A robust optimization approach to designing near-optimal strategies for constant-sum monitoring games

Abstract

We consider the problem of monitoring a set of targets, using scarce monitoring resources (e.g., sensors) that are subject to adversarial attacks. In particular, we propose a constant-sum Stackelberg game in which a defender (leader) chooses among possible monitoring locations, each covering a subset of targets, while taking into account the monitor failures induced by a resource-constrained attacker (follower). In contrast to the previous Stackelberg security models in which the defender uses mixed strategies, here, the defender must commit to pure strategies. This problem is highly intractable as both players’ strategy sets are exponentially large. Thus, we propose a solution methodology that automatically partitions the set of adversary’s strategies and maps each subset to a coverage policy. These policies are such that they do not overestimate the defender’s payoff. We show that the partitioning problem can be reformulated exactly as a mixed-integer linear program (MILP) of moderate size which can be solved with off-the-shelf solvers. We demonstrate the effectiveness of our proposed approach in various settings. In particular, we illustrate that even with few policies, we are able to closely approximate the optimal solution and outperform the heuristic solutions.