Mobility and terrain are two sides of the same coin. You cannot describe mobility unless you describe the terrain. For example, if my world is trench warfare, the tank may be the ideal vehicle. If my world is urban warfare, clearing buildings and such, the tank may not be an ideal vehicle, perhaps an anthropomorphic robot would be better. We seek a general framework for mobility that captures the relative value of different mobility strategies. Game theory is positively the right way to analyze the interactions of rational players who behave strategically. In this paper, we will describe the interactions between a mobility player, who is trying to make it from point A to point B with one chance to refuel, and a terrain player who is trying to minimize that probability by placing an obstacle somewhere along the path from A to B. In previous work, we used Monte Carlo methods to analyze this mobility game, and found optimal strategies for a discretized version of the game. Here we show the relationship of this game to a classic game of timing, and use solution methods from that literature to solve for optimal strategies in a continuous version of this mobility game.
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