Equilibria and Indivisibilities: Gross Substitutes and Complements

Abstract

This paper examines an exchange economy with heterogeneous indivisible objects that can be substitutable or complementary. We show that a competitive equilibrium exists in such economies, provided that all the objects can be partitioned into two groups, and from the viewpoint of each agent, objects in the same group are substitutes and objects across the two groups are complements. This condition generalizes the well-known Kelso–Crawford gross substitutes condition and is called gross substitutes and complements. We also provide practical and typical examples from which substitutes and complements are both jointly observed.

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