CREDIBILITY AND STRATEGIC LEARNING IN NETWORKS

• Published date: 01 August 2016
• DOI: http://doi.org/10.1111/iere.12175
• Date: 01 August 2016
• Author: Bhaskar Dutta,Kalyan Chatterjee

INTERNATIONAL

ECONOMIC

REVIEW

August 2016

Vol. 57, No. 3

CREDIBILITY AND STRATEGIC LEARNING IN NETWORKS∗

BYKALYAN CHATTERJEE AND BHASKAR DUTTA1

The Pennsylvania State University, U.S.A.; University of Warwick, U.K.

We analyze a model of diffusion in a fixed, finite connected network. There is an interested party that knows the

quality of the product being propagated and chooses an implant in the network to influence other agents to buy. Agents

are either “innovators,” who adopt immediately, or rational. Rational consumers buy if buying instead of waiting

maximizes expected utility. We consider the conditions on the network under which optimal diffusion of the good

product with probability 1 is a perfect Bayes equilibrium.

1. INTRODUCTION

1.1. Main Features. This article studies a model of diffusion and social learning (of what we

call broadly “technology”) in a connected network with the following essential features:

1. An individual, known henceforth as the firm, has private information about the quality of

the technology it seeks to diffuse to potential consumers. This firm is outside the network

but might choose to pay some agent in the network to propagate its product or idea. The

agent so chosen is referred to here as an “implant.”

2. The network is populated by agents or players, one at each node. Each agent observes

the actions of his or her neighbors over time and makes a decision on whether to adopt

the technology or not. These players come in two varieties, innovators, who always adopt

the technology, and standard players, each of whom is fully rational and makes a decision

on whether to adopt or not based on utility maximization.

3. The network is given exogenously. Agents with direct links can engage in restricted

communication with each other; however, agents who are not directly linked can have no

communication with each other. What the firm knows about individual agent interactions

is restricted to the direct neighbors of the implant chosen, if any. In particular, the firm

is unaware of who is an innovator and who is not before it chooses the implant. In the

extensions, we consider relaxing this requirement.

∗Manuscript received November 2013; revised May 2015.

1This is a substantially revised version of an earlier paper with the title “Word of Mouth Advertising, Credibility

and Learning in Networks.” We are very grateful to the editor, two referees, Drew Fudenberg, Parikshit Ghosh,

Sanjeev Goyal, Matt Jackson, Gilat Levy, and various seminar audiences for helpful comments on earlier versions of

the article. We also acknowledge the valuable assistance of Pathikrit Basu with the diagrams and Chun-Ting Chen

with the mumerical example. Chatterjee thanks the Human Capital Foundation (http://www.hcfoundation.ru/en/), and

especially Andrey Vavilov, for financial support to the Penn State Department of Economics and the Richard B. Fisher

endowment at the Institute for Advanced Study for supporting his 2014–15 membership. Please address correspondence

to: Kalyan Chatterjee, Department of Economics, The Pennsylvania State University, 201 Old Main, University Park,

PA 16802. E-mail: kchatterjee@psu.edu.

759

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(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

760 CHATTERJEE AND DUTTA

4. The structure of the network is common knowledge to the firm and to all agents.

The main novelty of this article is that the players rationally decide whether the communica-

tions they receive from their neighbors are credible or not. Learning therefore occurs through

strategic choices by agents and this affects whether diffusion occurs to the whole population or

dies out within some finite distance of the origin. As far as we know, ours is the first paper to

study this issue in the context of networks in any detail.

1.2. Motivation. There are several different economic problems that motivated us in study-

ing this issue, though the model we end up with does not fit every aspect of each of these

motivating problems. One example comes from a New York Times magazine article about viral

marketing. The article discusses a company called bzz.com. The article mentions that the com-

pany would “implant” agents, with good connections, to sell products like books, CDs, or party

food items to their friends and social “neighbors.” The company would provide talking points

to the agents, who would then “recommend” the product to their neighbors.2

Another example is suggested by the empirical study of social learning in the Green Rev-

olution in India in Munshi (2004). The government or its representative wants to push new

high-yielding varieties of seeds for wheat and rice.3It chooses an individual in the community

whose adoption of the new technology will have the most widespread impact. Neighbors of

this individual observe the percentage of the farm acreage he devotes to the new varieties and

each neighbor then makes a similar decision for his or her own farm, which is then observed by

neighbors of neighbors and so on.4In small villages, it is not unreasonable to assume common

knowledge of the network and that acreage planted is easily observable, so this example fits

some key features of the model.

The use of implants or “farmer facilitators” in such settings has also been reported.

“To spread the word [about soil micronutrients], Karnataka hired, on a seasonal basis, “farmer

facilitators” from within communities instead of outsiders, on the assumption that villagers were

more likely to listen to their peers than strangers.”5

Of course, our model is not going to capture all the characteristics associated with these

examples. However, our attempt has been to construct a tractable model that captures the main

features underlying these models.

1.3. The Model, a Brief Verbal Description. The players in this model are the seller or the

rm, which knows the quality of the product it seeks to sell, and potential buyers who are

arranged in a xed exogenous network, whose structure is common knowledge. We shall use this

terminology to describe the motivating examples in the last subsection. For instance, the seller

could be a medical technology company seeking adoption by doctors of a particular method

of surgery, with the buyers being the doctors. The given network is the exogenous structure of

social communication among the doctors in a particular specialty.

A buyer finds out the quality of the product and then makes a recommendation to her

neighbors if she finds that the product is “good.” Notice that we rule out the possibility of

negative recommendations. In many contexts, this is not a bad assumption. For instance, a

doctor may not want to publicize the fact that a particular method of treatment has not worked.

Thus “no recommendation” is noisy bad news and a “recommendation” is possibly good news.6

The seller can choose to “seed” the network by paying an agent at any given node in the

network to give a positive recommendation about the seller’s product. Only one node in the

2See Walker (2004).

3This example may seem inappropriate if one views the government as a benevolent agent because that would rule

out its promoting a bad technology. However, governments in developing countries are sometimes said to be “bought

out” by “big” business houses. Also, there is no reason why private entities such as companies producing new types of

agricultural inputs cannot replace the government in the story of Munshi (2004).

4A farmer is convinced about the efficacy of the seeds in some way, maybe by testing them,before devoting substantial

acreage to them instead of the existing varieties.

5Reported in The Guardian, March 13, 2013.

6In the “Extensions” section, we briefly discuss what happens if we allow agents to make negative recommendations.