Coalition and Anti-coalition Interaction in Cooperative Differential Games

Abstract

Abstract This paper is devoted to the study of how the coalition of players interact with the remaining players and vice versa. This is a key question when constructing the characteristic function in cooperative games. In this paper we consider three common approaches to the characteristic function construction in a cooperative differential game of n players: α—, δ— and ζ— characteristic functions and introduce a new characteristics of players’ behavior termed the reaction measure. Moreover, we introduce a new characteristic function which is technically much easy to construct. We study the properties of all considered characteristic functions and make the conclusion that the new characteristic function can be used instead of the classical α— characteristic function. The obtained results are illustrated for a differential game of pollution control.