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  • 2205.10017v1

    Submitted manuscript, 2 MB, PDF document

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A stochastic game framework for patrolling a border

Research output: Working paper › Preprint

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A stochastic game framework for patrolling a border. / Darlington, Matthew; Glazebrook, Kevin D.; Leslie, David S. et al.
Arxiv, 2022.

Research output: Working paper › Preprint

Harvard

Darlington, M, Glazebrook, KD, Leslie, DS, Shone, R & Szechtman, R 2022 'A stochastic game framework for patrolling a border' Arxiv. <https://arxiv.org/abs/2205.10017>

APA

Darlington, M., Glazebrook, K. D., Leslie, D. S., Shone, R., & Szechtman, R. (2022). A stochastic game framework for patrolling a border. Arxiv. https://arxiv.org/abs/2205.10017

Vancouver

Darlington M, Glazebrook KD, Leslie DS, Shone R, Szechtman R. A stochastic game framework for patrolling a border. Arxiv. 2022 May 20.

Author

Darlington, Matthew ; Glazebrook, Kevin D. ; Leslie, David S. et al. / A stochastic game framework for patrolling a border. Arxiv, 2022.

Bibtex

@techreport{c8980aa5716a4fdc84efdbaa339e199c,
title = "A stochastic game framework for patrolling a border",
abstract = "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 the Nash equilibrium to gain insight to 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 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.",
keywords = "cs.GT",
author = "Matthew Darlington and Glazebrook, {Kevin D.} and Leslie, {David S.} and Rob Shone and Roberto Szechtman",
year = "2022",
month = may,
day = "20",
language = "English",
publisher = "Arxiv",
type = "WorkingPaper",
institution = "Arxiv",

}

RIS

TY - UNPB

T1 - A stochastic game framework for patrolling a border

AU - Darlington, Matthew

AU - Glazebrook, Kevin D.

AU - Leslie, David S.

AU - Shone, Rob

AU - Szechtman, Roberto

PY - 2022/5/20

Y1 - 2022/5/20

N2 - 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 the Nash equilibrium to gain insight to 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 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.

AB - 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 the Nash equilibrium to gain insight to 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 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.

KW - cs.GT

M3 - Preprint

BT - A stochastic game framework for patrolling a border

PB - Arxiv

ER -