The Price of Anarchy for Network Formation in an Adversary Model

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.

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