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In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information…

Most existing results about \emph{last-iterate convergence} of learning dynamics are limited to two-player zero-sum games, and only apply under rigid assumptions about what dynamics the players follow. In this paper we provide new results…

In recent years, although the Alternating Direction Method of Multipliers (ADMM) has been empirically applied widely to many multi-convex applications, delivering an impressive performance in areas such as nonnegative matrix factorization…

In this paper, we investigate a competitive market involving two agents who consider both their own wealth and the wealth gap with their opponent. Both agents can invest in a financial market consisting of a risk-free asset and a risky…

We consider multi-agent decision making where each agent's cost function depends on all agents' strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at…

In this paper, a new method is proposed to compute the rolling Nash equilibrium of the time-invariant nonlinear two-person zero-sum differential games. The idea is to discretize the time to transform a differential game into a sequential…

Different types of dynamics have been studied in repeated game play, and one of them which has received much attention recently consists of those based on "no-regret" algorithms from the area of machine learning. It is known that dynamics…

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…

In this paper, we consider a learning problem among non-cooperative agents interacting in a time-varying system. Specifically, we focus on repeated linear quadratic network games, in which the network of interactions changes with time and…

In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow…

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the noisy gradient descent ascent method which in the…

This paper considers a networked aggregative game (NAG) where the players are distributed over a communication network. By only communicating with a subset of players, the goal of each player in the NAG is to minimize an individual cost…

Multi-agent policy-gradient methods have been shown to converge locally near stable Nash equilibria. Local convergence, however, does not determine which equilibrium is reached. We study this question through basin-entry probability with…

We introduce an online learning algorithm in the bandit feedback model that, once adopted by all agents of a congestion game, results in game-dynamics that converge to an $\epsilon$-approximate Nash Equilibrium in a polynomial number of…

Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…

The behaviour of multi-agent learning in competitive settings is often considered under the restrictive assumption of a zero-sum game. Only under this strict requirement is the behaviour of learning well understood; beyond this, learning…

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…

The framework of multi-agent learning explores the dynamics of how individual agent strategies evolve in response to the evolving strategies of other agents. Of particular interest is whether or not agent strategies converge to well known…

In large systems, it is important for agents to learn to act effectively, but sophisticated multi-agent learning algorithms generally do not scale. An alternative approach is to find restricted classes of games where simple, efficient…

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and…