Strategy‐proof and group strategy‐proof stable mechanisms: An equivalence

• Published date: 01 September 2020
• DOI: http://doi.org/10.1111/ijet.12214
• Date: 01 September 2020
• Author: Antonio Romero‐Medina,Matteo Triossi

doi: 10.1111/ijet.12214

Strategy-proof and group strategy-proof stable mechanisms:

An equivalence

Antonio Romero-Medina∗and Matteo Triossi†

We provethat group strateg y-proofnessand str ategy-proofness are equivalentrequirements on

stable mechanisms in priority-based resource allocation problems with multi-unit demand. The

result extends to the model with contracts.

Key wor ds multi-unit demand, stability, strategy-proofness, group strategy-proofness

JEL classification C78, D78

Accepted 19 December 2018

1 Introduction

We study the compatibility of efficiency, stability, and group strategy-proofness in priority-based

resource allocation problems with multi-unit demand, for example, situations when students with

time constraints want to sign up for multiple courses with capacity constraints. However, in this

problem, efficiency,stabilit y,and group strategy-proofness are not compatible when we consider the

general domain of priorities (see Roth and Sotomayor 1990).

Kojima (2013) shows that the existence of a stable and strategy-proof mechanism is equivalent

to the existence of an efficient and stable mechanism. He characterizes those priority structures

that allow stable and strategy-proof mechanisms as those that satisfy a condition called essential

homogeneity. If essential homogeneity is satisfied, courses can have differentpr iorities only for top-

ranked students. If some courses have few seats available, essential homogeneity is required. For

example, if one of the courses has only one seat available, essential homogeneity amounts to all

courses having the same priorities. On the other hand, if each course has a large supply of seats,

essential homogeneity has greater flexibility.

However, strategy-proofness does not prevent manipulation by coalitions of agents. This is a

relevant concern when the coalitions that can be formed are small and easy to coordinate.1Group

*Department of Economics, Carlos III University of Madrid, Madrid, Spain.

†Center of Applied Economics, Departament of Industrial Engineerin, University of Chile, Santiago, Chile. Email:

mtriossi@dii.uchile

We thank Fuhito Kojima for his insightful comments. Both authors acknowledge financial support from Ministe-

rio Econom´

ıa y Competitividad (Spain) under projects ECO2014 57442 P and ECO2017 87769 P, Fondecyt under

project No. 1151230 and the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Min-

isterio de Econom´

ıa, Fomento y Turismo (Chile). Romero-Medina acknowledges the financial support from Minis-

terio Econom´

ıa y Competitividad (Spain) under project MDM2014-0431, and Comunidad deMadrid, MadEco-CM

(2015/HUM-3444).

1Consider, for example, the problem of assigning landing slots (see Schummer and Vohra 2013; Schummer and Abizada

2017).

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