Improving Community-Participated Patrol for Anti-Poaching

TL;DR

The paper addresses anti-poaching patrol allocation by modeling both professional rangers and village-based patrollers within a Stackelberg game against a best-responding poacher, with per-target coverage $c_i = \min(e^{\mathrm{p}} p_i + e^{\mathrm{v}} v_i, 1)$. It develops three methods—MILP, a polynomial-time Two-Dimensional Binary Search, and an exact Hybrid Waterfilling algorithm—to compute defender strategies efficiently, and analyzes extensions for target-specific and villager-specific effectiveness. Empirical results on synthetic data and a Northeast China case study (Manchurian tiger habitat) show meaningful defender-utility improvements and provide practical guidance on budget allocation and terrain considerations. The work offers rigorous, deployable decision-support tools for conservation agencies across countries and highlights the tractability frontier: polynomial-time solutions under certain heterogeneity assumptions, with NP-hardness arising when villager-level heterogeneity is allowed.

Abstract

Community engagement plays a critical role in anti-poaching efforts, yet existing mathematical models aimed at enhancing this engagement often overlook direct participation by community members as alternative patrollers. Unlike professional rangers, community members typically lack flexibility and experience, resulting in new challenges in optimizing patrol resource allocation. To address this gap, we propose a novel game-theoretic model for community-participated patrol, where a conservation agency strategically deploys both professional rangers and community members to safeguard wildlife against a best-responding poacher. In addition to a mixed-integer linear program formulation, we introduce a Two-Dimensional Binary Search algorithm and a novel Hybrid Waterfilling algorithm to efficiently solve the game in polynomial time. Through extensive experiments and a detailed case study focused on a protected tiger habitat in Northeast China, we demonstrate the effectiveness of our algorithms and the practical applicability of our model.

Figures (6)

• Figure 1: Example of the process in \ref{['alg:exact_patroller']}. The 3 black rectangles represent 3 targets. The orange parts are the villager coverage and the blue ones are the ranger coverage. The green line is the utility sea level. (a) Target $i^{*} = 0$ and villager strategy $v_{i^{*}} = 1$ are given. We greedily allocate the remaining 3 villagers to target $i \in \{1, 2\}$ with the maximum $U^{\mathrm{a}}_{i}$ in the order of target 2, 2, 1. (b) Critical set is $\{1\}$. We distribute ranger efforts by Waterfilling, lowering the sea level, until we reach the critical point when the area of the blue part on target 3 is equal to the area of villager 3 above the sea level. (c) We swap ranger efforts on target 2 and villager 3 on target 2. (d) We proceed with Waterfilling until rangers are used up.
• Figure 2: Average runtime of MILP, TDBS, and HW over 30 runs under different combinations of $(n,r^{\mathrm{p}},r^{\mathrm{v}})$. The error bars indicate the standard deviation. The shaded areas represent the ranges from the minimum to the 97th percentile. We limit the maximum runtime for MILP in \ref{['subfigure:rv-runtime']} to 7200 seconds.
• Figure 3: The contour of the studied forest farm and case study results regarding advice on strategies and budget allocation.
• Figure 4: Average runtime of MILP, TDBS, and HW over 30 runs under different combinations of $(n,r^{\mathrm{p}},r^{\mathrm{v}})$ where $r^{\mathrm{v}} = 2 \cdot r^{\mathrm{p}}$. The error bars indicate the standard deviation. The shaded areas represent the ranges from the minimum to the 97th percentile. We limit the maximum runtime for MILP in \ref{['subfigure:rv-runtime2']} to 7200 seconds.
• Figure 5: Budget allocation with more settings

Theorems & Definitions (21)

• Definition 3.1
• Definition 4.1
• Definition 4.2
• Lemma 4.1
• Lemma 4.2
• Lemma 4.3
• Theorem 4.1
• Theorem 4.2
• proof : Proof Sketch of \ref{['theorem:exact_correctness']}
• Lemma 5.1