Global public goods and coalition formation under matching mechanisms

• DOI: http://doi.org/10.1111/jpet.12294
• Date: 01 June 2018
• Published date: 01 June 2018

Received: 16 October 2017 Accepted: 21 February2018

DOI: 10.1111/jpet.12294

ARTICLE

Global public goods and coalition formation under

matching mechanisms

Weifeng L iu

TheAustralian National University

WeifengLiu, Crawford School of Public Policy,

TheAustralian National University, Crawford

Building132, Lennox Crossing, Canberra, ACT,

2601,Australia (dr.weifeng.liu@gmail.com).

This paper links coalition theory with matching mechanisms in the

presence of global public goods among heterogeneous players. This

matching coalition may achieve Pareto-improving outcomes while

avoiding side payments. The paper characterizesconditions of coali-

tion profitability and stability at both interior and corner equilibria.

It is generally much harder to satisfy stability conditions than prof-

itability conditions. A matching coalition is more profitable but less

stablewith a larger matching rate. Empirically there is no stable coali-

tionbut this can be overcome by introducing reputation mechanisms.

There always existsa stable grand matching coalition if players value

their reputation. The matching coalition faces a trade-off between

matching depth and breadth.

1INTRODUCTION

As the world is increasingly moving toward economic globalization and integration, more and more transboundary

externalities emerge such as transnational pollution, international trade,financial crises, development aid, and conta-

gious diseases (Sandler, 2004). In the presence of such global public goods, international cooperation is required to

reach optimal outcomes, but this proves difficult in practice due to the absence of a supranational government with

enforcement power. The most relevant example is climate negotiations, which havegained much attention but little

progress. To overcomeunderprovision of such global public goods, a large literature examines cooperative games in

coalitional form (see, e.g., Barrett, 1994; Carraro & Siniscalco, 1993; Finus, Altamirano-Cabrera, &Van Ierland, 2005;

Hoel & Schneider, 1997).1A typical coalitional game is often comprised of four stages: (1) players decide whether to

sign an agreement or to behaveas singletons; (2) signatories decide on the public good provision cooperativelyso as to

maximize the aggregate welfare of the coalition when taking the reaction of the nonsignatories into account; (3) given

the public good provision of signatories, each nonsignatory chooses his or her public good provision so as to maximize

his or her own welfare; (4) signatories decide how the welfare gain is distributed.

There are two major issues of this coalitional game in practice particularly at the international level. First, even if

players decide to form a coalition, it is difficult to maximize the aggregate welfare of the coalition because of diver-

gent interests and incomplete information. At the international level, divergent interests involvemultiple dimensions

1Pelegand Sudholter (2003) provide a comprehensive coverage of cooperative games; Ray (2007) presents a general theory of coalition formation that com-

binescooperative and noncooperative approaches.

Journal of Public Economic Theory.2018;20:325–355. wileyonlinelibrary.com/journal/jpet c

2018 Wiley Periodicals,Inc. 325

326 LIU

including economic benefits, political relationships, and cultural background, and incomplete information includes

numerous uncertainties as to national incomes, aggregate preferences, and costs and benefits of public goods. One

solution to mitigate this issue is to form a coalition among subgroups of like-mindedplayers (see, e.g., Buchholz, Cornes,

& Rübbelke, 2014; Buchholz, Haslbeck, & Sandler, 1998). Countries with common culture, similar income levelsand

national preferences are more likelyto make ambitious agreements. However, one of the most challenging problems in

climatenegotiations is the conflict between developing and developed countries, and these two groups diverge in many

dimensions including historical responsibility,mitigation capability, and current welfare. Therefore, the first issue can-

not be solved by forming a coalition among like-minded countries. Instead, more realistically,countries should form a

coalition to achievea less ambitious solution—a Pareto-improving outcome, that is, each coalition member is better off

than without a coalition, rather than maximizing the aggregate welfare in a coalition.

The second issue involves side payments.In the conventional coalitional game, players have to decide how to share

costs or distribute gains among the coalition. This is also very difficult without a central government because players

often have subjective perceptions of equity in sharing costs or distributing gains and also because playersare subject

to political constraintsof international transfers. For example, developed and developing countries haveagreed to pro-

tect climate on the basis of equity as early as the 1990s when the United Nations Framework Conventionon Climate

Change was established, but it is difficult to reach a consensus on equity in practice given their different responsibil-

ity, capability,preferences, costs and benefits, and so forth. In addition, Summers (2007) argues that, due to political

constraints, governments are unlikely to write substantial checks to each other pursuant to international treaties in

climate change. Therefore, it would be pragmatically useful to apply a mechanism that can avoidside payments among

players.

This paper considers a coalitional setting under matching mechanisms and focuses on Pareto-improving outcomes

while avoiding side payments. The matching mechanisms, first suggested by Guttman (1978, 1987), work as a two-

stage game. At the first stage, each player announces a matching rate indicating by how much the player would sub-

sidize public good contributions of all other players; at the second stage, all players decide independently their flat

contributions to the public good while the players announcing matching rates at the first stage also provide matching

contributions to other players. For example,should one announce a matching rate of 0.1 at the first stage, the player

would provide 0.1 units of the public good as a matching contribution if another player providesone unit of the public

good at the second stage. The idea of this mechanism is still to stick to the noncooperative mode of public good pro-

vision but meanwhile to subsidize individual public good contributions and hence to lower the effective price of the

public good. Guttman (1978) shows that with quasi-linear preferences, the subgame perfect equilibrium in such a two-

stage game of two identical players is fully efficient. Danziger and Schnytzer (1991) generalize this result to multiple

agents with more general preferences. More broadly,Moore and Repullo (1988) show that subgame perfect equilibria

ofsuch multistage g amescan implement efficient allocations. However, these multistage games are far from implemen-

tationdue to their sophisticated structures. As Moore and Repullo also point out, “the mechanisms we c onstruct to deal

with a general environment are far from simple: agents move simultaneously at each stage and their strategysets are

unconvincingly rich. We present such mechanisms to demonstrate what is possible, not what is realistic.” Therefore,

this paper considers a realistic application of this matching approach into coalition formation. As an earlier study in

this direction, Buchholz et al. (2014) examine coalition formation under matching mechanisms among homogeneous

players.More specifically, they assume that all players are completely homogeneous in the preference and the income,

and consider a two-stage game: Coalition members cooperatively determine the matching rate at the first stage, and

then play a noncooperative game against coalition outsiders at the second stage. This model of homogeneous players

is a very special case with symmetric results across players.

This paper relaxes the assumption of homogeneity by allowing players to havedifferent income levels. This relax-

ation is clearly important given the large income heterogeneity across countries in the current world, but gives rise to

severaltheoretical issues. First, as the outcomes are asymmetric across players, not only the coalition size but also the

member identity matters for coalition formation. Second, given the income heterogeneity,it is a key issue to make poor

players better off in a matching coalition without resorting to side payments. Third, there are potentially corner equi-

libria in which a subgroup of either coalition insiders or outsiders provide no public good contributions. Fourth, there