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Rendezvous Search on the Line with More Than Two Players

Author

Listed:
  • Wei Shi Lim

    (National University of Singapore, Singapore and London School of Economics, London, England)

  • Steve Alpern

    (London School of Economic, London, England)

  • Anatole Beck

    (University of Wisconsin, Madison, Wisconsin and London School of Economics, London, England)

Abstract

Suppose n blind, speed one, players are placed by a random permutation onto the integers 1 to n , and each is pointed randomly to the right or left. What is the least expected time required form m ≤ n of them to meet together at a single point? If they must all use the same strategy we call this time the symmetric rendezvous value R n , m s ; otherwise the asymmetric value R n , m a . We show that R 3,2 a = 47/48, and that R n , n s is asymptotic to n /2. These results respectively extend those for two players given by Alpern and Gal (Alpern, S., S. Gal. 1995. Rendezvous search on the line with distinguishable players. SIAM J. Control Optim. 33 1270–1276.) and Anderson and Essegaier (Anderson, E. J., S. Essegaier. 1995. Rendezvous search on the line with indistinguishable players. SIAM J. Control Optim. 33 1637–1642.).

Suggested Citation

  • Wei Shi Lim & Steve Alpern & Anatole Beck, 1997. "Rendezvous Search on the Line with More Than Two Players," Operations Research, INFORMS, vol. 45(3), pages 357-364, June.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:3:p:357-364
    DOI: 10.1287/opre.45.3.357
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    Citations

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    Cited by:

    1. Steve Alpern & Wei Shi Lim, 2002. "Rendezvous of three agents on the line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 244-255, April.
    2. Steve Alpern & Anatole Beck, 1999. "Asymmetric Rendezvous on the Line Is a Double Linear Search Problem," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 604-618, August.
    3. Edward J. Anderson & Sándor P. Fekete, 2001. "Two Dimensional Rendezvous Search," Operations Research, INFORMS, vol. 49(1), pages 107-118, February.
    4. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.
    5. Steve Alpern & Anatole Beck, 2000. "Pure Strategy Asymmetric Rendezvous on the Line with an Unknown Initial Distance," Operations Research, INFORMS, vol. 48(3), pages 498-501, June.
    6. Steve Alpern & Anatole Beck, 1999. "Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting," Operations Research, INFORMS, vol. 47(6), pages 849-861, December.
    7. Qiaoming Han & Donglei Du & Juan Vera & Luis F. Zuluaga, 2008. "Improved Bounds for the Symmetric Rendezvous Value on the Line," Operations Research, INFORMS, vol. 56(3), pages 772-782, June.
    8. Vic Baston, 1999. "Note: Two rendezvous search problems on the line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(3), pages 335-340, April.
    9. L.C. Thomas & M. Pikounis, 2001. "Many‐player rendezvous search: Stick together or split and meet?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 710-721, December.

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