{"type":"ScholarlyArticle","title":"Layered Graph Security Games","authors":[{"name":"Jakub Cerny","slug":"jakub-cerny","given":"Jakub","family":"Cerny","affiliation":"Department of Industrial Engineering and Operations Research , Columbia University"},{"name":"Chun Kai Ling","slug":"chun-kai-ling","given":"Chun Kai","family":"Ling","affiliation":"Department of Industrial Engineering and Operations Research , Columbia University"},{"name":"Christian Kroer","slug":"christian-kroer","given":"Christian","family":"Kroer","affiliation":"Department of Industrial Engineering and Operations Research , Columbia University"},{"name":"Garud Iyengar","slug":"garud-iyengar","given":"Garud","family":"Iyengar","affiliation":"Department of Industrial Engineering and Operations Research , Columbia University"}],"abstract":"Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given graph). In this paper, we represent each player's strategy space using a layered graph whose paths represent an exponentially large strategy space. Our formulation entails not only classic pursuit-evasion games, but also other security games, such as those modeling anti-terrorism and logistical interdiction. We study two-player zero-sum games under two distinct utility models: linear and binary utilities. We show that under linear utilities, Nash equilibrium can be computed in polynomial time, while binary utilities may lead to situations where even computing a best-response is computationally intractable. To this end, we propose a practical algorithm based on incremental strategy generation and mixed integer linear programs. We show through extensive experiments that our algorithm efficiently computes epsilon-equilibrium for many games of interest. We find that target values and graph structure often have a larger influence on running times as compared to the size of the graph per se.","doi":"10.24963/ijcai.2024/298","url":"https://ijcai.org/proceedings/2024/298","pdf":"https://ijcai.org/proceedings/2024/0298.pdf","markdown":"https://ijcai.org/proceedings/2024/298.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/298","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":298,"pages":{"first":2695,"last":2703},"keywords":["Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[{"position":1,"raw":"[An et al., 2017] Bo An, Milind Tambe, and Arunesh Sinha. 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