Transiting areas patrolled by a mobile adversary

Abstract

We study the problem of a mobile agent trying to cross an area patrolled by a mobile adversary. The transiting agent aims to choose its route so as to minimize the probability of hostile encounter; the patroller agent, controlling one or more patrol units, aims at the opposite. We model the problem as a two-player zero-sum game (termed transit game) and search for an optimum route selection strategy as a mixed Nash equilibrium of the game. In contrast to existing game-theoretic models of this kind, we explicitly consider the limited endurance of patrols and the notion of bases to which the patrols need to repeatedly return. Noting the prohibitive size of the transit game, we employ two techniques for reducing the complexity of finding Nash equilibria - a compact network-flow-based representation of transit routes and iterative single- and double-oracle algorithms for incremental game matrix construction. We measure the computational time of all the methods on a range of transit game instances. In order to assess the practical relevance of the approach, we apply the transit game model and its solution to the real-world case of ship transit through areas affected by piracy. The results obtained using an agent-based simulation of maritime traffic show that the randomized game-theoretic transit routing strategy results in a lower number of pirate attacks than the currently employed method based on static transit corridors.

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