Restructuring of the power industry was intended to provide incentives for more efficient operation and investment. Designers of markets have to balance the desire for “supporting prices” and “incentive compatibility” with needs for transparency and computational practicality, as well as political objectives, such as to provide support for certain favored technologies. This talk will review some specific circumstances in which there have been difficult choices, and the (perhaps) helpful insights that equilibrium models can provide. One example is day-ahead markets, in which strong non-convexities in start-up costs and other features mean that socially optimal schedules might be money losing for power providers. Another is longer run capacity markets, where the marginal contribution of a resource to system reliability is not always what is rewarded.