Skip to main content Accessibility help
×
Home

Rendezvous Search with Revealed Information: Applications to the Line

  • Steve Alpern (a1)

Abstract

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 while playing the game. We consider the effect on rendezvous times of giving the players some information about past actions and chance moves, enabling each of them to apply Bayesian updates to improve his knowledge of the other's whereabouts. This technique can be used to give lower bounds on the rendezvous times of the original game (without any revealed information). We consider the case in which they are placed a known distance apart on the line graph Q (known as ‘symmetric rendezvous on the line’). Our approach is to concentrate on a general analysis of the effect of revelations, rather than compute the best bounds possible with our technique.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Rendezvous Search with Revealed Information: Applications to the Line
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Rendezvous Search with Revealed Information: Applications to the Line
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Rendezvous Search with Revealed Information: Applications to the Line
      Available formats
      ×

Copyright

Corresponding author

Postal address: Department of Mathematics, London School of Economics, London WC2A 2AE, UK. Email address: s.alpern@lse.ac.uk

References

Hide All
[1] Alpern, S. (1995). The rendezvous search problem. SIAM J. Control Optimization 33, 673683.
[2] Alpern, S. and Gal, S. (1995). Rendezvous search on the line with distinguishable players. SIAM J. Control Optimization 33, 12701276.
[3] Alpern, S. and Gal, S. (2003). The Theory of Search Games and Rendezvous (Internat. Ser. Operat. Res. Manag. Sci. 55). Kluwer, Boston, MA.
[4] Alpern, S. and Gal, S. (2006). Two conjectures on rendezvous in K_{3}. Res. Rep. LSE-CDAM-2006-21, Department of Mathematics, London School of Economics. Available at http://www.cdam.lse.ac.uk/Reports/reports2006.html.
[5] Alpern, S., Baston, V. and Essegaier, S. (1999). Rendezvous search on a graph. J. Appl. Prob. 36, 223231.
[6] Anderson, E. J. and Essegaier, S. (1995). Rendezvous search on the line with indistinguishable players. SIAM J. Control Optimization 33, 16371642.
[7] Anderson, E. J. and Weber, R. R. (1990). The rendezvous problem on discrete locations. J. Appl. Prob. 28, 839851.
[8] Baston, V. J. (1999). Two rendezvous search problems on the line. Naval Res. Logistics 46, 335340.
[9] Baston, V. and Gal, S. (2001). Rendezvous search when marks are left at the starting points. Naval Res. Logistics 48, 722731.
[10] Crawford, V. P. and Haller, H. (1990). Learning how to cooperate: optimal play in repeated coordination games. Econometrica 58, 571596.
[11] Han, Q., Du, D., Vera, J. and Zuluaga, L. F. (2006). Improved bounds for the symmetric rendezvous value on the line. To appear in Operat. Res.
[12] Lim, W. S., Alpern, S. and Beck, A. (1997). Rendezvous search on the line with more than two players. Operat. Res. 45, 357364.
[13] Uthaisombut, P. (2006). Symmetric rendezvous search on the line using move patterns with different lengths. Submitted.
[14] Weber, R. R. (2006). The optimal strategy for symmetric rendezvous search on K_{3}. Preprint, Statistical Laboratory, University of Cambridge. Available at http://www.statslab.cam.ac.uk/∼rrw1/research/weber-k3.pdf.

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed