This paper reviews the standard game models and its Nash equilibrium and then analyses Cournot oligopoly game from two firms to the case with more than two firms. Due to Cournot equilibrium point, the concept of Cournot equilibrium point is the same as the concept as the non-cooperative game with pure strategy but the strategy can be chosen in Cournot game is infinity and it can not be obtained base on Nash equilibrium theorem. Finally, the existence conditions of Cournot equilibrium point are given and the theorem and its proof of the existence Cournot equilibrium point are given too.
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