Designing centralized marketplaces that work gracefully with pre-existing decentralized ones, in Management Science, by Benjamin Roth and Ran Shorrer

 In Management Science (online ahead of print):

Making Marketplaces Safe: Dominant Individual Rationality and Applications to Market Design

 Benjamin N. Roth , Ran I. Shorrer 

Published Online:8 Dec 2020 https://doi.org/10.1287/mnsc.2020.3643

Abstract: Often market designers cannot force agents to join a marketplace rather than using pre-existing institutions. We propose a new desideratum for marketplace design that guarantees the safety of participation: dominant individual rationality (DIR). A marketplace is DIR if every pre-existing strategy is weakly dominated by some strategy within the marketplace. We study applications to the design of labor markets and the sharing economy. We also provide a general construction to achieve approximate DIR across a wide range of marketplace designs.

Introduction: "Many marketplaces operate in a broader economic environment, and often participants cannot be forced to use a marketplace rather than the pre-existing institutions it was meant to displace. For instance, although most hospitals and residents use the clearinghouse known as the National Residency Matching Program (NRMP) to coordinate job offers, there is no legal barrier that prevents members of either side of the market from finding matches outside of the clearinghouse.1 In school choice, charter schools sometimes opt not to participate in clearinghouses, instead recruiting students in a decentralized manner. In the private sector, marketplaces that comprise the gig and sharing economies demonstrate the primacy of attracting participants who have many outside alternatives. In each of these settings marketplaces are actively engaging with the challenge of recruitment. In other words, these are marketplaces in which participation is not always safe.

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"A designer may introduce a mediator (alternatively referred to as a marketplace), to which players may delegate their decision rights (i.e., participate in the marketplace). The mediator comprises a message space and a mapping from messages to outcomes (strategy profiles for the delegators). Players who delegate their decision rights select a message to send to the mediator, who then acts on their behalf according to the outcome mapping, as a function of the whole set of messages it receives. The mediator is voluntary in the sense that players may choose one of their original (outside) actions instead of sending it a message. And the mediator is restricted to condition the actions of participants only on the messages of other participants and not on the outside actions of nonparticipants.

"This framework highlights the endogeneity of the individual rationality constraint with respect to both the set of players who sign away their decision rights and the actions they take. We show by example that mediators that satisfy attractive criteria such as incentive compatibility and efficiency assuming that everyone participates may no longer do so in equilibria with partial participation. This motivates the search for mediators that can guarantee the safety of participation. In Section 3 we present our key desideratum: dominant individual rationality (DIR)."