Playing chemical plant protection game with distribution-free uncertainties

Abstract

A common criticism on game theoretic risk analysis of security threats is that it requires quantitative parameters of both the defender and the attacker, whereby the parameters of the attackers especially are difficult to estimate. In the present paper, a game theoretic model for chemical plant protection, able to deal with the defender's distribution-free uncertainties on the attacker's parameters (Interval CPP Game), is proposed. The Interval CPP Game only requires the interval(s) in which the attacker's parameter(s) is (are) located, instead of the exact number of the parameter(s). Two algorithms are developed, namely the Interval Bi-Matrix Game Solver (IBGS) and the Interval CPP Game Solver (ICGS), for solving general bi-matrix games with interval payoff uncertainties and especially for solving interval CPP games, respectively. Both algorithms are based on mixed integer linear programming (MILP). Theoretic analysis as well as a case study shows that including the defender's uncertainties on the attacker's parameters would reduce her equilibrium payoff.