Markov game analysis for attack-defense of power networks under possible misinformation

Electricity grids are critical infrastructures. They are credible targets of active (e.g., terrorist) attacks since their disruption may lead to sizable losses economically and in human lives. It is thus crucial to develop decision support that can guide administrators in deploying defense resources for system security and reliability. Prior work on the defense of critical infrastructures has typically used static or Stackelberg games. These approaches view network interdictions as one-time events. However, infrastructure protection is also a continual process in which the defender and attacker interact to produce dynamic states affecting their best actions, as witnessed in the continual attack and defense of transmission networks in Colombia and Yemen. In this paper, we use zero-sum Markov games to model these interactions subject to underlying uncertainties of real-world events and actions. We solve equilibrium mixed strategies of the players that maximize their respective minimum payoffs with a time-decayed metric. We also show how the defender can use deception as a defense mechanism. Using results for a 5-bus system, a WECC 9-bus system, and an IEEE standard 14-bus system, we illustrate that our game model can provide useful insights. We also contrast our results with those of static games, and quantify the gain in defender payoff due to misinformation of the attacker.