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Games 2011, 2(3), 302-332; doi:10.3390/g2030302
Article

The Price of Anarchy for Network Formation in an Adversary Model

Department of Computer Science, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, Kiel 24098, Germany
Received: 27 May 2011 / Revised: 18 July 2011 / Accepted: 8 August 2011 / Published: 23 August 2011
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Abstract

We study network formation with n players and link cost α > 0. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player ν incorporates the expected number of players to which ν will become disconnected. We focus on unilateral link formation and Nash equilibrium. We show existence of Nash equilibria and a price of stability of 1 + ο(1) under moderate assumptions on the adversary and n ≥ 9. We prove bounds on the price of anarchy for two special adversaries: one removes a link chosen uniformly at random, while the other removes a link that causes a maximum number of player pairs to be separated. We show an Ο(1) bound on the price of anarchy for both adversaries, the constant being bounded by 15 + ο(1) and 9 + ο(1), respectively.
Keywords: network formation; equilibrium; price of anarchy; unilateral link formation; adversary model; network robustness network formation; equilibrium; price of anarchy; unilateral link formation; adversary model; network robustness
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Kliemann, L. The Price of Anarchy for Network Formation in an Adversary Model. Games 2011, 2, 302-332.

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