Control of information horizon for cooperative differential game of pollution control

In this paper, we present a novel approach to defining the solution of a differential game. This approach allows to define optimal strategies in the differential games when players do not have the full information about the structure of the game along the time interval [t
₀
, T] on which the game is defined. It assumed that at each time instant the players have information about the structure of the game (payoff functions, motion equations) only for the next fixed time interval T̅̅, which is called the information horizon. Based on this information the players make their decision. Also in this work we consider the case when the players have the opportunity to control the informational horizon in order to receive the better joint payoff for the cooperating players. The problem is to define T̅̅ such that the imputation of each player computed on the basis of restricted information deviates from the imputation in classical cooperative differential game (with full information about the structure of the game known at the beginning of the game) by a value that does not exceed given M. The developed concept is applied to a cooperative differential game of pollution control.