Optimal Truncation in Matching Markets

Peter Coles and Ran Shorrer
Additional contact information
Peter Coles: Harvard Business School

No 2013.49, Working Papers from Fondazione Eni Enrico Mattei

Abstract: Since no stable matching mechanism can induce truth-telling as a dominant strategy for all participants, there is often room in matching markets for strategic misrepresentation (Roth [25]). In this paper we study a natural form of strategic misrepresentation: reporting a truncation of one's true preference list. Roth and Rothblum [28] prove an important but abstract result: in certain symmetric, incomplete information settings, agents on one side of the market (“the women”) optimally submit some truncation of their true preference lists. In this paper we put structure on this truncation, both in symmetric and general settings, when agents must submit preference lists to the Men-Proposing Deferred Acceptance Algorithm. We first characterize each woman's truncation payoffs in an incomplete information setting in terms of the distribution of her achievable mates. The optimal degree of truncation can be substantial: we prove that in a uniform setting, the optimal degree of truncation for an individual woman goes to 100% of her list as the market size grows large, when other women are truthful. In this setting, we demonstrate the existence of an equilibrium where all agents use truncation strategies. Compared to truthful reporting, in any equilibrium in truncation strategies, welfare diverges for men and women: women prefer the truncation equilibrium, while men would prefer that participants truthfully report. In a general environment, we show that the less risk averse a player, the greater the degree of her optimal truncation. Finally, when correlation in preferences increases, players should truncate less. While several recent papers have focused on the limits of strategic manipulation, our results serve as a reminder that without the pre-conditions ensuring truthful reporting, even in settings where agents have little information, the potential for manipulation can be significant.

Keywords: Matching Markets; Truncation (search for similar items in EconPapers)
JEL-codes: C62 C78 D47 D61 (search for similar items in EconPapers)
Date: 2013-05
New Economics Papers: this item is included in nep-cta, nep-dem, nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Journal Article: Optimal truncation in matching markets (2014)
Working Paper: Optimal Truncation in Matching Markets
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Persistent link: https://EconPapers.repec.org/RePEc:fem:femwpa:2013.49

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