Endogenous formation of multiple social groups

• Published date: 01 September 2020
• Author: Ngoc M. Nguyen,Lionel Richefort,Thomas Vallée
• DOI: http://doi.org/10.1111/jpet.12442
• Date: 01 September 2020

J Public Econ Theory. 2020;22:1368–1390.wileyonlinelibrary.com/journal/jpet1368

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© 2020 Wiley Periodicals, Inc.

Received: 4 December 2018

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Accepted: 21 March 2020

DOI: 10.1111/jpet.12442

ORIGINAL ARTICLE

Endogenous formation of multiple social

groups

Ngoc M. Nguyen |Lionel Richefort |Thomas Vallée

LEMNA, University of Nantes, Nantes,

France

Correspondence

Ngoc M. Nguyen, LEMNA, University of

Nantes, Nantes 44000, France.

Email: nguyenngocminh87@gmail.com

Abstract

This paper explores a model of group membership

formation in which agents decide to join or not

multiple social groups. The membership formation

process induces a bipartite graph structure with

social groups listed on one side and agents listed on

the other side. Among members of multiple social

groups, we consider two decisive types of agents: the

grand star and the mini star. The former type is

the unique agent in a society who participates in all

social groups. The latter type includes agents who

participate in more than one, but not all, social

groups such that every social group pair has one and

only one common member. We analyze the efficiency

and stability conditions of group membership

formation, and we establish sufficient conditions

under which a connected graph that contains either a

grand star or a set of mini stars becomes the unique

strongly efficient and stable graph.

1|INTRODUCTION

In modern societies, the potential physical or virtual connections between people naturally

create numerous social groups that, in turn, play an important role in people's lives. Primary

groups, such as family and friends, provide one of the most important elements of Maslow's

hierarchy of needs: the sense of belonging. However, these groups only partially satisfy

people's physiological and psychological needs. The unsatisfied needs can be fulfilled through

participation in secondary groups in college, at the office, or in other social environments

encountered in daily life.

Membership in a social group offers access to resources that are only shared among the

group's members. Moreover, a crucial feature of social groups is communication among

members to meet basic needs. This information exchange process allows members of a social

group to assist each other, enhance their individual capacities, and develop personality traits.

Additionally, to maintain their collective benefits, social groups should be considered as

representatives of all people in society (Richter & Hatch, 2013).

It should be noted that benefits from membership in social groups are not infinitive. Buchanan

(1965) characterized these benefits as excludable, congestible and divisible local public goods, and

proposed an efficient procedure for consuming these goods. Besides, if there exists a sufficient

number of social groups in society, agents can choose to participate in only some of them to

maximize their utility so that the benefits from memberships in social groups are (near) optimally

allocated (Tiebout, 1956). Wooders (1978) characterized the Tiebout equilibrium as a core

equivalence and developed a “market‐type”equilibrium for local public goods. Moreover, with the

presence of multiple memberships, the set of equilibrium outcomes is always reachable regardless

the sizes of social groups (Allouch & Wooders, 2008).Recentstudiescomparednetworksandlocal

public good when analyzing network formation mechanism (see, e.g., Haller, 2016).

In reality, agents must often pay participation costs to directly enjoy the collective benefits

provided by social groups. From the perspective of agents, however, these benefits can be

obtained both directly and indirectly. Consider a bipartite graph structure in which agents

choose to participate in two social groups, s

1

and

s

2

, as in Figure 1. If agent aiis a member of

social group s

1

, she obtains a direct benefit from her membership in s

1

. However, if aiis not a

member of s

1

, she may still obtain an indirect benefit from s

1

if she knows a member of s

1

.

More precisely, aimay obtain an indirect benefit from s

1

if she participates in another group,

s

2

, with a member, agent a

t

, who is also a member of s

1

. Thus, aiand a

t

know each other

through

s

2

. In other words, the connection between s

1

and

s

2

is through agent a

t

, and this

connection allows the members of

s

2

(including agent ai) to receive an indirect benefit from s

1

and vice versa. As a consequence, the decision of aito participate in s

1

depends on the values of

both the direct and indirect benefits that she can obtain from s

1

.

Studies on graph theory have demonstrated various applications of bipartite graphs. For

example, researchers have highlighted the bilateral bargaining process between traders and the

effect of exogenous graph structures on economic outcomes (Corominas‐Bosch, 2004; Kranton

& Minehart, 2001; Wang & Watts, 2006). Other studies have focused on the structural properties

FIGURE 1 An example bipartite graph structure of two social groups

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