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According to the fundamental theorems of welfare economics, any competitiveequilibrium is Pareto efficient. Unfortunately, competitive equilibrium pricesonly exist under strong assumptions such as perfectly divisible goods andconvex preferences. In many real-world markets, participants have non-convexpreferences and the allocation problem needs to consider complex constraints.Electricity markets are a prime example, but similar problems appear in manyreal-world markets, which has led to a growing literature in market design.Power markets use heuristic pricing rules based on the dual of a relaxedallocation problem today. With increasing levels of renewables, these ruleshave come under scrutiny as they lead to high out-of-market side-payments tosome participants and to inadequate congestion signals. We show that existingpricing heuristics optimize specific design goals that can be conflicting. Thetrade-offs can be substantial, and we establish that the design of pricingrules is fundamentally a multi-objective optimization problem addressingdifferent incentives. In addition to traditional multi-objective optimizationtechniques using weighing of individual objectives, we introduce a novelparameter-free pricing rule that minimizes incentives for market participantsto deviate locally. Our theoretical and experimental findings show how the newpricing rule capitalizes on the upsides of existing pricing rules underscrutiny today. It leads to prices that incur low make-whole payments whileproviding adequate congestion signals and low lost opportunity costs. Oursuggested pricing rule does not require weighing of objectives, it iscomputationally scalable, and balances trade-offs in a principled manner,addressing an important policy issue in electricity markets.

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