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We study network formation with n players and link cost \ubb > 0. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player &#x03bd; incorporates the expected number of players to which &#x03bd; 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 + &#x03bf;(1) under moderate assumptions on the adversary and n \ucf 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 &#x039f;(1) bound on the price of anarchy for both adversaries, the constant being bounded by 15 + &#x03bf;(1) and 9 + &#x03bf;(1), respectively

The Price of Anarchy for Network Formation in an Adversary Model