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  • 2015
  • Working Paper

Full Substitutability

By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
  • Format:Print
  • | Language:English
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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

Market Design; Balance and Stability

Citation

Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Working Paper, May 2015.
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About The Author

Scott Duke Kominers

Entrepreneurial Management
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Related Work

    • 2018
    • Faculty Research

    Full Substitutability

    By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
Related Work
  • Full Substitutability By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
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