Feedback and open-loop Nash equilibria in a class of differential games with random duration

Abstract

One class of differential games with random duration is considered. It is assumed that duration of the game is a random variable with values from a given finite interval. The game can be interrupted only on this interval. Methods of construction feedback and open-loop Nash equilibria for such games are proposed.

A Differential Game with Random Time Horizon and Discontinuous Distribution

“…This game formulation of stock investment game was investigated in [18]. Consider a cooperative form of the game:…”

“…The method of solution for such a wide class of problems by using dynamic programming methods [1], the maximum Pontryagin principle [16] and parametrization firstly was suggested in [17] for a class of differential games with random time horizon, with continuous but composite CDF, further generalized in [11]. Based on [11], a number of games with payoffs defined on adjoint time intervals were solved in [18,19].…”