  In Peer-to-Peer (P2P) network systems, content (object) delivery between
nodes is often required. One way to study such a distributed system is by
defining games, which involve selfish nodes that make strategic choices on
replicating content in their local limited memory (cache) or accessing content
from other nodes for a cost. These Selfish Replication games have been
introduced in [8] for nodes that do not have any capacity limits, leaving the
capacitated problem, i.e. Capacitated Selfish Replication (CSR) games, open.
  In this work, we first form the model of the CSR games, for which we perform
a Nash equilibria analysis. In particular, we focus on hierarchical networks,
given their extensive use to model communication costs of content delivery in
P2P systems. We present an exact polynomial-time algorithm for any hierarchical
network, under two constraints on the utility functions: 1) "Nearer is better",
i.e. the closest the content is to the node the less its access cost is, and 2)
"Independence of irrelevant alternatives", i.e. aggregation of individual node
preferences. This generalization represents a vast class of utilities and more
interestingly allows each of the nodes to have simultaneously completely
different functional forms of utility functions. In this general framework, we
present CSR games results on arbitrary networks and outline the boundary
between intractability and effective computability in terms of the network
structure, object preferences, and the total number of objects. Moreover, we
prove that the problem of equilibria existence becomes NP-hard for general CSR
games.
