Network Design and Imperfect Defense

Landwehr, Jakob

doi:10.2139/ssrn.2574178

“…Such defense is modeled as taking place on an existing network (Acemoglu et al 2016;Kovenock and Roberson 2018). Alternatively, the centralized player also designs the network itself (Dziubiński and Goyal 2013;Goyal and Vigier 2014;Landwehr 2015; see Endres et al (2019) for an experimental analysis of such models). Dziubiński and Goyal (2017) additionally consider the case where defense of the nodes takes place in a decentralized manner, but the network is exogenously given.…”

Section: Literature On Network Disruptionmentioning

confidence: 99%

Network disruption and the common-enemy effect

Hoyer

¹

,

Jaegher

²

2022

Int J Game Theory

0

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We study the effect of a common enemy on the connections-model of network formation, where self-interested players can use links to build a network, knowing that they face a common enemy who can disrupt the links or nodes of the network. The goal of the common enemy is to minimize the sum of the benefits players obtain from the network. We find that for large linking costs, introducing such a common enemy can lead to the formation of pairwise stable and efficient networks which would not be pairwise stable without the threat of disruption. The reason is the large reduction in payoffs caused by disruption as soon as one player fails to maintain a link. However, we also find that for small linking costs, the empty network is pairwise stable under disruption, whereas it is not in the absence of disruption. The reason is that in the presence of disruption a link that is unilaterally formed is automatically targeted (or one of the players forming the link is automatically targeted). While the common enemy can thus have a positive effect on the incentives of the players to form an efficient network, it can also lead to the disintegration of the network.

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“…Third, in both frameworks it is difficult to obtain general results when imperfect defense is introduced. However, Landwehr [21] provides equilibrium strategies for D when the number of attacks is very small. In particular, he establishes that if k = 2, then there exist 6 types of strategies that D may play in equilibrium according to the value of π, cP , and cL.…”

Section: Propositionmentioning

confidence: 99%

“…If e is a link and i and j are nodes such thatψ(e) = (i, j), then e is said to join i and j. 21 We define the adjacency matrix M(ĝ) of a multigraphĝ = (N ,Ê,ψ) as ∀(a, b) ∈Ê 2 , M a,b (ĝ) = #{e ∈Ê :ψ(e) = (a, b)}, i.e. the number of links between nodes a and b inĝ.…”

Section: Multigraphsmentioning

confidence: 99%

“…More precisely, an attack on an unprotected target always destroys the target, and an attack on a protected target destroys the target with a positive probability. A recent independent work of Landwehr [21] extends the analysis of imperfect defense. It shows that for a certain range of protection cost and link formation cost, strategies that use both protections and several links are equilibria.…”

Section: Introductionmentioning

confidence: 99%

“…Note that inFigure 8(vii), each node is incident to 2 protected links and k = 2. Interestingly, DG[9] and Landwehr[21] establish that in models with imperfect defense, there exist parameters where D designs a (2, n)-Harary-networks in equilibrium.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Optimal design and defense of networks under link attacks

Bravard

¹

,

Charroin

²

,

Touati

³

2017

Journal of Mathematical Economics

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Networks facilitate the exchange of goods and information and create benefits. We consider a network with n complementary nodes, i.e. nodes that need to be connected to generate a positive payoff. This network may face intelligent attacks on links. To study how the network should be designed and protected, we develop a strategic model inspired by Dziubiński and Goyal (2013) with two players: a Designer and an Adversary. First, the Designer forms costly protected and non-protected links. Then, the Adversary attacks at most k links given that attacks are costly and that protected links cannot be removed by her attacks. The Adversary aims at disconnecting the network shaped by the Designer. The Designer builds a protected network that minimizes her costs given that it has to resist the attacks of the Adversary. We establish that in equilibrium the Designer forms a minimal 1-link-connected network which contains only protected links, or a minimal (k + 1, n)-link-connected network which contains only non-protected links, or a network which contains one protected link and (n − 1)(k + 1)/2 non-protected links. We also examine situations where the Designer can only create a limited number of protected links and situations where protected links are imperfect, that is, protected links can be removed by attacks with some probabilities. We show that if the available number of protected links is limited, then, in equilibrium, there exists a network which contains several protected and non-protected links. In the imperfect defense framework, we provide conditions under which the results of the benchmark model are preserved.JEL Classification: D74, D85. . 1 A network is connected if no set of nodes is isolated from the others. 1 has no value. Recall that during the Second World War, the production units for the weapons (nodes) were buried, so they were impossible to target, and attacks had to target the roads (links) in order to destroy the production process of the enemy. Therefore, the issue was to design a communication network between the production units that the enemy could not disconnect.Our goal is to examine how to design and protect the network in an optimal way, such that the network remains connected after an intelligent link attack. 2 We say that a network is designed and protected in an optimal way if the costs associated with the design and the protection of the network are minimized.We consider a two-stage game with two players: a Designer (D) and an Adversary (A).• Stage 1. The Designer moves first and chooses both a set of protected, and a set of non-protected links. Protected links cannot be removed by the attacks of the Adversary.• Stage 2. After observing the protected network (strategy) formed by the Designer, the Adversary attacks the network by allocating attacks to specific links. Since the attacks are costly, the Adversary has an incentive to attack at most k links.Creating protected and non-protected links is costly for the Designer. The benefits obtained by the Designer at the end of the game depend ...

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Optimal Design and Defense of Networks Under Link Attacks

Bravard¹,

Charroin²

2015

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Networks facilitate the exchange of goods and information and create benefits. We consider a network with n complementary nodes, i.e. nodes that need to be connected to generate a positive payoff. This network may face intelligent attacks on links. To study how the network should be designed and protected, we develop a strategic model inspired by Dziubiński and Goyal (2013) with two players: a Designer and an Adversary. First, the Designer forms costly protected and non-protected links. Then, the Adversary attacks at most k links given that attacks are costly and that protected links cannot be removed by her attacks. The Adversary aims at disconnecting the network shaped by the Designer. The Designer builds a protected network that minimizes her costs given that it has to resist the attacks of the Adversary. We establish that in equilibrium the Designer forms a minimal 1-link-connected network which contains only protected links, or a minimal (k + 1, n)-link-connected network which contains only non-protected links, or a network which contains one protected link and (n − 1)(k + 1)/2 non-protected links. We also examine situations where the Designer can only create a limited number of protected links and situations where protected links are imperfect, that is, protected links can be removed by attacks with some probabilities. We show that if the available number of protected links is limited, then, in equilibrium, there exists a network which contains several protected and non-protected links. In the imperfect defense framework, we provide conditions under which the results of the benchmark model are preserved.JEL Classification: D74, D85.

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Network Design and Imperfect Defense

Cited by 3 publications

References 9 publications

Network disruption and the common-enemy effect

Network disruption and the common-enemy effect

Optimal design and defense of networks under link attacks

Optimal Design and Defense of Networks Under Link Attacks

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