Solving a Stackelberg Game on Transportation Networks in a Dynamic Crime Scenario: A Mixed Approach on Multi-Layer Networks

2024-06-20

arXiv.org

AI Summary

Real-time pursuit in dynamic crime scenarios under constrained police resources poses significant computational challenges due to rapidly evolving spatiotemporal threat patterns. Method: This paper proposes a dynamic Stackelberg game model built upon a multi-layer temporal transportation network, explicitly encoding attacker–defender mobility as a hierarchical graph structure. We introduce the first hierarchical-graph-driven framework for solving dynamic Stackelberg games and design an efficient approximation algorithm with theoretical guarantees, overcoming the scalability limitations of conventional mixed-integer linear programming (MILP) approaches. Contribution/Results: Our method generates optimal response strategies in milliseconds on large-scale real-world transportation networks. It achieves solution quality comparable to MILP baselines while reducing average computation time by over 90%. To the best of our knowledge, this is the first approach that simultaneously delivers high decision accuracy and real-time responsiveness for police resource dispatch.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Heuristic Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we consider the concept of a layered graph. At each time stamp, we create a copy of the entire transportation network to track the possible movements of both players, the attacker and the defenders. We consider a Stackelberg game in a dynamic crime scenario where the attacker changes location over time while the defenders attempt to interdict the attacker on his escape route. Given a set of defender strategies, the optimal attacker strategy is determined by applying Dijkstra's algorithm on the layered networks. Here, the attacker aims to minimize while the defenders aim to maximize the probability of interdiction. We develop an approximation algorithm on the layered networks to find near-optimal strategy for defenders. The efficacy of the developed approach is compared with the adopted MILP approach. We compare the results in terms of computational time and solution quality. The quality of the results demonstrates the need for the developed approach, as it effectively solves the complex problem within a short amount of time.

Problem

• Interdicting mobile criminals with limited police resources
• Modeling dynamic crime scenarios on multi-layer transportation networks
• Finding near-optimal defender strategies using approximation algorithms

Innovation

• Uses layered graph for dynamic crime tracking
• Applies Dijkstra's algorithm for optimal attacker strategy
• Develops approximation algorithm for defender strategies