Convex games and feasible sets in control theory

Abstract.

The presented TEM-model describes the economical interaction between several actors (players) which intend to minimize their emissions (E _i) caused by technologies (T _i) by means of expenditures of money (M _i) or financial means, respectively. The index stands for the i-th player, i=1, … ,n. The players are linked by technical cooperations and the market, which expresses itself in the nonlinear time-discrete dynamics of the Technology-Emissions-Means-model, in short: TEM-model. In the sense of environmental protection, the aim is to reach a state which is mentioned in Kyoto Protocol by choosing the control parameters such that the emissions of each player become minimized. The focal point is the realization of the necessary optimal control parameters via a played cost game, which is determined by the way of cooperation of the actors. In application to the work of Leitmann, but not regarding solution sets as feasible sets, the τ-value of Tijs [13] is taken as a control parameter. This leads to a new class of problems in the area of 1-convex games. We want to solve the problem for a special case. With this solution a reasonable model for a Joint-Implementation process is developed, where its necessary fund is represented by the non-empty core of the analyzed game. Steering with parameters of this feasible set, the TEM-model can be regarded as a useful tool to implement and verify a technical Joint-Implementation Program. For the necessary data is given to the Clearing House, we are able to compare the numerical results with real world phenomena.