Brief announcement: the price of anarchy for distributed network formation in an adversary model

We present a model for distributed network formation with cost expressing robustness in an adversary model. There are n players, each representing a vertex. Players may establish links to other players, building a link incurs a cost α. Individual cost comprises this building cost plus an indirect cost. After the network is built, an adversary deletes one link. The adversary is modeled by a random experiment, specified by a probability distribution on the links. Players know this distribution. Indirect cost for player v is the expected number of players to which v will become disconnected when the adversary strikes. We can prove an O(1) bound on the price of anarchy for two different adversaries under unilateral link formation. Under bilateral link formation, we can prove an O(1+√n/α) bound for one adversary, and for the other an asymptotically tight Ω(n) bound if α = Θ(1).