Security games with incomplete information

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. At each stage of the game iterations, the players make imperfect observations of each other's previous actions. The underlying decision process can be viewed as a fictitious play (FP) game, but what differentiates this class from the standard one is that the communication channels that carry action information from one player to the other, or the sensor systems, are error prone. Two possible scenarios are addressed in the paper: (i) if the error probabilities associated with the sensor systems are known to the players, then our analysis provides guidelines for each player to reach a Nash equilibrium (NE), which is related to the NE of the underlying static game; (ii) if the error probabilities are not known to the players, then we study the effect of observation errors on the convergence to the NE and the final outcome of the game. We discuss both the classical FP and the stochastic FP, where for the latter the payoff function of each player includes an entropy term to randomize its own strategy, which can be interpreted as a way of concealing its true strategy.