Games of timing with detection uncertainty and numerical estimates

Mobility and terrain are two sides of the same coin. We cannot speak to our mobility unless we describe the terrain's ability to thwart our maneuver. Game theory describes the interactions of rational players who behave strategically. In previous work1 we described the interactions between a mobility player, who is trying to maximize the chances that he makes 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. This relates to the literature of games of incomplete information, and can be thought of as a more realistic model of this interaction. In this paper, we generalize the game of timing studied in the previous paper to include the possibility that both players have imperfect ability to detect his adversary.