This paper tries to give a formal proof of the Coase Theorem. In a first step it is shown in a general bargaining model without bargaining costs, that the efficiency of a solution depends on the strategies used by the parties (stationary or non-stationary). By transforming the game into a modified Rubinstein-Game, a unique and efficient solution is obtained. In this, however, there is still a potential for strategic threats (extortion). If the parties use these threats, multiple equilibria will result, some of which are inefficient. Therefore, even without bargaining costs, the Coase Theorem is not generally valid.