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In this paper, a general model for cyber-physical systems (CPSs), thatcaptures the diffusion of attacks from the cyber layer to the physical system,is studied. In particular, a game-theoretic approach is proposed to analyze theinteractions between one defender and one attacker over a CPS. In this game,the attacker launches cyber attacks on a number of cyber components of the CPSto maximize the potential harm to the physical system while the system operatorchooses to defend a number of cyber nodes to thwart the attacks and minimizepotential damage to the physical side. The proposed game explicitly accountsfor the fact that both attacker and defender can have different computationalcapabilities and disparate levels of knowledge of the system. To capture suchbounded rationality of attacker and defender, a novel approach inspired fromthe behavioral framework of cognitive hierarchy theory is developed. In thisframework, the defender is assumed to be faced with an attacker that can havedifferent possible thinking levels reflecting its knowledge of the system andcomputational capabilities. To solve the game, the optimal strategies of eachattacker type are characterized and the optimal response of the defender facingthese different types is computed. This general approach is applied to smartgrid security considering wide area protection with energy marketsimplications. Numerical results show that a deviation from the Nash equilibriumstrategy is beneficial when the bounded rationality of the attacker isconsidered. Moreover, the results show that the defender's incentive to deviatefrom the Nash equilibrium decreases when faced with an attacker that has highcomputational ability.

On Bounded Rationality in Cyber-Physical Systems Security: Game-Theoretic Analysis with Application to Smart Grid Protection