Rendezvous Search on the Line With Distinguishable Players
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Rendezvous Search: A Personal Perspective
Operations Research
How to meet in anonymous network
Theoretical Computer Science
Improved Bounds for the Symmetric Rendezvous Value on the Line
Operations Research
Strategy for Quickest Second Meeting of Two Agents in Two Locations
Mathematics of Operations Research
Strategy for Quickest Second Meeting of Two Agents in Two Locations
Mathematics of Operations Research
Hi-index | 0.00 |
In the symmetric rendezvous search game played on n locations two players are initially placed at two distinct locations. The game is played in discrete steps, at each of which each player can either stay where he is or move to a different location. The players share no common labelling of the locations. We wish to find a strategy such that, if both players follow it independently, then the expected number of steps until they are in the same location is minimized. Informal versions of the rendezvous problem have received considerable attention in the popular press. The problem was proposed by Alpern in 1976 [Alpern, S. 1976. Hide and seek games. Seminar at the Institut für Höhere Studien, Vienna], and it has proved notoriously difficult to analyse. In this paper we prove a 20-year-old conjecture that the following strategy is optimal for the game on three locations: in each block of two steps, stay where you are, or search the other two locations in random order, doing these with probabilities 1/3 and 2/3, respectively. This is now the first nontrivial symmetric rendezvous game of any type to be fully solved.