Related papers: Differential Games for a Mixed ODE-PDE System
In this paper we study zero-sum two-player stochastic differential games with the help of theory of Backward Stochastic Differential Equations (BSDEs). At the one hand we generalize the results of the pioneer work of Fleming and Souganidis…
We study a zero-sum stochastic differential switching game in infinite horizon. We prove the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities…
We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the…
Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with…
We consider a finite-horizon, zero-sum game in which both players control a stochastic differential equation by invoking impulses. We derive a control randomization formulation of the game and use the existence of a value for the randomized…
In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a…
We generalize the results of Fleming and Souganidis (1989) on zero sum stochastic differential games to the case when the controls are unbounded. We do this by proving a dynamic programming principle using a covering argument instead of…
This paper studies a two-player nonzero-sum stochastic differential game governed by a controlled convection-diffusion stochastic partial differential equation (SPDE) with spatially heterogeneous coefficients. The diffusion and transport…
In this paper, we study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and…
We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some…
We consider two-player zero-sum differential games (ZSDGs), where the state process (dynamical system) depends on the random initial condition and the state process's distribution, and the objective functional includes the state process's…
We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity…
The paper is concerned with a two-player nonzero-sum differential game in the case when players are informed about the current position. We consider the game in control with guide strategies first proposed by Krasovskii and Subbotin. The…
We study a zero-sum stochastic differential game (SDG) in which one controller plays an impulse control while their opponent plays a stochastic control. We consider an asymmetric setting in which the impulse player commits to, at the start…
This paper is about a set-based computing method for solving a general class of two-player zero-sum Stackelberg differential games. We assume that the game is modeled by a set of coupled nonlinear differential equations, which can be…
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…
This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…
We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary…