Patrol Strategies to Maximize Pristine Forest Area

Illegal extraction of forest resources is fought, in many developing countries, by patrols that try to make this activity less profitable, using the threat of confiscation. With a limited budget, officials will try to distribute the patrols throughout the forest intelligently, in order to most effectively limit extraction. Prior work in forest economics has formalized this as a Stackelberg game, one very different in character from the discrete Stackelberg problem settings previously studied in the multiagent literature. Specifically, the leader wishes to minimize the distance by which a profit-maximizing extractor will trespass into the forest---or to maximize the radius of the remaining ``pristine'' forest area. The follower's cost-benefit analysis of potential trespass distances is affected by the likelihood of being caught and suffering confiscation. In this paper, we give a near-optimal patrol allocation algorithm and a 1/2-approximation algorithm, the latter of which is more efficient and yields simpler, more practical patrol allocations. Our simulations indicate that these algorithms substantially outperform existing heuristic allocations.