Pricing Optimal Outcomes in Coupled and Non-Convex Markets: Theory and Applications to Electricity Markets

In many real-world markets, participants have non-convex preferences, and the allocation problem needs to consider complex constraints. Electricity markets are a prime example, but similar problems appear in many markets, which has led to a growing literature on market design. Competitive equilibrium does not generally exist in such markets. Today, power markets use heuristic pricing rules based on the dual of a relaxed allocation problem. With increasing levels of renewables, these rules have come under scrutiny as they lead to high out-of-market side payments to some participants and inadequate congestion signals. We show that existing pricing heuristics optimize specific design goals that can be conflicting. The tradeoffs can be substantial, and we establish that the design of pricing rules is fundamentally a multiobjective optimization problem addressing different incentives. In addition to traditional multiobjective optimization techniques that involve weighting individual objectives, we introduce a novel parameter-free pricing rule that minimizes incentives for market participants to deviate locally. Our theoretical and experimental findings show how the new pricing rule capitalizes on the upsides of existing pricing rules under scrutiny today. It leads to prices that incur low make-whole payments while providing adequate congestion signals and low lost opportunity costs. Our suggested pricing rule does not require weighing objectives, it is computationally scalable, and balances tradeoffs in a principled manner, addressing a critical policy issue in electricity markets.