Constrained optimal transport with an application to large markets with indivisible goods
TLDR
Introduces a constrained optimal transport duality to prove equilibrium existence in large markets with indivisible goods.
Key contributions
- Develops a Monge–Kantorovich duality variant for constrained transport with linear constraints.
- Identifies and corrects a flaw in prior equilibrium existence proof for indivisible goods markets.
- Proves equilibrium existence using the new duality framework.
- Characterizes equilibrium prices as minimizers of a potential function for computational methods.
Why it matters
This paper fixes a key gap in equilibrium theory for large indivisible goods markets and offers a practical way to compute equilibrium prices, advancing market design and economic theory.
Original Abstract
We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model of indivisible goods in Azevedo et al. (2013), identify a flaw in the original equilibrium-existence proof stemming from an incorrect compactness claim, and recover equilibrium existence via our duality approach. We also characterize equilibrium prices as minimizers of a potential function, which yields a method for computing equilibrium prices.
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