Bayesian hypergame approach to equilibrium stability and robustness in moving target defense

TL;DR

This paper introduces a Bayesian hypergame framework to analyze equilibrium stability and robustness in moving target defense scenarios with incomplete information and asymmetric cognition, providing new conditions for stable and robust equilibria.

Contribution

It develops a hyper Bayesian Nash equilibrium concept and linear conditions for stability and robustness in moving target defense games with asymmetric knowledge.

Findings

Conditions for strategic and cognitive stability are derived.

Robust HBNE conditions are established under knowledge perturbations.

Experimental results validate the theoretical conditions.

Abstract

We investigate the equilibrium stability and robustness in a class of moving target defense problems, in which players have both incomplete information and asymmetric cognition. We first establish a Bayesian Stackelberg game model for incomplete information and then employ a hypergame reformulation to address asymmetric cognition. With the core concept of the hyper Bayesian Nash equilibrium (HBNE), a condition for achieving both the strategic and cognitive stability in equilibria can be realized by solving linear equations. Moreover, to deal with players' underlying perturbed knowledge, we study the equilibrium robustness by presenting a condition of robust HBNE under the given configuration. Experiments evaluate our theoretical results.