  We consider the capacitated selfish replication (CSR) game with binary
preferences, over general undirected networks. We first show that such games
have an associated ordinary potential function, and hence always admit a
pure-strategy Nash equilibrium (NE). Further, when the minimum degree of the
network and the number of resources are of the same order, there exists an
exact polynomial time algorithm which can find a NE. Following this, we study
the price of anarchy of such games, and show that it is bounded above by 3; we
further provide some instances for which the price of anarchy is at least 2. We
develop a quasi-polynomial algorithm O(n^2D^{ln n}), where n is the number of
players and D is the diameter of the network, which can find, in a distributed
manner, an allocation profile that is within a constant factor of the optimal
allocation, and hence of any pure-strategy NE of the game. Proof of this result
uses a novel potential function.
