  In this article, we study a discounted stochastic game to model resource
optimal intrusion detection in wireless sensor networks. To address the problem
of uncertainties in various network parameters, we propose a globalized robust
game theoretic framework for discounted robust stochastic games. A robust
solution to the considered problem is an optimal point that is feasible for all
realizations of data from a given uncertainty set. To allow a controlled
violation of the constraints when the parameters move out of the uncertainty
set, the concept of globalized robust framework comes into view. In this
article, we formulate a globalized robust counterpart for the discounted
stochastic game under consideration. With the help of globalized robust
optimization, a concept of globalized robust Markov perfect equilibrium is
introduced. The existence of such an equilibrium is shown for a discounted
stochastic game when the number of actions of the players is finite. The
contraction mapping theorem, Kakutani fixed point theorem and the concept of
equicontinuity are used to prove the existence result. To compute a globalized
robust Markov perfect equilibrium for the considered discounted stochastic
game, a tractable representation of the proposed globalized robust counterpart
is also provided. Using the derived tractable representation, we formulate a
globalized robust intrusion detection system for wireless sensor networks. The
simulation result reveals that the proposed globalized solution is much less
sensitive to data perturbations than the robust solution.
