Figure 2: Potential inefficiency of Nash equilibria illustrated by two clusters of n 2 servers. The intra-cluster distances are all zero and the distance between clusters is α −1, where α is the placement cost. The dark nodes replicate the object. Network (a) shows a Nash equilibrium in the basic game, where one server in a cluster caches the object. Network (b)shows the social optimum where two replicas, one for each cluster, are placed. The price of anarchy is O(n) and even the optimistic price of anarchy is O(n). This high price of anarchy comes from the undersupply of replicas due to the selfish nature of servers. Network (c) shows a Nash equilibrium in the payment game, where two replicas, one for each cluster, are placed. Each light node in each cluster pays 2/n to the dark node, and the dark node replicates the object. Here, the optimistic price of anarchy is one.