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March 13, 2026Open Access

Competitive equilibrium and indivisibles

LNLuciano Méndez NayaUniversidade de Santiago de Compostela

Key Points

The aim is to explore the existence of competitive equilibrium in markets where goods cannot be divided.
Analyzed competitive equilibrium in the context of indivisible goods.
Utilized a theorem connecting equilibrium existence to cooperative game theory.
Characterized equilibrium in a two-agent, three-good economy.
Demonstrated improved conditions for equilibrium existence compared to classical results.
Established that equilibrium is more likely with complementary goods than substitute goods.

Abstract

This paper studies the existence of competitive equilibrium in markets with indivisibles. The basis of the paper is a theorem that relates the existence of equilibrium to the core of certain associated cooperative games. From this result, we obtain a significant improvement on a classical result in this literature. We then characterize the existence of equilibrium in a two-agent three-good economy, showing that, in this particular context, the existence of equilibrium is more likely when goods are complements than when they are substitutes.

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