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Rendezvous search on a graph

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Steve Alpern ,
V. J. Baston  and
Skander Essegaier
Steve Alpern*
Affiliation:
London School of Economics
V. J. Baston*
Affiliation:
University of Southampton
Skander Essegaier*
Affiliation:
Columbia University
*
∗Postal address: Mathematics Department, London School of Economics, Houghton St, London WC2A 2AE, UK. Email address: alpern@lse.ac.uk. Supported by NATO Collaborative Research Grant #972991
∗∗Postal address: Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO9 5NH, UK.
∗∗∗Postal address: Columbia University, Graduate School of Business, Uris Hall #804, New York, NY 10027, USA.
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Abstract

Two agents are placed randomly on nodes of a known graph. They are aware of their own position, up to certain symmetries of the graph, but not that of the other agent. At each step, each agent may stay where he is or move to an adjacent node. Their common aim is to minimize the expected number of steps required to meet (occupy the same node). We consider two cases determined by whether or not the players are constrained to use identical strategies. This work extends that of Anderson and Weber on ‘discrete locations’ (complete graph) and is related to continuous (time and space) rendezvous as formulated by Alpern. Probabilistic notions arise in the random initial placement, in the random symmetries determining spatial uncertainty of agents, and through the use of mixed strategies.

Keywords

Rendezvous searchsearch game

MSC classification

Primary: 90B40: Search theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 223 - 231
Copyright
Copyright © Applied Probability Trust 1999 

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