RENDEZVOUS SEARCH ON THE LINE WITH MORE THAN 2 PLAYERS

Suppose n blind. speed one, players are placed by a random permutation onto the integers 1 to n, and each is pointed randomly to the right o r left. What is the least expected time required for m less than or eq ual to n of them to meet together at a single point? If they must all use the same strategy we call this time the symmetric rendezvous value R-n,m(s); otherwise the asymmetric value R-n,m(a). We show that R-3,2 (a) = 47/48, and that R-n,n(s), is asymptotic to n/2. These results re spectively extend those for two players given by Alpern and Gal (1995) and Anderson and Essegaier (1995).