Surviving in cyberspace: A game theoretic approach

As information systems become ever more complex and the interdependence of these systems increases, a mission-critical system should have the fight-through ability to sustain damage yet survive with mission assurance in cyberspace. To satisfy this requirement, in this paper we propose a game theoretic approach to binary voting with a weighted majority to aggregate observations among replicated nodes. Nodes are of two types: They either vote truthfully or are malicious and thus lie. Voting is strategically performed based on a node's belief about the percentage of compromised nodes in the system. Voting is cast as a stage game model that is a Bayesian Zero-sum game. In the resulting Bayesian Nash equilibrium, if more than a critical proportion of nodes are compromised, their collective decision is only 50% reliable; therefore, no information is obtained from voting. We overcome this by formalizing a repeated game model that guarantees a highly reliable decision process even though nearly all nodes are compromised. A survival analysis is performed to derive the total time of mission survival for both a one-shot game and the repeated game. Mathematical proofs and simulations support our model.