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This paper considers a strategic power producer that trades electric energy in an electricity pool. It provides a procedure to derive the optimal offering strategy of this producer. A multiperiod network-constrained market-clearing algorithm is considered. Uncertainty on demand bids and offering strategies of rival producers is also modeled. The proposed procedure to derive strategic offers relies on a bilevel programming model whose upper-level problem represents the profit maximization of the strategic producer while the lower-level one represents the market clearing and the corresponding price formation. This bilevel model is reduced to a mixed-integer linear programming problem using the duality theory and the Karush-Kuhn-Tucker optimality conditions. Results from an illustrative example and a case study are reported and discussed. Finally, some relevant conclusions are duly drawn.