边界巡逻的随机博弈框架

Matthew Darlington, K. Glazebrook, D. Leslie, Robert Shone, R. Szechtman
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引用次数: 0

摘要

在本文中,我们考虑一个随机博弈来模拟走私者和边境巡逻人员之间的相互作用。我们研究的问题涉及一群相互合作的走私者,他们经常试图将少量非法货物带过边境。一名巡逻人员的目标是阻止走私者这样做,但必须支付从一个地方到另一个地方的费用。我们将这个问题建模为一个二人随机博弈,并寻找纳什均衡,以获得对现实世界问题的洞察力。我们的框架通过假设走私者选择一个连续数量的违禁品来扩展文献,使游戏分析复杂化。我们讨论了纳什均衡的一些性质,包括走私者的聚集,参与者的折扣因素,以及零和博弈的等价性。此外,我们提出的算法,以找到纳什均衡是更有效的计算比现有的方法。我们还考虑了模型参数的某些假设,这些假设为参与者提供了有趣的均衡策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A stochastic game framework for patrolling a border
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.
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