Cable laying ambush games

Abstract

A cable laying ambush game is a two-person zero-sum game in which one player wishes to cross some interval while the other player has n cables that he can lay within the interval to ambush the infiltrator. In the literature solutions have been found for some cases in continuous and discrete cable laying ambush games when n = 2. The culmination of this thesis gives a complete solution for this much studied two cable game. However, prior to this numerous important results are established for the n cable game. It is first shown that the continuous game always possesses a value. This is done by showing that optimal strategies in a new finite game are also optimal in the continuous game. Further to this it is then shown that the discrete game can also be reduced to the same finite game and thus shown that it is equivalent to a finite game. This enables us to find many new results in both games. We also carry out much computational work enabling us to convert games into linear programmes and thus find the game value and optimal strategies. Using these techniques, we produce numerous new results in the three cable ambush game. Analysis of the game value function is then carried out which shows that it is a lower semi-continuous function and enables us to show how the game can be divided into regions which share the same value. By combining these with strategies in special cases for the ambusher, we produce a complete solution for the two cable game without having to calculate strategies for the infiltrator.

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