Browsing by Author "Labbé, Martine"

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    Novel valid inequalities and branch-and-price for Stackelberg security games
    (2025) Bustamante Faúndez, Pamela; Bucarey L., Víctor; Labbé, Martine; Marianov, Vladimir; Ordoñez, Fernando
    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.
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    Playing Stackelberg Security Games in perfect formulations
    (2024) Bustamante Faúndez, Pamela Alejandra; Bucarey L., Víctor; Labbé, Martine; Marianov Kluge, Vladimir; Ordoñez, Fernando
    Protecting critical infrastructure from intentional damage requires foreseeing the strategies of possible attackers. We formulate this problem as a Stackelberg Security Game. A defender must decide which specific targets to protect with limited resources, thus maximizing their expected utility (e.g., minimizing damage value) and considering that a second player (or players), called an attacker, responds in the best possible way. Since Stackelberg Security Games are generally NP-hard, the main challenge in finding optimal strategies in real applications is to develop efficient methodologies for large instances. We propose a general methodology to find a Strong Stackelberg Equilibrium for Stackelberg Security Games, exploiting the structure in the defender’s strategy set. This methodology consists of two steps. First, we formulate the problem by using variables representing the probability of defending each target. The formulation must be either a polynomial-size MILP and/or an MILP with an exponential number of constraints that are separable in polynomial time through branch-and-cut. In the second step, we recover the mixed strategies in the original space efficiently (in polynomial time) by using column generation. We apply this methodology to various security applications studied in the last decade. We generalize known examples and propose new examples. Finally, we provide an extensive computational study of the various formulations based on marginal probabilities.