Group identity in a network formation game with cost sharing

• DOI: http://doi.org/10.1111/jpet.12286
• Author: Pritha Dev
• Published date: 01 June 2018
• Date: 01 June 2018

Received: 30 August 2016 Accepted: 9 November2016

DOI: 10.1111/jpet.12286

ARTICLE

Group identity in a network formation game

with cost sharing

Pritha Dev

IndianInstitute of Management, Ahmedabad

PrithaDev, Indian Institute of Management

Ahmedabad,IIMA Vastrapur,Ahmedabad, India

(pritha@iima.ac.in).

Iam extremely thankful to Jurjen Kamphorst for

hisinvaluable contributions to an earlier draft of

thepaper.

This paper introduces the choice of group identity, which is com-

prised of characteristics and commitments to these characteristics,

in a network formation model where links costs are shared. Players

want to link to the largest group given that linking costs for play-

ers of the same (different) characteristic are decreasing (increas-

ing) in their commitments. The equilibrium concepts used are Nash

equilibrium as well as one that looks for stability allowing for bilat-

eral negotiations. Conditions are shown under which the endoge-

nous choice of characteristics and commitments allow for multiple

groups with segregated or connected networks. When group iden-

tityis partly endogenous, such that characteristics are fixed and play-

ers only choose commitment, it is shown that the equilibrium popu-

lation commitment profile dictates whether the resulting network is

segregated or connected. When group identity is fully endogenous, it

is shown that multiple groups and segregated networks are possible

equilibrium outcomes but such outcomes are not stable unless the

group size additionally affects the costs of link formation.

1INTRODUCTION

This paper considers a model of network formation where the cost of a link depends on the group identity of players.

The study of group or social identity has been long incorporated into the social sciences through the pioneering works

of Mead (1934), Stryker (1968), Tajfeland Turner (1979), and Stryker and Burke (2000). Embedded in the literature

on social identity theory is the concept of identification with the social group as seen in Doosje, Ellemers, and Spears

(1995) and Terry and Hogg (1996). Identification measures the individual's feeling of connectedness with the group

where such identification might vary from being very strong to being very weak. With the insights from that litera-

ture in mind, in this paper the group identity of a player is captured by two variables; the first is a quantitative variable

capturing the group membership of the player, and the second is a qualitative variable called commitment capturing

the importance he attaches to that group membership. A person's group identity is thus the pair {group membership,

commitment}. Group identity is incorporated in a network formation game such that similar group memberships and

high commitments make the link cheaper to form, whereas different group memberships and high commitments make

the link more expensive to form. The network formation game analyzed is the standard connections model where

players want to link to the maximum number of other players at the minimum possible cost. The model allows for

390 c

2018 Wiley Periodicals,Inc. wileyonlinelibrary.com/journal/jpet Journal of Public Economic Theory.2018;20:390–415.

DEV 391

(a) Segregated (b) Connected

FIGURE 1 Differentcommitments, indicated by different shades, explain fragmentation in networks

(a) Segregated with Two Groups (b) Connected with One Group

FIGURE 2 Introductionof group identity, shape ={square, circle}, changes network structure

commitments and group memberships to be chosen simultaneously with the link offers. Hence, groups and the net-

work arise at the same time. The paper seeks to explore the conditions under which, instead of the entire population

choosing the same group membership and forming a connected network, multiple group memberships and segregated

networks are observed in equilibrium.

As an example,group memberships may involve players choosing political ideology: Republican or Democrat. At the

same time, players also choose their commitment to their chosen ideology.1Linkingto people with the same ideology

and higher commitments for the ideology is cheaper, whereas linking to a player with a different ideology and very

high commitment to the ideology is very expensive. If everyoneonly cared to belong to the largest possible network,

we should expect to see everyone choosing the same political ideology and there being one connected network. This

paper then shows, given ideologies, that the endogenous choice of commitment to ideology explains the division of

society by ideology. Further, this paper also shows, given that ideology and commitment to ideology are both choice

variables, it is possible for both ideologies to exist and for the network be divided along ideology if the costs of link

formation within a group vary by group size.

Figures 1 and 2 represent the main ideas discussed in the paper. The importance of the choice of commitment in

a network formation model is illustrated in Figure 1. The shapes Square or Circle represent the group membership,

whereas commitment is represented in the figure by different shades within a shape (darker shade =higher commit-

ment). The figure shows two panels with the same distribution of underlying group memberships but with different

1A Republican with very high commitment can be thought of as one who takesas the truth everything that is thought to be the Republican way of thinking.

On the other hand, a Republican with very low commitment believesin the basic Republican tenet of liberty, but might believe in other ideas not includedin

theRepublican way of thinking.