Related papers: Open-loop potential difference games with inequali…

In this paper, we consider a linear quadratic stochastic two-person nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are introduced. The existence of the former is characterized by the solvability of a system of…

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…

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential…

An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…

Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…

We investigate the linear quadratic stochastic optimal control problems in infinite dimension without Markovian restriction for coefficients. The necessary and sufficient conditions for open-loop optimal controls are presented. We prove the…

This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system.…

In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification…

In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…

In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction…

We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction…

A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…

Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…

We observe that a significant class of Nash equilibrium problems in non-potential games can be associated with monotone inclusion problems. We propose splitting techniques to solve such problems and establish their convergence. Applications…

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…

We consider dynamic games defined over an infinite horizon, characterized by linear, discrete-time dynamics and quadratic cost functionals. Considering such linear-quadratic (LQ) dynamic games, we focus on their solutions in terms Nash…

When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…