Globalized Robust Markov Perfect Equilibrium for Discounted Stochastic Games and its Application on Intrusion Detection in Wireless Sensor Networks: Part I -- Theory

Abstract: 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.