  Modern distributed communication networks like the Internet and
censorship-resistant networks (also a part of the Internet) are characterized
by nodes (users) interconnected with one another via communication links. In
this regard, the security of individual nodes depend not only on their own
efforts, but also on the efforts and underlying connectivity structure of
neighboring network nodes. By the term 'effort', we imply the amount of
investments made by a user in security mechanisms like antivirus softwares,
firewalls, etc., to improve its security. However, often due to the large
magnitude of such networks, it is not always possible for nodes to have
complete effort and connectivity structure information about all their neighbor
nodes. Added to this is the fact that in many applications, the Internet users
are selfish and are not willing to co-operate with other users on sharing
effort information. In this paper, we adopt a non-cooperative game-theoretic
approach to analyze individual user security in a communication network by
accounting for both, the partial information that a network node possess about
its underlying neighborhood connectivity structure, as well as the presence of
positive externalities arising from efforts exerted by neighboring nodes. We
investigate the equilibrium behavior of nodes and show 1) the existence of
symmetric Bayesian Nash equilibria of efforts and 2) better connected nodes
choose lower efforts to exert but earn higher utilities with respect to
security improvement irrespective of the nature of node degree correlations
amongst the neighboring nodes. Our results provide ways for Internet users to
appropriately invest in security mechanisms under realistic environments of
information uncertainty.
