Pamela Bustamante-Faúndez , Víctor Bucarey L. , Martine Labbé , Vladimir Marianov , Fernando Ordoñez
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A <em>defender</em> 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 <em>attacker</em>, responds in the best possible way.</p><p>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.</p><p>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.</p></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":null,"pages":null},"PeriodicalIF":6.7000,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Playing Stackelberg Security Games in perfect formulations\",\"authors\":\"Pamela Bustamante-Faúndez , Víctor Bucarey L. , Martine Labbé , Vladimir Marianov , Fernando Ordoñez\",\"doi\":\"10.1016/j.omega.2024.103068\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Protecting critical infrastructure from intentional damage requires foreseeing the strategies of possible attackers. We formulate this problem as a Stackelberg Security Game. A <em>defender</em> 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 <em>attacker</em>, responds in the best possible way.</p><p>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.</p><p>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. 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Playing Stackelberg Security Games in perfect formulations
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.
期刊介绍:
Omega reports on developments in management, including the latest research results and applications. Original contributions and review articles describe the state of the art in specific fields or functions of management, while there are shorter critical assessments of particular management techniques. Other features of the journal are the "Memoranda" section for short communications and "Feedback", a correspondence column. Omega is both stimulating reading and an important source for practising managers, specialists in management services, operational research workers and management scientists, management consultants, academics, students and research personnel throughout the world. The material published is of high quality and relevance, written in a manner which makes it accessible to all of this wide-ranging readership. Preference will be given to papers with implications to the practice of management. Submissions of purely theoretical papers are discouraged. The review of material for publication in the journal reflects this aim.