Title: Study on the three players' linear rendezvous search problem

Authors: Mohamed Abd Allah El-Hadidy

Addresses: Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia; Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Abstract: This paper considers the symmetric rendezvous problem of three players on the line. This problem asks how the players forced to use the same mixed strategy, can minimise their expected meeting time. This minimum is called the 'symmetric' rendezvous value of the line. In our problem we consider the effect on rendezvous time of giving the players some information about past actions and chance moves, enabling each of them to apply Bayesian updates to improve the knowledge of the other's whereabouts. This technique can be used to give lower bounds on rendezvous time 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.

Keywords: rendezvous search problem; mixed strategy; Bayesian updates.

DOI: 10.1504/IJOR.2018.095623

International Journal of Operational Research, 2018 Vol.33 No.3, pp.297 - 314

Received: 11 Sep 2015
Accepted: 25 Oct 2015
Published online: 16 Oct 2018 *

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