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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