OBVIOUSLY STRATEGY‐PROOF IMPLEMENTATION OF TOP TRADING CYCLES

• Published date: 01 August 2019
• DOI: http://doi.org/10.1111/iere.12384
• Author: Peter Troyan
• Date: 01 August 2019

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 3, August 2019 DOI: 10.1111/iere.12384

OBVIOUSLY STRATEGY-PROOF IMPLEMENTATION OF TOP TRADING

CYCLES∗

BYPETER TROYAN1

University of Virginia, U.S.A.

Although there is a rich theoretical literature extolling the virtues of the top trading cycles (TTCs) mechanism,

it is rarely used in practice. Anecdotal evidence suggests that one possible explanation is that TTC is difficult for

participants to understand. This article formalizes this intuition by asking whether it is possible to implement

TTC in an obviously strategy-proof (OSP) way. I identify an acyclicity condition that is both necessary and

sufficient for OSP implementation of TTC. The condition is unlikely to hold in most applications, which may

explain why TTC is rarely used, despite its many appealing theoretical properties.

1. INTRODUCTION

An important consideration when designing institutions to allocate scare resources is the

incentives given to agents to report their preferences truthfully. For example, in school choice,

it is well known that the so-called “Boston” mechanism gives students (or their parents) very

clear incentives to lie about their true preference and can harm students who may be unable

to strategize appropriately. Because of this, economists have generally advised against using

manipulable mechanisms such as the Boston mechanism in favor of mechanisms that ensure it

is always an optimal strategy for agents to report their true preferences; in other words, they

recommend that the mechanism be strategy-proof.2

There are three canonical strategy-proof ways to assign indivisible objects in the absence

of transfers that are used in practice: serial dictatorship (SD), deferred acceptance (DA), and

top trading cycles (TTCs). However, just because a mechanism is strategy-proof in theory does

not mean that participants will be truthful in practice. The agents participating in it must also

understand that it is strategy-proof.

One formalization of what it means for participants to “understand” that a mechanism is

strategy-proof is the concept of obvious strategy-proofness(OSP) due to Li (2017). A mechanism

is OSP if each agent has an obviously dominant strategy, which, informally, is a strategy such

that even the worst possible outcome from following it is better than the best case from any

possible deviation. Li (2017) shows that obviously dominant strategies are those that can be

seen as optimal by a cognitively limited agent who cannot engage in contingent reasoning.

For no-transfer settings like those considered in this article, Li (2017) shows that SDs are

OSP when implemented dynamically and provides experimental evidence that rates of truth

telling are higher when using such a dynamic implementation compared to a static one, which

∗Manuscript received November 2017; revised July 2018.

1I would like to thank Itai Ashlagi, Yannai Gonczarowski, Fuhito Kojima, and Marek Pycia for helpful conversations

relating to this project, as well as the editor, Rakesh Vohra, and anonymous referees for comments that have improved

the article. Please address correspondence to: Peter Troyan, Department of Economics, University of Virginia, P.O.

Box 400182, Charlottesville, VA 22904. E-mail: troyan@virginia.edu.

2Pathak and S ¨

onmez (2008) argue that nonstrategy-proof mechanisms may harm parents who are unable to strategize

well, and incentive considerations were key concerns for the New York City and Boston school districts when deciding

upon which mechanism to use (Abdulkadiro˘

glu et al., 2005a, 2005b). At the same time, strategy-proofness is not without

costs, and recent literature has begun to reexamine nonstrategy-proof mechanisms such as the Boston mechanism and

show that they may outperform strategy-proof mechanisms from an ex ante perspective in some settings, at least under

equilibrium play (e.g., Miralles, 2009; Abdulkadiro˘

glu et al., 2011; Troyan, 2012; Featherstone and Niederle, 2016).

1249

C

(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association