Novel valid inequalities and branch-and-price for Stackelberg security games

Anticipating the strategies of potential attackers is crucial for protecting critical infrastructure. We can represent the challenge of the defenders of such infrastructure as a Stackelberg security game. The defender must decide how to allocate limited resources to protect specific targets, aiming to maximize their expected utility (such as minimizing the extent of damage) and considering that attackers will respond in a way that is most advantageous to them.

We present novel valid inequalities to find a Strong Stackelberg Equilibrium in both Stackelberg games and Stackelberg security games. We also consider a Stackelberg security game that aims to protect targets with a defined budget. We use branch-and-price in this game to show that our approach outperforms the standard formulation in the literature, in terms of both solution speed and memory usage.

Additionally, we present an extensive computational study to assess the impact of various parameters in branch-and-price, such as the number of initial columns, the number of columns generated per iteration, and the effects of stabilization techniques. The results show that our approach reduces the solution time of the problem to less than a fifth of the time required by the state-of-the art methods.