The complexity of searching a graph
Journal of the ACM (JACM)
The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Introduction to Linear Optimization
Introduction to Linear Optimization
Randomized Pursuit-Evasion in Graphs
Combinatorics, Probability and Computing
Randomized pursuit-evasion with limited visibility
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Capturing augmented sensing capabilities and intrusion delay in patrolling-intrusion games
CIG'09 Proceedings of the 5th international conference on Computational Intelligence and Games
Strategy generation in multi-agent imperfect-information pursuit games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
How to protect a city: strategic security placement in graph-based domains
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
A double oracle algorithm for zero-sum security games on graphs
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Solving Stackelberg games with uncertain observability
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Multiagent Communication Security in Adversarial Settings
WI-IAT '11 Proceedings of the 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology - Volume 02
Randomized sensing in adversarial environments
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Solving non-zero sum multiagent network flow security games with attack costs
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
Security scheduling for real-world networks
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Optimal patrol strategy for protecting moving targets with multiple mobile resources
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Security games with contagion: handling asymmetric information
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Protecting moving targets with multiple mobile resources
Journal of Artificial Intelligence Research
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We study a multi-step hider-seeker game where the hider is moving on a graph and, in each step, the seeker is able to search c subsets of the graph nodes. We model this game as a zero-sum Bayesian game, which can be solved in weakly polynomial time in the players' action spaces. The seeker's action space is exponential in c, and both players' action spaces are exponential in the game horizon. To manage this intractability, we use a column/constraint generation approach for both players. This approach requires an oracle to determine best responses for each player. However, we show that computing a best response for the seeker is NP-hard, even for a single-step game when c is part of the input, and that computing a best response is NP-hard for both players for the multi-step game, even if c = 1. An integer programming formulation of the best response for the hider is practical for moderate horizons, but computing an exact seeker best response is impractical due to the exponential dependence on both c and the horizon. We therefore develop an approximate best response oracle with bounded suboptimality for the seeker. We prove performance bounds on the strategy that results when column/constraint generation with approximate best responses converges, and we measure the performance of our algorithm in simulations. In our experimental results, column/constraint generation converges to near-minimax strategies for both players fairly quickly.