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A stochastic non-linear Nash game for all the players in multi-zone supply auctions is established in this paper. The bidding strategies of power suppliers in multi-zone energy markets are functions of their own generation costs as well as the bidding behaviors of their competitors. The effects of the uncertainty and the risk are considered in constructing the bid functions of power suppliers. Physical constraints of multi-zone power systems are considered in the model. Dynamic programming algorithm is used to solve the Nash Game problem. A simplified three-zone model is used as a case study. The numerical outcome shows that our model is feasible and applicable.