The rendezvous dilemma is a logical dilemma, typically formulated in this way:
If they both choose to wait, they will never meet. If they both choose to walk there are chances that they meet and chances that they do not. If one chooses to wait and the other chooses to walk, then there is a theoretical certainty that they will meet eventually; in practice, though, it may take too long for it to be guaranteed. The question posed, then, is: what strategies should they choose to maximize their probability of meeting?
Examples of this class of problems are known as rendezvous problems. These problems were first introduced informally by Steve Alpern in 1976,and he formalised the continuous version of the problem in 1995. This has led to much recent research in rendezvous search. Even the symmetric rendezvous problem played in n discrete locations (sometimes called the Mozart Cafe Rendezvous Problem) has turned out to be very difficult to solve, and in 1990 Richard Weber and Eddie Anderson conjectured the optimal strategy. Only recently has the conjecture been proved for n = 3 by Richard Weber. This was the first non-trivial symmetric rendezvous search problem to be fully solved. Note that the corresponding asymmetric rendezvous problem has a simple optimal solution: one player waits at his original location and the other player looks for him using a random permutation of the locations.
Steve Alpern is a professor of Operational Research at the University of Warwick, where he recently moved after working for many years at the London School of Economics. His early work was mainly in the area of dynamical systems and ergodic theory, but his more recent research has been concentrated in the fields of search games and rendezvous. He informally introduced the rendezvous problem as early as 1976. His collaborators include Shmuel Gal, Vic Baston and Robbert Fokkink.
Richard Robert Weber is a mathematician working in operational research. He is Churchill Professor of Mathematics for Operational Research in the Statistical Laboratory, University of Cambridge.
As well as being problems of theoretical interest, rendezvous problems include real-world problems with applications in the fields of synchronization, operating system design, operations research, and even search and rescue operations planning.
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Shmuel Gal is a mathematician and professor of statistics at the University of Haifa in Israel.
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