Two rendezvous search problems on the line

A new upper bound is obtained for the two-person symmetric rendezvous value on the real line when the distribution function of their initial distance apart is bounded. A second result shows that if three players are placed randomly on adjacent integers on the real line facing in random directions and able to move at a speed of at most 1, then they can ensure a three-way meeting time of at most 7/2; the fact that 7/2 is a best possible result follows from work already in the literature.