In this paper, we consider dynamical system, in the presence of parameter uncertainties. We apply max-min principles to determine the saddle point solution for the class of differential game arising from the associated dynamical system. We also provide sufficient condition for the existence of this saddle point.

This study focuses on planning flexibility and environmental scanning from the standpoint of corporate entrepreneurship, as represented by Top management. Game theory was applied in this study. In doing this, the problem was viewed from a “worst case design concept” which can be summarised as follows: The intrapreneur (the entrepreneur within a firm or corporate entrepreneurs) wishes to minimise the cost of operation while the environment tries to maximize the cost of operation. Hence, we introduce a cost functional, which is the cost of risk faced by the intrapreneur. We assume that the entrepreneur can apply flexibility in planning, hence denote this as control, while the environment that is needed to be scanned is denoted as uncertainty. The model of game is applied to allow for saddle point (a point where there is no ‘gain’ no ‘loss’) solution. The implication of this is that for a saddle point to exist in a “worst case” situation, the intrapreneur is likely to breaking-even. Thus, a proper mathematical treatment is given for such a game problem

This paper examined a class of multidimensional differential games. In particular, it considered a situation in which the pursuer and evader are affected by uncertain disturbances. A necessary and sufficient condition for the existence of saddle point for this class of games was developed.