Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2007-05

February 2007

Rendezvous Search with Revealed Information: Applications to the Line

Steve Alpern

The symmetric rendezvous problem on a network Q asks how two players, forced to use the same mixed strategy, can minimize their expected meeting time, starting from a known initial distribution on the nodes of Q. This minimum is called the (symmetric) `rendezvous value' of Q. Traditionally, the players are assumed to receive no information during the play of the game. We consider the effect on rendezvous times of giving the players some information about past actions and chance moves, enabling them to apply Bayesian updates to improve their knowledge of their partner's whereabouts. We consider the case where they are placed a known distance apart on the line graph Q (`symmetric rendezvous on the line'). These techniques can be used to give lower bounds on the rendezvous times of the original game (without any revealed information). Our approach is to concentrate on a general analysis of the effect of revelations, rather than compute the best bounds possible with our techniques.

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