Related papers: Solution to Zero-Sum Differential Game with Fracti…
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…
In this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…
We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority…
The paper is concerned with a zero-sum differential game in the case where a payoff is determined by the exit time, that is, the first time when the system leaves the game domain. Additionally, we assume that a part of domain's boundary is…
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $\alpha \in (0, 1)$ and a Bolza cost functional. The differential game is associated to the…
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 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 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…
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…
Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. Dynamic games model a wide variety of applications in economics, defense, and energy systems. However, compared to single-agent…
We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…
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…
This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions ($c$ and $\chi$ not decreasing in time).…
We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…
Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two…