactions with other agents, which often occur without explicit communication. Recent work has identified game theory, particularly the…

Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage…