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The introduction of competition in electricity markets has given rise to the problem of strategic bidding by rational market participants (or players) in pursuit of individual profit (or welfare) maximization. Given the simultaneous action of all players, Nash equilibria are the solutions in the bidding space that simultaneously satisfy their individual objectives. The paper addresses the problem of finding Nash equilibria in a centralized competitive electricity market (PoolCo model) in which we assume that the players have reasonable estimates about all the other players' utility functions. In addition, we assume that a central decision maker-the independent grid operator or IGO-dispatches the market using an OPF tool that accepts as its inputs the bids and offers freely submitted by the participants. The paper shows how to search for multiple equilibria in a systematic manner if we make specific assumptions for the grid model and for the utility functions.