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We study the computational complexity of Nash equilibria in concurrent games with limit-average objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

Distributed optimization and Nash equilibrium (NE) seeking problems have drawn much attention in the control community recently. This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative…

In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…

We study the computation of Nash equilibria in a two-player normal form game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement…

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for…

Shared-constraint games are noncooperative $N$-player games where players are coupled through a common coupling constraint. It is known that such games admit two kinds of equilibria -- generalized Nash equilibria (GNE) and variational…

One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural…

In this paper, a Nash-type fictitious game framework is introduced to handle a time-inconsistent linear-quadratic optimal control. The Nash-type game in this framework is called fictitious as it is between the decision maker (called real…

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…

We propose a projected variational quantum extragradient (VQEG) framework for computing approximate Nash equilibria in two-player zero-sum matrix games. Mixed strategies are parameterized as Born distributions of parameterized quantum…

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in…

Power system operators and electric utility companies often impose a coincident peak demand charge on customers when the aggregate system demand reaches its maximum. This charge incentivizes customers to strategically shift their peak usage…

Drawing intuition from a (physical) hydraulic system, we present a novel framework, constructively showing the existence of a strong Nash equilibrium in resource selection games (i.e., asymmetric singleton congestion games) with nonatomic…

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…

This paper investigates a fully distributed adaptive Nash equilibrium (NE) seeking algorithm for constrained noncooperative games with prescribed-time stability. On the one hand, prescribed-time stability for the proposed NE seeking…

We study the complexity of computing stationary Nash equilibrium (NE) in n-player infinite-horizon general-sum stochastic games. We focus on the problem of computing NE in such stochastic games when each player is restricted to choosing a…

Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium.…

We consider a class of targeted intervention problems in dynamic network and graphon games. First, we study a general dynamic network game in which players interact over a graph and maximize their heterogeneous, concave goal functionals,…

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a…