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The price of anarchy for network formation in an adversary model. (English) Zbl 1311.91058
Summary: We study network formation with $$n$$ players and link cost $$\alpha>0$$. After the network is built, an adversary randomly deletes one link according to a certain probability distribution. Cost for player $$v$$ incorporates the expected number of players to which $$v$$ will become disconnected. We focus on unilateral link formation and Nash equilibrium. We show existence of Nash equilibria and a price of stability of $$1+o(1)$$ under moderate assumptions on the adversary and $$n\geq 9$$. 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 $$O(1)$$ bound on the price of anarchy for both adversaries, the constant being bounded by $$15+o(1)$$ and $$9+o(1)$$, respectively.

##### MSC:
 91A43 Games involving graphs 91A06 $$n$$-person games, $$n>2$$
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##### References:
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