Communication networks, externalities, and the price of information

• Author: Arnold Polanski
• Date: 01 June 2019
• DOI: http://doi.org/10.1111/1756-2171.12277
• Published date: 01 June 2019

RAND Journal of Economics

Vol.50, No. 2, Summer 2019

pp. 481–502

Communication networks, externalities, and

the price of information

Arnold Polanski∗

Information goods (or information for short) play an essential role in modern economies. We

consider a setup where information has some idiosyncratic value for each consumer, exerts ex-

ternalities, and can be freely replicated and transmitted in a communication network. Prices paid

for information are determined via the (asymmetric) Nash Bargaining Solution with endogenous

disagreement points. This decentralized approach leads to unique prices and payoffs in any ex-

ogenous network. We use these payoffs to find connection structures that emerge under different

externality regimes in pre-trade network formations tage.An application to citation graphs results

in eigenvector-like measures of intellectual influence.

1. Introduction

Information plays an ever more important role in modern economies. The growing infor-

mation industry (or sector) comprises not only companies that produce information goods (e.g.,

media products, software) and services (e.g., consulting, education) but also companies that

process (e.g., banking, insurance) and disseminate (e.g., telephone, Internet) information. Nowa-

days, information created in this sector is traded predominantly in electronic form and appears

in various manifestations, for example, as music, e-books, patents, or (fake) news. Following

Shapiro and Varian (1999), we use the term information good (IG or information for short) very

broadly.Essentially, anything that can be digitized—encoded as a stream of bits—is information.

Muto (1986) identified the following distinctive properties of IGs: free replication, indivisibility,

irreversibility of trade, and negative external effects.1In this work, we assume the first three

properties and generalize the last one to external effects of any sign (with no externalities as a

special case). We posit further that individual consumption values of the IG and its externalities

are known to all players before they acquire information. This premise of complete information

extends to all other aspects of the model. Finally, we assume that information diffuses sufficiently

fast—potentially,at the speed of light—to all prospective consumers. Then, we can neglect its de-

preciation and the discounting of (dis)utilities resulting from its consumption. This is a reasonable

approximation for, for example, automated transmission of digitized contents.

∗University of East Anglia; A.Polanski@uea.ac.uk.

1Freereplication: Each trader can create identical replicas of the IG at no cost. Indivisibility: A possessor benefits

from exactly one unit of the IG. Irreversibility:Buyers cannot return the IG or cancel the trade. Negative external effects:

Each agent is negatively affectedif others acquire this good.

C2019, The RAND Corporation. 481

482 / THE RAND JOURNAL OF ECONOMICS

Information propagates through transmission channels that form a communication network,

for example, a distribution network for IGs, data transmission infrastructure, or a virtual network

implied by copyright regulations. Social and business contacts also serve as an ideal vehicle for

information exchange. The importance of social networks for information diffusion is exemplified

by the huge success of online networking communities such as Facebook and Twitter. Generally,

a link in a communication network represents a channel through which a holder of an IG can

transfer a copy of it to a connected agent.

In this article, we analyze the impact of communication networks, externalities, and valua-

tions on the price of IGs that display the aforementioned properties. Our analysis is based on a

(nonstrategic) model of bilateral trade in networks. Like similar models, we assume that a seller

and a prospective buyer can trade if and only if they are connected. The price paid in a bilateral

transaction is calculated via the (asymmetric) Nash Bargaining Solution (NBS) (e.g., Binmore,

Rubinstein, and Wolinsky, 1986) with endogenous disagreement points. As natural disagreement

values, players in each trading pair use their respective (expected) payoffs from a hypothetical

perpetual disagreement. This setup leads to unique prices and payoffs in any exogenous network.

We use these payoffs to analyze a network formation stage that precedes information diffusion.

Our analysis yields the following main insights. First,infor mation diffusesto all players who

can be reached along a (directed) path in the underlying network from the initial set of sellers.

The order in which trades occur and information is transferred has, however, no impact on payoffs

and prices of information. Second, we devise a recursive algorithm to calculate the unique prices

and payoffs for any given network, externalities, and initial set of sellers. We characterize the

connectivity of nodes that obtain information for free and provide an explicit formula for the

payoff to a single seller of information. This formula elucidates the role of externalities exerted

along critical paths2from this seller to prospective buyers. Third, we use the unique payoffs in

fixed networks to find connection structures that emerge under different externality regimes in

a pre-trade network formation stage. Finally, in an application to citation networks, we derive

eigenvector-like measures (Bonacich and Lloyd, 2001) of intellectual influence.

In order to illustrate the broad spectrum of applications of the model, we consider the

following stylized examples (see Figure 1 for their graphical representation). We consider gener-

alizations of these examples in Section 5 in the context of network formation.

(a) Positive externalities, tree network (Figure 1a). A firm can use a medium (television, print,

Internet, etc.) to advertise its product in order to attract prospective customers. We model

this situation as a (directed and rooted) tree with the root (advertiser) that is connected to an

internal vertex (e.g., a TV station) that in turn is connected to a set of leaf nodes (viewers,

prospective customers). Whenever a prospective customer watches an ad, the probability

that she will buy the product increases, which we interpret as a positive externality on the

advertising firm. Interestingly, the ad itself has no (or has, perhaps, evena negative) intrinsic

value for all agents.

(b) Negative externalities, star network(Figure 1b). In a bleak future scenario, a biotech company

creates a deadly virus (and the antidote) and then offers its know-how to rival countries. Ob-

viously,such a biological weapon in the arsenal of a country amounts to a threat (and a heavy

cost) for its adversaries. A less bellicose example is motivated by the growing importance

of markets for information and data brokers. Data brokers (or information resellers) collect,

process, and package data that they then sell to other firms. Accurate information about the

business environment and market conditions can be hugely beneficial to a firm, giving it an

advantage over uninformed competitors. In a simplified form, we model this situation as a

star network, where the center (data broker) is connected to a set of spokes (competing firms)

and each spoke is harmed by information acquired by another spoke.

(c) No externalities, complete network (Figure 1c). Copyright regulations shape a virtual con-

nection structure by defining property rights for IGs. Assume, for example, that an IG with

2Wedefine critical paths in Section 3.

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