A model of informal favor exchange on networks

• DOI: http://doi.org/10.1111/jpet.12306
• Published date: 01 October 2018
• Date: 01 October 2018

639

Journal of Public Economic Theory. 2018;20:639–656. wileyonlinelibrary.com/journal/jpet © 2018 Wiley Periodicals, Inc.

Received: 1 December 2017 Revised: 1 March 2018 Accepted: 7 April 2018

DOI: 10.1111/jpet.12306

ARTICLE

A model of informal favor exchange on networks

V.Masson1S. Choi2A. Moore1M. Oak1

1Schoolof Economics, University of Adelaide

2Schoolof Economics, University of Seoul

V.Masson, School of Economics, University

ofAdelaide, 10 Pulteney Street, Adelaide,

SouthAustralia, Australia

(virginie.masson@adelaide.edu.au).

S.Choi, School of Economics, University of Seoul,

163Siripdaero, Dongdaemun-gu, Seoul, Korea

(schoi22@uos.ac.kr).

A.Moore, School of Economics, University of

Adelaide,Adelaide, South Australia, Australia

(angusmoore9@gmail.com).

M.Oak, School of Economics, University of

Adelaide,Adelaide, South Australia, Australia

(mandar.oak@adelaide.edu.au).

We develop a model of informal favor exchangewithin a social net-

work where the cost of providing a favor is stochastic. The commu-

nity has a norm, which specifies a cost threshold under which one

should perform a favor if asked, as well as a punishment—exclusion

from the network of the “noncompliers,” that is, of those who do

not perform favors despite their cost being below the threshold,

and those who refuse to punish nonperformers. We show that there

always existsa cost threshold such that all agents participating in the

favor exchangesystem receive strictly positive expected utility,and

the system is a stable system. Forsystems involving stars and regular

networks, we provide an ordering of the highest cost threshold sup-

porting their stability. We also identify the conditions under which

systems are efficient and show that, among all efficient systems, the

onewith the complete network provides the highest sum of expected

utilities. An efficient system, however,need not be stable.

1INTRODUCTION

Social networks play an important role in shaping economic behavior by embedding individual economic decisions in

the social context in which they occur.Many important questions in public economics such as voluntary provision of

public goods, participation in collective action, voting, acquisition and dissemination of information are influenced by

an agent's position in the social network; see Bravard and Sarangi (2016) for a review.1Ofparticular interest in public

economics is how cooperative behavioremerges among self-interested rational agents.

The origins of cooperative behavior have been fiercely debated bya number of authors from various disciplines. 2

However,from the seminal studies of Simmel (1950) and Coleman (1988), it appears that cooperation among individ-

uals in social groups is motivated by the desire of individuals to conform and the fear of punishment. Favor exchange

communities thus present an ideal framework to study cooperation. Indeed, exchangesare reciprocal and capture the

idea of conformity.Also, communities develop norms on whether or not a favor request can be turned down, with the

threat of exclusionoften being the instrument that ensures adherence to the norms.

Until recently, most of the scholarly work on patterns of favorexchanges used predetermined network structures

as grids on which such interactions take place; see for example Neilson (1999). However, a recent paper by Jackson,

1Forrecent specific applications, also see Stupnytska and Zaharieva (2017), Datta and Fraser (2017), Manski (2017), and Hoyer and Jaegher (2016) among

others.

2Seede Waal (1997) for an overview of the literature on this topic.

2MASSON ET AL.

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Rodriguez-Barraquer,and Tan (2012) made the first attempt to simultaneously determine both the evolution of a net-

work structure and the pattern of favor exchanges on it. Wefurther explore this idea by providing a noncooperative

foundation of the network structure using a link deletion network game.

In this paper,we model the informal exchange of favors where the value of a favor is the same for all agents, but the

cost for providing a favor is stochastic. The stochasticity of the cost is a novelfeature that offers a realistic framework

by capturing the fact that the cost of a favor depends on severalcomponents, such as the nature of the favor and the

characteristics of the provider.Agents follow a social norm, which is comprised of two components: one, it consists of

a cost threshold c∗below which one is expected to perform a favor when asked, and two, a social punishment which

consists of exclusionfrom the network of the “noncompliers,” that is, of those who do not perform favors despite their

cost being below the threshold, and those who refuse to punish nonperformers. In essence, the cost threshold reflects

the tolerance of a community toward the nonperformance of favors.

When in need of a favor, an agent approaches the least cost provider among her neighbors who then decides

whether or not to perform the favor. Agents are aware of deviations from the norm and exclude from the network

those who refuse to conform. Such punishment reflects the commonsense idea that people take a dim view of nonper-

formers for refusing to perform a favor despite facing a reasonably low cost for providingit. Our aim is to identify cost

thresholds that support stable and efficient favor exchangesystems.

Our underlying motivation is very similar to the “new manager” portrayed byKrackhardt (1996) as it lies in under-

standing how systems of informal favor exchanges work and how their stability gets affected rather than how they

form. In that respect, it is similar to Jackson et al. (2012) who also focus their interest in understanding how communi-

ties in ruralIndia function as opposed to how they form. Furthermore, the adoption of a norm that sets the expectations

and obligations of performing favorsis largely motivated by sociological evidence. As stated by Coleman (1988), norms

that promote the interest of the group rather than self-interest are important in supporting the public good problems

that existin communities. The success of those norms relies on external rewards for selfless actions and disapproval of

selfish actions.

Our analysis yields severalresults, such as the existence of multiple participation–compatible, (restricted) pairwise

stable, and Nash stable systems. Participationcompatibility refers to the strictly positive expected utility agents derive

from being part of the favor exchangesystem. Restricted pairwise stability (RPS) is an adaptation to our link deletion

game of the traditional notion of pairwise stability, wherebyan agent has no incentive to delete a link. It is similar to

the one employed by Jackson et al. (2012)and captures the idea that it takes time and coordination to form a new link

whereas an existing link can be unilaterallysevered. Nash stable systems are those resistant to multiple link deletions.

Interestingly,we show that the set of Nash stable systems and the set of (restricted) pairwise stable systems are iden-

tical. This result, which has been proven for nonstochastic link maintenance cost by Calvó-Armengoland Ilkilic (2009),

thus applies to other environments. Furthermore, we provide a comparisonof the cost thresholds supporting the sta-

bility of the systems with stars and regular networks. In a nutshell, stable systems with regular networks require a

lower cost threshold as the density of the network increases, while systems with star networks require the lowest cost

threshold of all systems involvingregular and star networks. This reflects the intuitive idea that exchanging favors with

a larger number of agents requires a higher tolerance toward the nonperformance of favors. Finally,we identify the

conditions under which systems are efficient and show that, among all efficient systems, the one with the complete

network provides the highest sum of expected utilities. Interestingly,efficient systems need not be stable. This result

emanates from the fact that there is a positiveexternality (on to neighbors) from an agent having additional links, which

is not internalized by the agent.

Our model contrasts with the basic framework of Jackson et al. (2012) where each pair of neighbors has a given

probability of being in a favorexchange relationship. In their set-up the probability that one needs a favor as well as the

probability that one receives a favor increases with the number of neighbors. Our framework is different. Although

an agent is more likely to be asked for favors as the number of her neighbors increases, she does not need more

favors. Furthermore, the structure of our model givesrise to positive externalities from links, similar to the models by

Jacksonand Wolinsky (1996), Johnson and Giles (2000), Calvó-Armengol (2004), and Jackson and Rogers (2005). How-

ever, unlike information transmission models, our externality comes from a different source. It arises from the fact

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