Global public goods and unilateral matching mechanisms

• DOI: http://doi.org/10.1111/jpet.12300
• Author: Weifeng Liu,Wolfgang Buchholz
• Published date: 01 April 2020
• Date: 01 April 2020

Received: 21 March2017 Accepted: 26 February2018

DOI: 10.1111/jpet.12300

ARTICLE

Global public goods and unilateral matching

mechanisms

Wolfgang Buchholz1Weifeng Liu2

1Universityof Regensburg and CESifo Munich

2CrawfordSchool of Public Policy, The Australian

NationalUniversity

WolfgangBuchholz, Department of Economics,

Universityof Regensburg, 93040 Regensburg,

Germany(wolfgang.buchholz@ur.de).

WeifengLiu, Crawford Building 132, Lennox

Crossing,Canberra, ACT,2601, Australia

(dr.weifeng.liu@gmail.com).

While conventional agreements on international public goods

require bilateral or multilateralcooperation, we show that unilateral

actionthrough matching mechanismswith a self-commitmentdevice

can possibly generate Pareto-improving outcomes. Even without

commitment, unilateral matching may also benefit both players at

corner situations. We further characterize the conditions under

which this desirable outcome is achieved, particularly highlighting

the role of the income distribution and its interplay with the pref-

erences. Moreover,we propose a variant of unilateral matching that

can generate Pareto-improving outcomes regardless of the prefer-

ences and the income distribution, indicating that income inequality

may not be an obstacle for improving public good provision through

unilateral matching.

1INTRODUCTION

It is well known that public goods are generally underprovided when provision depends on agents'voluntary contri-

butions (see Cornes & Sandler, 1996). At the national level, conventional centralized approaches such as Pigouvian

taxes and subsidies can be used to cure this underprovision through government intervention. However, in the case

of global public goods, there is no supranational government so that international cooperation is required to improve

public good provision.In general, such international agreements require bilateral or multilateral cooperation, but inter-

national cooperation proves very difficult in practice. The most relevant exampleis climate negotiations, which have

gained much attention but whose effect has been rather limited so far. In this context, a large literaturehas investi-

gated international agreements from a game-theoretic perspective showing the difficulties of attaining a stable and

effective agreement (see, e.g., Barrett, 2003, 2007; Finus, 2001; Sandler,1997, 2004).

Against this background, this paper aims at exploring unilateral solutions that can improve global public good pro-

vision and generate Pareto-improvingoutcomes when one player takes actions as a leader while the other player plays

a Nash game as a follower.If the outcome is profitable for both players, then the leader has strong incentives to imple-

ment the actions and, more importantly,does not require cooperation by the other player.Very rare literature explores

such unilateral mechanisms to improve public good provisionas, for example, Buchholz, Cornes, Peters, and Rübbelke

(2015) who examine a unilateral matching approach in a two-player model of a public good economy. This approach

envisages one player subsidizing public good contributions of the other player through matching, thus reducing the

effective public good price of the recipient. More specifically, at the first stage, one player announces a matching

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2ANDLIU

rate indicating by how much the player would subsidize public good contributions of the other player; at the second

stage, both players decide independently their flat contributions to the public good while the player who announces

the matching rate at the first stage also provides matching contributions. For example,should one player announce a

matching rate of 0.1 at the first stage, she would provide 0.1 units of the public good as a matching contribution if the

other player providesone unit of the public good at the second stage. 1

Under such a unilateral matching mechanism it has been shown that the matching player is better off while the

matched player is worse off (see Bergstrom, 1989; Roberts, 1987). Toachieve a Pareto improvement, the matching

player therefore must apply an ancillary instrument besides unilateral matching. Buchholz et al. (2015) show that a

commitment device can serve as such an instrument. More specifically, theyestablish that at an interior equilibrium

where both players make positive public good contributions, the matching equilibrium would be Pareto improvingif

the matching player commits not to reduce her flat contribution to the public good below her initial level and at the

same time if the private and the public good are substitutes for the matched player.

In general, given such two instruments—a matching mechanism and a commitment device—the leader's unilateral

action can potentially achieve Pareto-improvingoutcomes, but there may be infinite pairs of matching rates and com-

mitment levelsfor attaining such outcomes. In this paper,we restrict our attention to the case in which the leader com-

mits her flat contribution to the public good at her level in the initial Nash equilibrium and proposes a small matching

rate. Our motivation of focusing on this case is twofold. First, the Nash equilibrium as the outcome of noncooperative

public good provision is normally considered to be the starting point from which policies or mechanisms are designed

to bring public good supply closer to the efficient level. Second, focusing our analysis on small matching ratesis related

tothe literature on tax policy design. From the perspective of informational requirement, it is much easier to implement

small Pareto-improvingtax reforms than to attain overall optimal tax policy because the former requires only informa-

tion of the current position while the latter requires information of a large range of positions (see, e.g., Deaton, 1987;

Myles, 1995). In practice, the information required for small tax reforms is often directly observable or can be inferred

from the current position, but the information of entire preferences, demands, and production possibilities needed

for optimal taxation is simply not obtainable. This information problem obviously becomes even more severe at the

international level because it is much more difficult to obtain aggregate information for countries with heterogeneous

agents.

In the same spirit as Pareto-improving tax reforms, in this paper we are interested in Pareto-improving outcomes

in the context of unilateral matching, and thus consider a marginal matching rate and a commitment with regard to

the initial position, which is observable and thus servesas a convenient focal point for both players. Given this marginal

variation,we systematically examine sufficient conditions of achieving Pareto improvements under unilateral matching

with commitment, and extendthe analysis of Buchholz et al. (2015) in several aspects, particularly highlighting the role

of the income distribution and its interplay with the preferences.

More specifically, first we show that the possibility for Paretoimprovements not only depends on the preferences

of the recipient but also on the income distribution between the two players. At an interior equilibrium, if the match-

ing player commits to her initial public good contribution and announces a marginal matching rate,a Pareto-improving

equilibrium occurs in either of the two cases: (1) the private and the public good are substitutes for the matched player;

(2) the private and the public good are complements for the matched player and the income of the recipient is suffi-

ciently large compared to the matching player.

Second, we examine unilateral matching schemes at corner equilibria, in which the income inequality is large so

that one player does not provide public good contributions at the initial equilibrium (see Bergstrom, Blume, & Varian,

1986). Such corner equilibria are important not only in theory,but also in reality due to large income inequality in the

current world, which has constantly been a major concern in international climate negotiations. There are two cases

of unilateral matching at the corner.One is that the contributing player matches the noncontributing player while the

1Matching mechanisms were first suggested by Guttman (1978, 1987) and have been refined and applied in various waysbut all in bilateral or multilateral

contexts.See, for example, Boadway, Pestieau, and Wildasin (1989), Danziger and Schnytzer(1991), Althammer and Buchholz (1993), Varian (1994a, 1994b),

Falkinger(1996), Boadway, Song, and Tremblay(2007, 2011), Buchholz, Cornes, and Rübbelke (2011, 2012, 2014), and Liu (2018).

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