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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

Received: 27 May 2011; in revised form: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Kliemann, L. The Price of Anarchy for Network Formation in an Adversary Model. Games 2011, 2, 302-332.

AMA Style

Kliemann L. The Price of Anarchy for Network Formation in an Adversary Model. Games. 2011; 2(3):302-332.

Chicago/Turabian Style

Kliemann, Lasse. 2011. "The Price of Anarchy for Network Formation in an Adversary Model." Games 2, no. 3: 302-332.

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