  According to the fundamental theorems of welfare economics, any competitive
equilibrium is Pareto efficient. Unfortunately, competitive equilibrium prices
only exist under strong assumptions such as perfectly divisible goods and
convex preferences. 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
real-world markets, which has led to a growing literature in market design.
Power markets use heuristic pricing rules based on the dual of a relaxed
allocation problem today. 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 to inadequate congestion signals. We show that existing
pricing heuristics optimize specific design goals that can be conflicting. The
trade-offs can be substantial, and we establish that the design of pricing
rules is fundamentally a multi-objective optimization problem addressing
different incentives. In addition to traditional multi-objective optimization
techniques using weighing of 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 of objectives, it is
computationally scalable, and balances trade-offs in a principled manner,
addressing an important policy issue in electricity markets.
