Playing games for security: An efficient exact algorithm for solving Bayesian Stackelberg games

Praveen Paruchuri, Jonathan P. Pearce, Janusz Marecki, Milind Tambe, Fernando Ordonez, Sarit Kraus

Research output: Contribution to journalArticlepeer-review

321 Scopus citations


In a class of games known as Stackelberg games, one agent (the leader) must commit to a strategy that can be observed by the other agent (the follower or adversary) before the adversary chooses its own strategy. We consider Bayesian Stackelberg games, in which the leader is uncertain about the types of adversary it may face. Such games are important in security domains, where, for example, a security agent (leader) must commit to a strategy of patrolling certain areas, and a robber (follower) has a chance to observe this strategy over time before choosing its own strategy of where to attack. This paper presents an efficient exact algorithm for finding the optimal strategy for the leader to commit to in these games. This algorithm, DOBSS. is based on a novel and compact mixed-integer linear programming formulation. Compared to the most efficient algorithm known previously for this problem, DOBSS is not only faster, but also leads to higher quality solutions, and does not suffer from problems of infeasibility that were faced by this previous algorithm. Note that DOBSS is at the heart of the ARMOR system that is currently being tested for security scheduling at the Los Angeles International Airport. Copyright © 2008, International Foundation for Autonomous Agents and Multiagent Systems ( All rights reserved.


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