  This paper studies a stochastic game theoretic approach to security and
intrusion detection in communication and computer networks. Specifically, an
Attacker and a Defender take part in a two-player game over a network of nodes
whose security assets and vulnerabilities are correlated. Such a network can be
modeled using weighted directed graphs with the edges representing the
influence among the nodes. The game can be formulated as a non-cooperative
zero-sum or nonzero-sum stochastic game. However, due to correlation among the
nodes, if some nodes are compromised, the effective security assets and
vulnerabilities of the remaining ones will not stay the same in general, which
leads to complex system dynamics. We examine existence, uniqueness, and
structure of the solution and also provide numerical examples to illustrate our
model.
