论文标题
巡逻边界的随机游戏框架
A stochastic game framework for patrolling a border
论文作者
论文摘要
在本文中，我们考虑了一种随机游戏，用于建模走私者与边境巡逻人之间的互动。我们研究的问题涉及一群合作的走私者，定期尝试将少量的非法商品带到边境。一个巡逻者的目标是防止走私者这样做，但必须支付从一个地点到另一个位置旅行的费用。我们将问题模型为两人随机游戏，并希望找到NASH均衡，以了解对现实世界中的问题。我们的框架通过假设走私者选择连续数量的违禁品来扩展文献，从而使游戏分析变得复杂。我们讨论了纳什平衡的许多属性，包括走私者的聚集，玩家的折扣因素以及与零和游戏的等效性。此外，我们提出算法，以找到比现有方法更有效的NASH平衡。我们还考虑了模型参数的某些假设，这些假设为玩家提供了有趣的平衡策略。
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.
