Abstract: In this paper, the authors first point out that game players are faced with some risk of decision-making when mixed strategy Nash equilibrium is achieved, and that the risk can not be directly measured with the conventional methods applied in weighing risks of general decision-making because this is the case with a g ame. Therefore, by integrating the expected utility, uncertainty and the absolut e risk aversion coefficient of players, the authors present a new method to meas ure the risk facing the players in a game, on the basis of which the authors dis cuss the effects on the realization of equilibrium in game playing.