Publications
Publications
- 2015
Full Substitutability
By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
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' canonical
definitions of substitutability to settings in which an agent can be both a buyer in some
transactions and a seller in others, and show that all these definitions are equivalent. We introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We then prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and
limited liability. We also show that substitutability corresponds to submodularity of the
indirect utility function, the single improvement property, and a no complementarities
condition. Finally, we show that substitutability implies the monotonicity conditions
known as the Laws of Aggregate Supply and Demand.
Keywords
Citation
Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Working Paper, May 2015.