相关论文: Game Theoretical Methods in Nonlinear PDEs

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed…

This article is related to risk-sensitive nonzero-sum stochastic differential games in the Markovian framework. This game takes into account the attitudes of the players toward risk and the utility is of exponential form. We show the…

We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that…

We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and…

We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…

We study nonlinear pantograph-type reaction-diffusion PDEs, which, in addition to the unknown $u=u(x,t)$, also contain the same functions with dilated or contracted arguments of the form $w=u(px,t)$, $w=u(x,qt)$, and $w=u(px,qt)$, where $p$…

Multiagent systems where agents interact among themselves and with a stochastic environment can be formalized as stochastic games. We study a subclass named Markov potential games (MPGs) that appear often in economic and engineering…

Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential…

We present a framework that incorporates the idea of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is characterized, in general, by its (Nash) equilibria in feedback form. However,…

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an…

We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper…

In this paper, we establish a large deviations principle (LDP) for interacting particle systems that arise from state and action dynamics of discrete-time mean-field games under the equilibrium policy of the infinite-population limit. The…

We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach…

Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables…

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…

We study a class of reflected backward stochastic differential equations with nonpositive jumps and upper barrier. Existence and uniqueness of a minimal solution is proved by a double penalization approach under regularity assumptions on…

Except for special classes of games, there is no systematic framework for analyzing the dynamical properties of multi-agent strategic interactions. Potential games are one such special but restrictive class of games that allow for tractable…

For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in…

We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash…

This paper is concerned with stochastic differential games (SDGs) defined through fully coupled forward-backward stochastic differential equations (FBSDEs) which are governed by Brownian motion and Poisson random measure. For SDGs, the…