The Economics of Equilibrium with Indivisible Goods

TL;DR

This paper develops a demand-based theory of competitive equilibrium for indivisible goods, unifying conditions for existence across complementarity and substitutability, with implications for auction design.

Contribution

It introduces a demand-centric framework for equilibrium with indivisible goods, providing unified conditions for existence applicable to complements and substitutes.

Findings

Provides necessary and sufficient conditions for equilibrium existence.

Unifies analysis of complements and substitutes in indivisible goods.

Implications for designing auctions with indivisible items.

Abstract

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.