Rendezvous search on the line with limited resources: Maximizing the probability of meeting

Two players are placed on a line at a distance d which is drawn from a know n distribution F. The players have no common notion of direction on the lin e, and each has a resources bound on the total distance he can travel. VF i s bounded and the resources are sufficiently large, then the players can en sure a meeting. The expected time minimization problem in that case has bee n studied by the authors in a previous paper. Aside from that case the most the players can do is maximize the probability that they meet. This is the problem studied here, for general and specific distributions. This problem generalizes that of Foley et al. (1991), where one of the players is stati onary (zero resources).