November 2019
Article
Theoretical Economics

Full Substitutability

By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp

Format:Print

Abstract

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.

Keywords

Substitutability; Mathematical Methods; Auctions; Market Design

Citation

Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Theoretical Economics 14, no. 4 (November 2019): 1535–1590.