Game theory to characterize solutions of a discrete-time Hamilton-Jacobi equation

4th National Meeting in Chaos, Complex System and Time Series

Toledo, Porfirio^1

Facultad de Matemáticas, UV, Zona Universitaria, Xalapa, Ver. 91090, Mexico^1

关键词: Behavior of solutions;    Critical value;    Discrete time;    Hamilton;    Jacobi equations;    Minimax;    Optimal trajectories;    Real number;    Zero-sum game;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/475/1/012013/pdf
DOI  :  10.1088/1742-6596/475/1/012013

来源: IOP

【 摘 要 】

We study the behavior of solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework of game theory. The solutions of this problem represent the optimal payoff of a zero-sum game of two players, where the number of moves between the players converges to infinity. A real number, called the critical value, plays a central role in this work; this number is the asymptotic average action of optimal trajectories. The aim of this paper is to show the existence and characterization of solutions of a Hamilton-Jacobi equation for this kind of games.