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We consider the capacitated selfish replication (CSR) game with binarypreferences, over general undirected networks. We first show that such gameshave an associated ordinary potential function, and hence always admit apure-strategy Nash equilibrium (NE). Further, when the minimum degree of thenetwork and the number of resources are of the same order, there exists anexact polynomial time algorithm which can find a NE. Following this, we studythe price of anarchy of such games, and show that it is bounded above by 3; wefurther provide some instances for which the price of anarchy is at least 2. Wedevelop a quasi-polynomial algorithm O(n^2D^{ln n}), where n is the number ofplayers and D is the diameter of the network, which can find, in a distributedmanner, an allocation profile that is within a constant factor of the optimalallocation, and hence of any pure-strategy NE of the game. Proof of this resultuses a novel potential function.

Approximation Algorithm for the Binary-Preference Capacitated Selfish Replication Game and a Tight Bound on its Price of Anarchy