Optimization under linear side conditions using inverse monotone matrice

Environmental problems belong to the main challenging problems of the 21th century. There is a lack of new allocation principles for investments. Several approaches from the field of game theory concerning this topic may be found in [5] and [11], for example. Additionaly to that approaches the improvement of technical effectivity through cooperation (JI) is in the center of interest ([2], [8] and [9]). For that reason the TEM model was developed giving the possibility to combine this two intentions. In this paper such an allocation problem of the fund is solved for a special case. The fund is build from the cost game determined by the TEM model. The allocation problem leads to a new result in the area of the determination of Nash Equilibria and the optimization under linear side conditions. If we assume inverse monotony of the underlying matrices the actors can achieve the best possible individual result by solving a linear system which can be regarded as suitable solution to our problem in a public economy.