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A method is presented that allows finding the market clearance prices within a hydrothermal power exchange market that incorporates network constraints. An analysis is made of the degree of market power exerted by the various agents. The Nash-Cournot equilibrium solution of the market is achieved using the Nikaido-Isoda function, which is derived from the profit maximization functions calculated by the generating companies. Both thermal, hydro generation, and network constraints are considered in the model, with coupling constraints of the hydro units also taken into account. The model is applied to the main Chilean interconnected power system, whose abundant hydro production and existing network bottlenecks make it a valuable suitable case for study. The results for pool-based and bilateral contract markets highlight the strength of the method and show the contribution of the transmission system and hydro constraints.