{"type":"ScholarlyArticle","title":"Dinkelbach-Type Algorithm for Computing Quantal Stackelberg Equilibrium","authors":[{"name":"Jakub Cerny","slug":"jakub-cerny","given":"Jakub","family":"Cerny","affiliation":"School of Computer Science and Engineering , Nanyang Technological University , Singapore"},{"name":"Viliam Lisý","slug":"viliam-lisy","given":"Viliam","family":"Lisý","affiliation":"Dept. of Computer Science , Faculty of El. Engineering , Czech Technical University in Prague , Czechia"},{"name":"Branislav Bošanský","slug":"branislav-bosansky","given":"Branislav","family":"Bošanský","affiliation":"Dept. of Computer Science , Faculty of El. Engineering , Czech Technical University in Prague , Czechia"},{"name":"Bo An","slug":"bo-an","given":"Bo","family":"An","affiliation":"School of Computer Science and Engineering , Nanyang Technological University , Singapore"}],"abstract":"Stackelberg security games (SSGs) have been deployed in many real-world situations to optimally allocate scarce resource to protect targets against attackers. However, actual human attackers are not perfectly rational and there are several behavior models that attempt to predict subrational behavior. Quantal response is among the most commonly used such models and Quantal Stackelberg Equilibrium (QSE) describes the optimal strategy to commit to when facing a subrational opponent. Non-concavity makes computing QSE computationally challenging and while there exist algorithms for computing QSE for SSGs, they cannot be directly used for solving an arbitrary game in the normal form. We (1) present a transformation of the primal problem for computing QSE using a Dinkelbach's method for any general-sum normal-form game, (2) provide a gradient-based and a MILP-based algorithm, give the convergence criteria, and bound their error, and finally (3) we experimentally demonstrate that using our novel transformation, a QSE can be closely approximated several orders of magnitude faster.","doi":"10.24963/ijcai.2020/35","url":"https://ijcai.org/proceedings/2020/35","pdf":"https://ijcai.org/proceedings/2020/0035.pdf","markdown":"https://ijcai.org/proceedings/2020/35.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/35","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":35,"pages":{"first":246,"last":253},"keywords":["Agent-based and Multi-agent Systems: Noncooperative Games","Humans and AI: Cognitive Modeling","Agent-based and Multi-agent Systems: Algorithmic Game Theory"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25395/file_25395.m3u8","length_sec":300,"provider":"hls"}],"references":[{"position":1,"raw":"[Boyd and Vandenberghe, 2004] Stephen Boyd and Lieven Vandenberghe. 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