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

TL;DR

This paper models a dynamic crime interdiction problem on transportation networks as a layered Stackelberg game, proposing an approximation algorithm that outperforms MILP in efficiency and solution quality.

Contribution

It introduces a layered graph approach for dynamic Stackelberg games on transportation networks and develops an approximation algorithm for defender strategies.

Findings

The layered network approach effectively models dynamic attacker movements.

The approximation algorithm provides near-optimal defender strategies efficiently.

Compared to MILP, the approach reduces computational time while maintaining solution quality.

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.