相关论文: Forward Backward Stochastic Differential Equation …

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…

This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual…

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

In practical applications, decision-makers with heterogeneous dynamics may be engaged in the same decision-making process. This motivates us to study distributed Nash equilibrium seeking for games in which players are mixed-order (first-…

This paper introduces a new recursive stochastic optimal control problem driven by a forward-backward stochastic differential equations (FBSDEs), where the ter?minal time varies according to the constraints of the state of the forward…

This paper investigates an optimal control problem where the system is described by a stochastic differential equation with extended mixed delays that contain point delay, extended distributed delay, and extended noisy memory. The model is…

In this paper, we study the infinite-time mean field games with discounting, establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution. To solve this problem, we partition all agents…

In this work, we study stochastic non-cooperative games, where only noisy black-box function evaluations are available to estimate the cost function for each player. Since each player's cost function depends on both its own decision…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…

This paper studies the Nash equilibrium seeking problem for stochastic games under heavy-tailed noise. The gradient noise is considered to have a finite $\delta$-th moment ($1<\delta\le 2$), which generalizes the Gaussian noise and covers…

In this study, we investigate $N$-player stochastic differential games with regime switching, where the player dynamics are modulated by a finite-state Markov chain. We analyze the associated Nash system, which consists of a system of…

Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations.…

We study the convergence problem for mean field games with common noise and controlled volatility. We adopt the strategy recently put forth by Lauri\`ere and the second author, using the maximum principle to recast the convergence problem…

Finite-player dynamic games with dispersed private information are difficult because actions both move payoffs and reshape what opponents learn, generating hierarchies of beliefs about beliefs. This paper provides a recursive representation…

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum…

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 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,…

Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like…