Two dimensional rendezvous search

We consider rendezvous problems in which two players move on the plane and wish to cooperate to minimise their first meeting time. We begin by conside ring the case where both players are placed such that the vector difference is chosen equiprobably from a finite set. We also consider a situation in which they know they are a distance d apart, but they do not know the direc tion of the other player. Finally, we give some results for the case in whi ch player 1 knows the initial position of player 2, while player 2 is given information only on the initial distance of player 1.