We consider a security problem on a distributed network.
We assume a network whose nodes are vulnerable to infection
by threats (e.g. viruses), the attackers. A system security
software, the defender, is available in the system. However,
due to the networkĘs size, economic and performance reasons,
it is capable to provide safety, i.e. clean nodes from
the possible presence of attackers, only to a limited part of
it. The objective of the defender is to place itself in such a
way as to maximize the number of attackers caught, while
each attacker aims not to be caught.
In , a basic case of this problem was modeled as a
non-cooperative game, called the Edge model. There, the
defender could protect a single link of the network. Here,
we consider a more general case of the problem where the
defender is able to scan and protect a set of k links of the
network, which we call the Tuple model. It is natural to expect
that this increased power of the defender should result
in a better quality of protection for the network. Ideally,
this would be achieved at little expense on the existence and
complexity of Nash equilibria (profiles where no entity can
improve its local objective unilaterally by switching placements
on the network).
In this paper we study pure and mixed Nash equilibria
in the model. In particular, we propose algorithms for computing
such equilibria in polynomial time and we provide a
polynomial-time transformation of a special class of Nash
equilibria, called matching equilibria, between the Edge
model and the Tuple model, and vice versa. Finally, we
establish that the increased power of the defender results in
higher-quality protection of the network.