Strategic Network Disruption and Defense

• Date: 01 October 2016
• Author: KRIS DE JAEGHER,BRITTA HOYER
• Published date: 01 October 2016
• DOI: http://doi.org/10.1111/jpet.12168

STRATEGIC NETWORK DISRUPTION AND DEFENSE

BRITTA HOYER

Paderborn University

KRIS DE JAEGHER

Utrecht University

Abstract

We study a game between a network designer, who uses costly links to

connect nodes in a network, and a network disruptor who tries to dis-

rupt the resulting network as much as possible by deleting either nodes

or links. For low linking costs networks with all nodes in symmetric posi-

tions are a best response of the designer under both link deletion and

node deletion. For high linking costs the designer builds a star net-

work under link deletion, but for node deletion excludes some nodes

from the network to build a smaller but stronger network. For inter-

mediate linking costs the designer again builds a symmetric network

under node deletion but a star-like network with weak spots under link

deletion.

1. Introduction

A large part of the recent economic literature regarding networks (for an overview, see

Goyal 2007; Jackson 2008) has focused on strategic network formation and games be-

ing played on networks. Consequently, one of the principal concerns of this literature

is the cooperative side of networks.1What has been generally ignored so far (at least in

economics research) is that networks, once they are formed, may be attacked from the

outside. If the network itself is a commodity, such as is the case for military communi-

cations networks or terrorist networks, the network or the players within the network

might become targets of an outside force. Consequently, not only are the individuals

in the network threatened by an attack but also the network as a whole is threatened.

1Note that cooperation within networks may be modeled by means of noncooperative game theory,

e.g., Bala and Goyal (2000).

Britta Hoyer, Paderborn University, Warburger Str. 100, 33098 Paderborn, Germany (britta.hoyer@

wiwi.upb.de). Kris De Jaegher, Utrecht School of Economics, Utrecht University, Kriekenpitplein 21-

22, 3584 EC, Utrecht, the Netherlands (K.Dejaegher@uu.nl).

We would like to thank Sanjeev Goyal, Henk Meijer,Stephanie Rosenkranz, Bastian Westbrock, Vin-

cent Buskens and Kirby Fears as well as participants at the EEA (2011), the ICS-USE Workshop (2010),

the Second Brazilian Workshop of the Game Theory Society (2010), the NAKE Research Day (2010)

and the 21st Game Theory Festival at Stony Brook (2010) for useful comments and suggestions. Any

remaining errors, however, remain our own.

Received April 28, 2015; Accepted June 5, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (5), 2016, pp. 802–830.

802

Strategic Network Disruption 803

Arguilla and Ronfeldt (2000) refer to this concept of fighting against networked ad-

versaries as “netwars.” Dekker and Colbert (2004) find that two trends have recently

emerged in military as well as civilian communications. The first is that the communica-

tions sector has become increasingly centered around networks and the second is that

there is an “increasing threat to communications infrastructure. In the civilian sphere,

the threat is from terrorist attacks, while in the military sphere this comes from the

increasing tendency to view communications networks as high-value targets” (Dekker

and Colbert 2004, p. 359). What we look at in this paper is the addition of links to the

network to keep the players within the network safe, where in the absence of a network

adversary these links would be redundant. The following example illustrates the type of

games we are looking at.

rMilitary units and the communication links between them can together be con-

sidered as military networks.2Particularly, if communication has to be achieved

over larger distances these communications links are subject to interruptions that

can be caused, for example, by the deliberate jamming of frequencies3(link dele-

tion) or by the deliberate elimination of units that enable communication (node

deletion). Designers of such communications networks must therefore take such

deliberate attacks into account and build networks that will still be functional in

the event of such an attack. Thus, in the absence of a threat, sending the same

signal via multiple routes to communicate between two units is redundant and

causes the network designer to incur unnecessary costs. If there is a threat, how-

ever, they can be used to make the network safe against the disruption of links.

While it is important to understand how these networks are created, how they work

together, and what technologies they use, Arguilla and Ronfeldt (2000, p. xi) state that

“the defining level of a netwar actor is its organizational design. . . . To cope with a

network, analysts must first learn what kind of network it is and then draw on the best

methods for analysis.” Therefore, in this paper, we focus purely on the structure of the

network and how to best defend it given a certain type of attack strategy. What are the

implications for the design and defense strategy of network designers when taking the

possibility of disruption into account? Given the fact that additional links are used to

keep the network safe, how does the cost of adding links affect network structure? Does

it matter if the attack is targeted at nodes or links in the network? And are there certain

network structures that are inherently “safe” against the disruption of a number of links

or nodes? These are the questions addressed in this paper.

To capture the influence of the threat of an attack on the structure of the network,

our paper models a sequential game between a network designer and a network disrup-

tor. We model network structure as being determined by a network designer, because in

the first instance we want to gain insight into what is an efficient defense strategy for the

network as a whole. Therefore, we can simply model the game as being played between

a network designer and a network disruptor. We begin by looking at the benchmark case

in which there is no threat of a disruption. We then proceed to look at cases where the

network designer faces a network disruptor, where we consecutively look at low, high,

2Lipsey (2006) contains an overview of military and security networks with references outside the field

of game theory.

3That such a threat actually exists can be seen from the efforts taken by government agencies to find a

disruption-tolerant network. Raytheon BBN Technologies reportedly “was awarded a $81 million con-

tract to create a collaborative technology alliance in network science” (Baburajan 2010) and in 2010

demonstrated a field experiment of a disruption-tolerant military network (Baburajan 2010).