Designing marketplaces in complex settings requires both novel economic theory and real-world engineering, often drawing upon ideas from fields such as computer science and operations research. In Discovering Prices: Auction Design in Markets with Complex Constraints, Milgrom (2017) explains the theory and design of the United States’ “incentive auction” that reallocated wireless spectrum licenses from television broadcasters to telecoms. Milgrom’s account teaches us how economic designers can grapple with complexity both in theory and in practice. Along the way, we come to understand several different types of complexity that can arise in marketplace design.

We show how frictions and continuous transfers jointly affect equilibria in a model of matching in trading networks. Our model incorporates distortionary frictions such as transaction taxes and commissions. When contracts are fully substitutable for firms, competitive equilibria exist and coincide with outcomes that satisfy a cooperative solution concept called trail stability . However, competitive equilibria are generally neither stable nor Pareto‐efficient.

We show that with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents’ substitution effects, not their income effects. Our equilibrium existence duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability—which is a strictly weaker condition than gross substitutability—is sufficient for the existence of competitive equilibrium. Further applications give new existence results beyond the case of (net) substitutes. Our results have implications for auction design.