EFFICIENT LARGE‐SIZE COORDINATION VIA VOLUNTARY GROUP FORMATION: AN EXPERIMENT

• Author: Fang‐Fang Tang,Mao‐Long Xu,Chun‐Lei Yang,Juanjuan Meng
• DOI: http://doi.org/10.1111/iere.12230
• Published date: 01 May 2017
• Date: 01 May 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 2, May 2017

EFFICIENT LARGE-SIZE COORDINATION VIA VOLUNTARY GROUP

FORMATION: AN EXPERIMENT∗

BYCHUN-LEI YANG,MAO-LONG XU,JUANJUAN MENG,AND FANG-FANG TANG1

Nanjing Audit University, China; Tilburg University,The Netherlands; Peking University,

China; Peking University, China

Efficient coordination in large groups is a fundamental issue in economic organizations. We consider the

weak-link game with the feature of economies of scale that is necessary for voluntary group growth, in a

minimal setup with exit and merger options. We show that large groups with efficient outcomes prevail in most

communities. Seed groups form that seem to set a norm of both maximal effort level and mutual trust that there

will be no panic when seeing noisy dips. Initial doubters are eventually converted into norm abiders. A restart

further speeds up the process of coordination success.

1. INTRODUCTION

Social welfare in many situations is crucially dependent on solving the problem of efficient

coordination where individual inputs are complementary for the production of group outcomes.

The coordination problem is a crucial issue in economics and organization theory, salient in

contexts such as conflict resolution, global games, and bank runs, among others.2The essence

of the problem can be captured in the weak-link game (van Huyck et al., 1990), where the

individual cost in the group production process is strictly increasing in one’s own effort, but the

individual benefit is determined by minimum effort among all group members.3For example,

when each family in a village is made responsible for one piece in an embankment construction

along the river nearby, the total level of protection against potential flooding is determined by

the lowest quality of the individual pieces.4Whenever all group members choose exactly the

same level of effort, we have a Nash equilibrium situation where nobody has an incentive to

unilaterally change his action. Although a higher-effort Nash equilibrium Pareto dominates a

lower-effort one, the former is also riskier from the individual perspective, which often causes

inefficient outcomes to prevail in the game.

∗Manuscript received August 2013; revised July 2015.

1We are grateful to Jordi Brandts, Gary Charness, Jacob Goeree, Vivian Lei, Paul Resnick, Lan Yao, and Maoliang

Yefor helpful comments. Chun-Lei Yang acknowledges financial support by the National Science Council in Taiwan (99-

2410-H-001-011-MY2). Juanjuan Meng acknowledges financial support from the National Natural Science Foundation

of China (Grant Nos. 71103003 and 71471004) and the Beijing Higher Education Young Elite Teacher Project (Grant

No. YETP0040). Please address correspondence to: Chun-Lei Yang, Institute for Social and Economic Research,

Nanjing Audit University, Nanjing 211815, China. E-mail: ycl@nau.edu.cn; and Research Center for Humanities and

Social Sciences, Academia Sinica, Taipei 115, Taiwan, ROC. Phone: 886-2-27898161. E-mail: cly@gate.sinica.edu.tw

2See, for example, Coase (1937), Schelling (1960), Hirshleifer (1983), Milgrom and Roberts (1992), Friedman (1993),

Cooper (1999), and Morris (2008).

3To underline the generality of the game, we note that the repeated prisoners’ dilemma can be conceptually treated

as a one-shot stag-hunt game, a 2-person (2-p) version of the weak-link game. See Skyrms (2004) and Dal Bo et al.

(2010) for details.

4Brandts et al. (2011) offer further excellent illustrations: “When individuals’ inputs to firm production are strong

complements, the group’s performance is constrained by its lowest performing individual. An assembly line moves no

faster than the slowest person in the line, a report doesn’t get finished until the last person completes their section, and a

meeting can’t start when a key attendee is late. If the benefits of coordinating are low and the costs of providing wasted

effort are high, groups can easily become trapped in situations where everyone understands that all would benefit if all

group members put forth their best effort, but no individual can unilaterally change the outcome for the better.”

651

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

652 YANG ET AL.

Since more people in the same group a priori means more sources for behavioral uncertainty

in an imperfect real world, the risk of inefficiency may increase with size. In fact, laboratory

experiments consistently show that coordination succeeds much better in small groups. As

stylized facts, groups larger than four almost surely converge to the most inefficient equilibrium,

whereas groups of sizes no greater than four have a chance to achieve higher coordination

levels up to the maximum.5Note that the problem of coordination in reality often features

economies of scale such that failure to achieve efficient coordination in larger groups implies

additional welfare loss in the form of missing the size advantage of production. For example,

in a generalized stag-hunt game where payoffs could vary with the group size, larger groups

of hunters may be more effective at hunting simply by additional options afforded such as

task specialization. Although perfect coordination among two hunters gets them a stag that is

worth more than two hares, a group of four may hunt down a buffalo, and eight may bag an

elephant, which is worth more than two buffalo or four stags in tribal trading. Can we identify

organizational mechanisms that induce efficient coordination in a large group to exploit the size

advantage?

As a starting point, the rather robust evidence of coordination success in 2-p lab groups hints

at the possibility that sufficient experience of such success may carry over into the larger groups

that the same subjects form later, in order to realize the size advantage. However, the risk of

miscoordination also increases with the group size—only one group member losing faith in his

fellow members may start a bank-run type of downward spiral that ruins it for all. As noted

by Weber (2006), real-world groups much larger than those in experiments, such as firms and

communities, have often managed to achieve efficient coordination. How do they manage to

do so, beating the odds of the risk-driven downward spiral to the bottom? One approach is to

note that in the real world, breakups and exits take place if they are institutionally admissible.

If group association is voluntary, the hope is that people might learn from earlier failures,

consolidate their mutual trust, and achieve better coordination performance via retreat and

regrouping.

This seems to be what happened with the development of China’s rural area mutual-aid

teams (MATs) in the 1950s to exploit size advantages. Upon earlier experiences in which

initial MATs of 20–25 families broke up immediately (Hinton, 1966), the communist party

specifically recommended that MATs ought to start small with 3–5 families and hoped that they

would slowly grow into larger ones voluntarily. The average size of MATs indeed increased

from 4.2 households in 1950 to 8.4 by the end of 1955, accompanied by steady growth of

agricultural productivity and output (Lin, 1990). After 1956, however, peasants were forced

into large People’s Communes without an exit option, which caused agricultural productivity to

plummet.6This failure is very much reminiscent of the coordination failure witnessed in large

groups in previous experimental designs without voluntary regrouping. Yet, the success up until

1956 suggests that a voluntary association setup might indeed solve the large-size coordination

problem, by slowly building up internal trust and increasing the size of the cooperatives while

learning from failures as documented in reoccurring exits and collapses. More generally, real-

world firms (or production and project teams) often start small and some get dissolved and

some grow larger, in a similar vein.

In this study, we investigate in experiments how efficient coordination fully exploiting

economies of scale might naturally result in a voluntary group formation environment with

a minimal set of rules that allow for bidirectional variations in group size. In a 10-p community,

groups of various sizes separately play the weak-link game for a cycle of three rounds before

they enter the next cycle in a different group composition. In the regrouping stage, each person

first decides whether to exit the current group. Then, each casts a merger vote on each of the

5See van Huyck et al. (1990), Camerer and Knez (2000), Knez and Camerer (1994), Cachon and Camerer (1996),

and Chaudhuri et al. (2009). Table 2 in Weber (2006) offers a summary.

6Lin (1990) specifically singles out lack of voluntary exit as the most crucial factor behind this failure.