Networks as Public Infrastructure: Externalities, Efficiency, and Implementation

• DOI: http://doi.org/10.1111/jpet.12139
• Published date: 01 April 2016
• Date: 01 April 2016
• Author: HANS HALLER

NETWORKS AS PUBLIC INFRASTRUCTURE:EXTERNALITIES,

EFFICIENCY,AND IMPLEMENTATION

HANS HALLER

Virginia Polytechnic Institute and State University

Abstract

First, a noncooperative model of network formation is investigated

where link formation is one-sided and information flow is two-way. For

that model, the relationship between different notions of efficient net-

works is studied: Pareto-optimal networks on the one hand and welfare-

maximizing networks on the other hand. Strategic network formation

is compared with funding schemes for public goods. Second, we ex-

tend the model and review earlier findings how a preexisting network

affects existence of Nash equilibria and efficiency of Nash equilibrium

outcomes of the strategic network formation game. It can foster or

prohibit existence of Nash equilibria. It can improve or worsen equi-

librium welfare. Finally, we treat the preexisting network as public in-

frastructure and design and analyze a subscription game for the public

provision of that infrastructure.

1. Introduction

The standard competitive equilibrium model—of pure exchange or with production—

assumes private goods without externalities. Allowing for externalities renders the anal-

ysis more cumbersome and, as a rule, affects the welfare conclusions. Introduction of

public goods leads to the Samuelsonian characterization of Pareto-optimal allocations

and implementation of the latter by means of mechanisms different from the standard

market mechanism, for instance by means of personalized or Lindahl prices. Both the

treatment of externalities and of public goods are considered special fields of microe-

conomic theory. In contrast, externalities are the essence of strategic game theory and

its applications, like those in industrial organization and other areas of economics. A

strategic game where none of the players is affected by the actions of others is justifiably

termed “inessential.”

Following the seminal contributions of Jackson and Wolinsky (1996) and Bala and

Goyal (2000) and the less well-known earlier example by Myerson (1991, p. 448), a

sizeable game-theoretic literature on network formation has emerged. The aim of the

current paper is to address several issues that arise when (a) a network is viewed as a

public infrastructure and (b) the network or part of it is the outcome of a game in

Hans Haller,Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg,

VA 24061 (haller@vt.edu). The comments of a referee and the suggestions of an associate editor are

appreciated.

Received August 22, 2014; Accepted September 21, 2014.

C2015 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (2), 2016, pp. 193–211.

193

194 Journal of Public Economic Theory

strategic form. The main issues to be addressed or at least touched upon in a first pass

are network externalities (and public good features of networks), efficiency, and imple-

mentation; and those are obviously related.

In accordance with my prior work and for ease of exposition, I shall adhere to

the purely noncooperative approach of Bala and Goyal (2000) where addition and

deletion of links are unilateral decisions of the player from whom the respective links

originate.1More specifically, I shall focus on the so-called two-way flow connections

model `

alaGaleotti, Goyal, and Kamphorst (2006) both as a benchmark and an il-

lustrative prototype. That model incorporates cost and value heterogeneity. A player

receives valuable information from others not only through direct links, but also via

indirect links. The player incurs the cost of the direct links she initiates. Before contin-

uing the detailed description of the model, I make a digression on each of the three

themes, network externalities (and public good features of networks), efficiency, and

implementation.

1.1. Network Externalities

A strategic network formation game like any interesting strategic game inherently

involves externalities. So-called “network externalities” prove relevant for network

formation as well as network utilization, for both positive and normative analysis. A

classic and popular example for positive network externalities or “network effects” is

the telephone. Having a telephone is only of interest to the user if there is a significant

number of other users one can reach (and wants to reach) through the same network.

If additional users join the network, then they increase the value of the telephone to the

already existing users, even if that is not their intention. The two-way flow connections

model shares this property. If a player creates a direct link to another player, the

initiating player receives valuable information from the other player. In addition, the

first player receives valuable information from third players via indirect links and other

players receive valuable information from him through direct and indirect links. A

player can only benefit and never gets harmed when others create links.

The telephone also illustrates the possibility of negative network externalities or

“congestion effects.” If too many users attempt to make calls simultaneously, service

may be disrupted, delayed, or noisy. This was particularly the case before the digital age

because of overloaded lines and relays, but can still occur nowadays. Modifications of

the two-way flow connections model can accommodate negative network externalities.

I will briefly comment on such model variations in Section 7. However, the emphasis of

the paper is going to be on positive network externalities.

1.2. Local Public Good Aspects of Networks

If in the standard two-way flow connections model (without decay and with perfectly

reliable links), an isolated player forms a link to another player, then the first player gets

access to all the information available within the connected component of the second

player. He would receive the same information when establishing instead a link to

another player of that connected component. However, the costs of link formation may

be different. Investing in one of these links is like paying a fee to enter the particular

1In contrast, pairwise stability `

alaJackson and Wolinsky (2005) treats addition of a link in a network

as a bilateral decision by the two players involved, whereas severance of a link constitutes a unilateral

decision.