Price of anarchy and an approximation algorithm for the binary-preference capacitated selfish replication game

We consider the capacitated selfish replication (CSR) game with binary preferences, over general undirected networks. We study the price of anarchy of such games, and show that it is bounded above by 3. We develop a quasi-polynomial algorithm O(n2+lnD), 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 Nash equilibrium (NE) of the game. Proof of this result uses a novel potential function. We further show that when the underlying network has a tree structure, every globally optimal allocation is an NE, which can be reached in only linear time. We formulate the optimal solutions and NE points of the CSR game using integer linear programs. Finally, we introduce the LCSR game as a localized version of the CSR game, wherein the actions of the players are restricted to only their close neighborhoods.