Ravi Jagadeesan

This paper develops a theory of competitive equilibrium with indivisible goods based entirely on economic conditions on demand. The key idea is to analyze complementarity and substitutability between bundles of goods, rather than merely between goods themselves. This approach allows us to formulate sufficient, and essentially necessary, conditions for equilibrium existence, which unify settings with complements and settings with substitutes. Our analysis has implications for auction design.

In matching models, pairwise stable outcomes do not generally exist without substantial restrictions on both preferences and the topology of the network of contracts. We address the foundations of matching markets by developing a matching model with a continuum of agents that allows for arbitrary preferences and network structures. We show that pairwise stable outcomes are guaranteed to exist. When agents can interact with multiple other counterparties, pairwise stability is too weak of a solution concept, and we argue that a refinement of it called tree stability is the most appropriate solution concept in this setting. Our main results show tree-stable outcomes exist for arbitrary preferences and network topologies.

Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in their setting, full substitutability is equivalent to the assumption that all indirect utility representations of each firm's preferences are quasisubmodular; we show here that this claimed equivalence result does not hold in general. We show instead that full substitutability is equivalent to weak quasisubmodularity of all indirect utility representations.

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. We also extend the ``demand types'' classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.

This paper develops a class of equilibrium-independent predictions of competitive equilibrium with indivisibilities. Specifically, we prove an analogue of the “Lone Wolf Theorem” of classical matching theory for the Baldwin and Klemperer (Econometrica 87(3):867–932, 2019) model of exchange economies with transferable utility, showing that any agent who does not participate in trade in some competitive equilibrium must receive her autarky payoff in every competitive equilibrium. Our results extend to approximate equilibria and to settings in which utility is only approximately transferable.

Sönmez (2013) and Sönmez and Switzer (2013) used matching theory with unilaterally substitutable priorities to propose mechanisms to match cadets to military branches. This paper shows that, alternatively, the Sönmez and Sönmez–Switzer mechanisms can be constructed as descending salary adjustment processes in Kelso-Crawford (1982) economies in which cadets are (grossly) substitutable. The lengths of service contracts serve as (inverse) salaries. The underlying substitutability explains the unilateral substitutability of the priorities utilized by Sönmez and Sönmez-Switzer. (JEL C78, D82, D86, J31, J45)

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.