Public good agreements under the weakest‐link technology

• Author: Alejandro Caparrós,Michael Finus
• Published date: 01 June 2020
• DOI: http://doi.org/10.1111/jpet.12426
• Date: 01 June 2020

J Public Econ Theory. 2020;22:555–582. wileyonlinelibrary.com/journal/jpet

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555

Received: 30 November 2018

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Accepted: 8 January 2020

DOI: 10.1111/jpet.12426

ORIGINAL ARTICLE

Public good agreements under the

weakest‐link technology

Alejandro Caparrós

1

|Michael Finus

2,3

1

Institute for Public Goods and Policies

(IPP), Spanish National Research Council

(CSIC), Madrid, Spain

2

Department of Economics, University of

Graz, Graz, Austria

3

Department of Economics, University of

Bath, Bath, UK

Correspondence

Michael Finus, Department of Economics,

University of Graz, 8010 Graz, Austria.

Email: michael.finus@uni-graz.at and

m.finus@bath.ac.uk

Funding information

University of Bath, Grant/Award Number:

Global Mobility Scheme (VB‐EC3BMF);

Spanish Ministry of Economy and

Competitiveness project TRENGOOD,

Grant/Award Numbers: ECO2017‐84461‐R,

project ACBPA, ECO2012‐35432.

Abstract

We analyze the formation of public good agreements

under the weakest‐link technology. Whereas policy co-

ordination is not necessary for symmetric players, it

matters for asymmetric players; however, this fails in the

absence of transfers. By contrast, with a transfer scheme,

asymmetry may be an asset for cooperation. We char-

acterize various types and degrees of asymmetry and

relate them to the stability of self‐enforcing agreements.

Asymmetric distributions of autarky public good provi-

sion levels (also representing asymmetric interests in

cooperation) that are positively skewed tend to be con-

ducive to the stability of agreements. We show that un-

der such conditions, even a coalition including all players

can be stable. However, asymmetries that foster stability

(instability) tend to be associated with low (high) gains

from cooperation.

KEYWORDS

agreement formation, public goods, weakest‐link technology

JEL CLASSIFICATION

C7; D7; H4; H7

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

© 2020 The Authors. Journal of Public Economic Theory Published by Wiley Periodicals, Inc.

1|INTRODUCTION

A central aspect of the theory of public goods is the understanding of the incentive structure that

typically leads to the underprovision of public goods as well as the possibilities of rectifying this. In

this study, we answer the research question already posed by Cornes (1993): how do cooperative

institutions develop under different aggregation technologies? Among the three typical technol-

ogies, namely, the summation, best‐shot, and weakest‐link technology, we focus on the latter.

Under a weakest‐link technology the benefits of public good provision depend on the smallest

contribution.

1

Many policy issues are characterized by the weakest‐link technology, including the

classical example in Hirshleifer (1983) of building dykes to protect against flooding on an island:

the lowest (rather than the average or the highest) dyke determines the level of protection. Other

examples (e.g., Arce, 2001; Barrett, 2007; Sandler, 1998,2004) include the spread of an epidemic or

infectious diseases such as small‐pox and polio. Only global vaccination programs helped eradicate

these diseases. If some countries had been omitted from this global effort, success would have been

jeopardized. In addition, the success of the inspection of invasive species at ports, security mea-

sures at airports to protect against terrorist attacks, and protection of the integrity of computer

networks through firewalls and antivirus programs depend on the weakest‐link effort. Moreover,

the success of European Union (EU) measures to address illegal migration depends on the

“weakest”member at the periphery of the EU area, irrespective of the measures taken by

“stronger”members. Similarly, measures against money laundering and tax evasion will fail as

long as some countries offer tax havens and have lax financial monitoring standards. Finally, the

fight of a fire that threatens several communities will be as successful as the quality of the weakest

fire brigade. Local fires will spread to other communities if not extinguished.

In most examples above, the benefits and costs of public good provision are expected to be

unevenly distributed because of the range of preferences for public good supply as well as

different technologies used to provide the public good. Therefore, asymmetry is the central

focus of our study. See also Barbieri and Malueg (2019).

By cooperative institutions, we mean agreements among a group of players who depart from Nash

equilibrium provision levels. We assume that players need to agree on the terms of an agreement but

can leave an agreement at any time if the gains from free‐riding outweigh the gains from the

agreement. We call this a “self‐enforcing”treaty. The possibility of leaving an agreement appears to be

adequate in most of the examples above, especially for global public goods affecting several sovereign

nations and jurisdictions, as no global entity has the ultimate enforcement power. However, co-

ordination across several communities may also not be as straightforward as one may hope.

Based on the foregoing, we examine the conditions under which stable agreements emerge

as well as how large they will be and under which conditions the associated gains from

cooperation will be large.

For our analysis, we combine approaches from two strands of the literature that have devel-

oped independently: the literature on noncooperative or privately provided public goods under the

weakest‐link technology and the literature on cooperatively provided public goods under the

summation technology. We subsequently review these two strands of the literature in Section 2

and set out our two‐stage coalition formation model in Section 3. We argue that coalition for-

mation is only interesting in the context of asymmetric players and we, therefore, analyze the

existence of stable agreements under this assumption in Section 4. We show that transfers are a

1

Measures to address climate change are typically related to the summation technology and missile protection is often viewed as a type of best‐shot technology.

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CAPARRÓS AND FINUS