On competitive search games for multiple vehicles

We investigate the competitive search game where a group of vehicles compete to locate the target on a ring in ℝ² where the probability density function of the target is known a priori. In order to compute Nash strategies for vehicles, we first perform a game reduction and determine an auxiliary Nash game which, on one hand, has a much smaller dimension, and on the other hand, is equivalent to the competitive search game. For the auxiliary Nash game, we first provide a counter-example where Nash equilibrium does not exist. Then we study computation algorithms to seek a class of constrained Nash equilibrium under certain sufficient conditions.