The economic dispatch problem is to determine a socially optimal allocation of supply and demand subject to transmission constraints. With strategic generators possessing market power, the locational marginal pricing mechanism may not induce the economic dispatch. We investigate the market outcomes from a game-theoretic perspective, employing piecewise constant offer curves as in practice, in contrast to affine offer curves as in the literature. We present counterexamples to show that a Nash equilibrium may not exist, or that the price of anarchy can be arbitrarily large. On the other hand, we provide sufficient conditions under which there exist efficient Nash equilibria. We then study the LMP mechanism with Cournot offers. As an alternative, we propose the marginal contribution pricing mechanism that guarantees efficient outcomes.