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We study the problem of a mobile target (the mouse) trying to evade detection by one or more mobile sensors (we call such a sensor a cat) in a closed network area. We view our problem as a game between two players: the mouse, and the collection of cats forming a single (meta-)player. The game ends when the mouse falls within the sensing range of one or more cats. A cat tries to determine its optimal strategy to minimize the worst case expected detection time of the mouse. The mouse tries to determine an optimal counter movement strategy to maximize the expected detection time. We divide the problem into two cases based on the relative sensing capabilities of the cats and the mouse. When the mouse has a larger sensing range than the cats, we show how the mouse can determine its optimal movement strategy based on local observations of the cats' movements. When the mouse has a sensing range smaller than or equal to the cats', we develop a dynamic programming solution for the mouse's optimal strategy, assuming high level information about the cats' movement model. We discuss how the cats' chosen movement model will affect its presence matrix in the network, and hence its payoff in the game. Extensive experimental results verify and illustrate the analytical results, and evaluate the game's payoffs as a function of several important system parameters.
Date of Conference: 8-11 Oct. 2007