A differential game of pollution control with participation of developed and developing countries

In this paper, a 2-player non-cooperative differential game is considered. We assume that he first player is a developed country with linear-quadratic utility function while the second player is a developing country whose utility function explicitely depends on time. Furthermore, the duration of the game is considered to be a random variable which reflects the instability of the economical development of developing countries. In the paper the duration of the game is assumed to be exponentially distributed. The optimal strategies are sought in the class of open-loop strategies.