Optimization of an n-Person Game Under Linear Side Conditions

This paper is concerned with n-person games which typically occur in mathematical con ict models [cf. [4], [7],[8]]. These games are so called cost-games, in which every actor tries to minimize his own costs and the costs are interlinked by a system of linear inequalities. It is shown that, if the players cooperate, i.e., minimize the sum of all the costs, they achieve a Nash Equilibrium. In order to determine Nash Equilibria, the simplex method can be applied with respect to the dual problem. An important special case is discussed and numerical examples are presented.