A stochastic game framework for patrolling a border

Darlington, Matthew and Glazebrook, Kevin and Shone, Robert and Leslie, David and Szechtman, Roberto (2023) A stochastic game framework for patrolling a border. European Journal of Operational Research, 311 (3). pp. 1146-1158. ISSN 0377-2217

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In this paper we consider a stochastic game for modelling the interactions between smugglers and a patroller along a border. The problem we examine involves a group of cooperating smugglers making regular attempts to bring small amounts of illicit goods across a border. A single patroller has the goal of preventing the smugglers from doing so, but must pay a cost to travel from one location to another. We model the problem as a two-player stochastic game and look to find a Nash equilibrium to gain insight into real world problems. Our framework extends the literature by assuming that the smugglers choose a continuous quantity of contraband, complicating the analysis of the game. We discuss a number of properties of Nash equilibria, including the aggregation of smugglers, the discount factors of the players, and the equivalence of our non zero-sum game to a zero-sum game. Additionally, we present algorithms to find Nash equilibria that are more computationally efficient than existing methods. We also consider certain assumptions on the parameters of the model that give interesting equilibrium strategies for the players.

Item Type:
Journal Article
Journal or Publication Title:
European Journal of Operational Research
Uncontrolled Keywords:
Research Output Funding/yes_externally_funded
?? game theoryor in defencepatrol problemsyes - externally fundedmodelling and simulationmanagement science and operations researchinformation systems and management ??
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Deposited On:
26 Jul 2023 15:35
Last Modified:
15 Jul 2024 23:54