Ambushing Random Walks III: More Continuous Models

Abstract

We continue our study of the following game theory problem: a traveler (BLUE) wishes to choose a path across a rectangle from left to right in such a way to avoid certain obstacles in the rectangle (called ambushes) which are chosen by his antagonist (RED). The game theoretic payoff might depend upon whether BLUE's path and the ambushes have a common point, or the payoff may be a function of how far the path proceeds before meeting the first ambush. These ambush games have analogous search games.