Cooperative differential game theoretic models of innovations control

Creation and use of innovations determine a mainstream of the sustainable development of organizations of any type and are a necessary condition of the economic growth. In this paper we consider the problems of incentives of the employees for promotion of innovations by means of their reward allocation. The problems are formalized as cooperative differential games. In building of such games we used three different characteristic function: the classical Neumann-Morgenstern function as well as the functions proposed by Petrosyan and Zaccour, and Petrosyan and Gromova. The first function is always superadditive but is based on a not very realistic hypothesis of antagonism between a coalition and its complement. The second function more adequately used the players' payoffs in a Nash equilibrium but cannot guarantee the superadditivity. The third characteristic function provides a superadditive trade-off by guaranteeing the maximal payoff of a coalition when its members use their cooperative strategies. In all three cases the Shapley value is used as the optimality principle. Its components are calculated analytically and numerically by means of the Maple package. A comparative analysis of the results is made for a model example with three players for different values of the model parameters. The conclusions about the efficiency of the described methods of reward allocations are made.