Population invariance properties of social and economic networks

• DOI: http://doi.org/10.1111/ijet.12128
• Author: Bong Chan Koh,Sunghoon Hong,Youngsub Chun
• Published date: 01 September 2017
• Date: 01 September 2017

doi: 10.1111/ijet.12128

Population invariance properties of social and economic

networks

Youngsub Chun,∗Sunghoon Hong†and Bong Chan Koh‡

This paper investigates how a pairwise stable network changes upon the arrival of a new agent.

Comparing the new networks obtained for the society after the arrival of a new agent with the

initially pairwise stable network, we propose four different population invariance properties of a

network: link invariance,distance invariance, connectedness invariance, and network invariance.

We showthat pair wise stability is incompatible with link invariance under certain assumptions

on the allocation rule. However,if we consider specific models, positive results can be obtained.

For instance, in the symmetric connections model, pairwise stability implies connectedness

invariance.

Key wor ds network formation, variable population, pairwise stability, invariance property

JEL classification C70, D70, D85

Accepted 22 June2016

1 Introduction

A standard model of network formation is concerned with the following situation: given a set of

agents, two agents can add a link if they agree on it; any agent can sever a link if she wants to; and

adding a link is beneficial but also costly. In many studies (see, for example, Jackson and Wolinsky

1996; Watts 2001; Jacksonand Watts 2002), agents are assumed to behave myopically, that is, agents

do not consider how their behavior might affect others’ decisions in the future.1An improving path

is a sequence of adjacent networks that can be obtained when agents add or sever a link based on

the myopic expectation, and a pairwise stable network is one in which no agent has an incentive

to add or sever a link.2Jackson and Wolinsky (1996) introduce pairwise stability and analyze the

relation between pairwise stability and efficiency. Watts (2001) studies a dynamic process of network

formation in a specific model, the connections model. Jackson and Watts(2002) extend the dynamic

network formation model to a general setting where agents can add or sever a link by mistake and

investigate the implications of stochastic stability.

∗Department of Economics, Seoul National University,Seoul, South Korea. Email: ychun@snu.ac.kr

†Korea Instituteof Public Finance, Songpa-Gu, Seoul, South Korea.

‡Department of Economics, Seoul National University,Seoul, South Korea.

Weare gr atefulto Chris Chambers, Matt Jackson, Makoto Yano, and a referee for their comments.Y. C.’swork was sup-

ported by a NationalResearch Foundation of Korea grant funded by the KoreanGovernment (NRF-2013S1A3A2055391),

and the Institute of Economic Research,Seoul National University.

1For studies on the farsighted behavior of agents in the context ofnetworks, see Deroian (2001), Watts (2002), Dutta et al.

(2005), Page and Wooders(2009), and Herings et al. (2009).

2For other definitions of stability,see D utta and Mutuswami(1997), Slikker and van den Nouweland (2001), Jackson and

van den Nouweland (2005), Bloch and Jackson(2006), Galeotti et al. (2010), and Bramoulle et al. (2014).

International Journal of Economic Theory 13 (2017) 255–267 © IAET 255

International Journal of Economic Theory