A Branch-and-Cut Algorithm for Submodular Interdiction Games

Many relevant applications from diverse areas such as marketing, wildlife conservation, or defending critical infrastructure can be modeled interdiction games. In this work, we introduce games whose objective is a monotone and submodular set function. Given ground of items, the leader interdicts usage some items follower in order to minimize value achievable by follower, who seeks maximize function over uninterdicted subject knapsack constraints. We propose an exact branch-and-cut algorithm for these kind The based on cuts which allow capture follower's given decision exploit submodularity also present extensions liftings discuss additional preprocessing procedures. test our solution framework weighted maximal covering game bipartite inference game. For both applications, improved variants cut perform significantly better than its basic version. mixed-integer bilevel linear programming (MIBLP) formulation available, compare results with those state-of-the-art MIBLP solver. While solver yields minimum 54% optimality gap within one hour, best setting solves all but 4 108 instances maximum 3% among unsolved ones.