Computing the optimal strategy to commit to
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Computing optimal randomized resource allocations for massive security games
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Stackelberg vs. Nash in security games: interchangeability, equivalence, and uniqueness
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Solving Stackelberg games with uncertain observability
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Multi-objective optimization for security games
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Game-theoretic resource allocation for malicious packet detection in computer networks
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Game theory for security: an important challenge for multiagent systems
EUMAS'11 Proceedings of the 9th European conference on Multi-Agent Systems
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Defender (mis)coordination in security games
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
An extended study on multi-objective security games
Autonomous Agents and Multi-Agent Systems
Protecting moving targets with multiple mobile resources
Journal of Artificial Intelligence Research
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Algorithms for finding game-theoretic solutions are now used in several real-world security applications. This work has generally assumed a Stackelberg model where the defender commits to a mixed strategy first. In general two-player normal-form games, Stackelberg strategies are easier to compute than Nash equilibria, though it has recently been shown that in many security games, Stackelberg strategies are also Nash strategies for the defender. However, the work on security games so far assumes that the attacker attacks only a single target. In this paper, we generalize to the case where the attacker attacks multiple targets simultaneously. Here, Stackelberg and Nash strategies for the defender can be truly different. We provide a polynomial-time algorithm for finding a Nash equilibrium. The algorithm gradually increases the number of defender resources and maintains an equilibrium throughout this process. Moreover, we prove that Nash equilibria in security games with multiple attackers satisfy the interchange property, which resolves the problem of equilibrium selection in such games. On the other hand, we show that Stackelberg strategies are actually NP-hard to compute in this context. Finally, we provide experimental results.