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This paper investigates the distributed Nash equilibrium seeking problem for two-network zero-sum games with set constraints, where the two networks have the opposite nonsmooth cost functions. The interaction of the agents in each network…

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…

To regulate a social system comprised of self-interested agents, economic incentives are often required to induce a desirable outcome. This incentive design problem naturally possesses a bilevel structure, in which a designer modifies the…

This paper explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on internal model are proposed for the case with…

We design the first fully-distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the…

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 considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…

We study the problem of maximizing Nash social welfare, which is the geometric mean of agents' utilities, in two well-known models. The first model involves one-sided preferences, where a set of indivisible items is allocated among a group…

In this article, we revisit a communication-control co-design problem for a class of two-player stochastic differential games on an infinite horizon. Each 'player' represents two active decision makers, namely a scheduler and a remote…

We investigate asynchronous distributed algorithms with delayed information for seeking generalized Nash equilibrium over multi-agent networks. The considered game model has all players' local decisions coupled with a shared affine…

Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the…

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance,…

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…

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…

To achieve an optimal outcome in many situations, agents need to choose distinct actions from one another. This is the case notably in many resource allocation problems, where a single resource can only be used by one agent at a time. How…

We develop a scheme based on active learning to compute equilibria in a generalized Nash equilibrium problem (GNEP). Specifically, an external observer (or entity), with little knowledge on the multi-agent process at hand, collects sensible…

We consider a subclass of $n$-player stochastic games, in which players have their own internal state/action spaces while they are coupled through their payoff functions. It is assumed that players' internal chains are driven by independent…

In this paper we propose a new operator splitting algorithm for distributed Nash equilibrium seeking under stochastic uncertainty, featuring relaxation and inertial effects. Our work is inspired by recent deterministic operator splitting…

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…

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…