Contract Design and Stability in Many-to-Many Matching

John William Hatfield; Scott Duke Kominers

Article | Games and Economic Behavior | January 2017

Contract Design and Stability in Many-to-Many Matching

by John William Hatfield and Scott Duke Kominers

Abstract

We develop a model of many-to-many matching with contracts that subsumes as special cases many-to-many matching markets and buyer/seller markets with heterogeneous and indivisible goods. In our setting, substitutable preferences are sufficient to guarantee the existence of stable outcomes; moreover, in contrast to results for the setting of many-to-one matching with contracts, if any agent’s preferences are not substitutable, then the existence of a stable outcome cannot be guaranteed. In many-to-many matching with contracts, a new market design issue arises: the design of the contract language can impact the set of stable outcomes. Bundling contractual primitives encourages substitutability of agents’ preferences over contracts and makes stable outcomes more likely to exist; however, bundling also makes the contractual language less expressive. Consequently, we see that, in choosing contract language, market designers face a tradeoff between expressiveness and stability.

Keywords: Many-to-Many Matching; stability; Substitutes; Contract Design; Contracts; Marketplace Matching; Balance and Stability;

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Hatfield, John William, and Scott Duke Kominers. "Contract Design and Stability in Many-to-Many Matching." Games and Economic Behavior 101 (January 2017): 78–97.

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Contract Design and Stability in Many-to-Many Matching

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