A Method of Determining Characteristic Functions for Cooperative Differential Games without Side Payment

Abstract

Many person games are treated as non-cooperative games or cooperative games. Cooperative games are divided into games with side payment and without side payment. It is known that cooperative games without side payment can be analyzed and solved in the form of characteristic functions. It is necessary to determine the characteristic functions for differential games which are not described in the form of the characteristic functions. In this paper, a method of determining the characteristic functions is presented. Two kinds of characteristic functions are obtained according to the α-effectiveness and β-effectiveness, respectively. Determining the characteristic functions is reduced to solving the parametric minimax and maximin problems, two person differential games. The necessary conditions for the solutions of the problems are obtained.