Skip to main content
SpringerLink
Log in

A Numerical Approach to the ‘Princess and Monster’ Game on an Interval

  • Chapter
  • First Online:
Advances in Dynamic Games and Their Applications

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 10))

Abstract

Rufus Isaacs introduced Princess and Monster games in the final chapter of his classic book. The value of the Princess and Monster game on an interval is as of yet unknown. We present some numerical results to estimate this value.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Alpern (1974). The search game with mobile hider on the circle, Proceedings of the Conference on Differential Games and Control Theory, Kingston, Rhode Island, July 1973. In Differential Games and Control Theory (E. O. Roxin, P. T. Liu, and R.L Sternberg, eds), 181–200. M. Dekker, New York.

    Google Scholar 

  2. S. Alpern and S. Gal. A mixed strategy minimax theorem without compactness, S.I.A.M. J. Control Optim. 33 (1998), no. 2 311–323,.

    MathSciNet  Google Scholar 

  3. S. Alpern and S. Gal. The Theory of Search Games and Rendezvous. Kluwer International Series in Operations Research and Management Sciences, 319 pp, Kluwer, Boston, 2003.

    Google Scholar 

  4. S. Alpern, R. Fokkink, R. Lindelauf, G.J. Olsder (2006). The Princess and Monster Game on an interval, SIAM J. of Control Optim., to appear.

    Google Scholar 

  5. T. Başar and G. J. Olsder, Dynamic Noncooperative Game Theory (second edition), SIAM, Philadelphia, 1999.

    MATH  Google Scholar 

  6. A. Dagan and S. Gal, Searching a network from an arbitrary starting point, Networks, in press.

    Google Scholar 

  7. S. Gal, Search Games. Academic Press, New York, 1980.

    MATH  Google Scholar 

  8. S. Gal, On the optimality of a simple strategy for searching graphs, Int. J. Game Theory 29 (2000), 533–542.

    Article  MathSciNet  Google Scholar 

  9. A. Y. Garnaev, Search Games and Other Applications of Game Theory. Springer-Verlag, Berlin, 2000.

    MATH  Google Scholar 

  10. J. V. Howard, Rendezvous search on the interval and the circle, Operations Res. 47 (1999), 550–557.

    Article  MATH  MathSciNet  Google Scholar 

  11. R. Isaacs, Differential Games. Wiley, New York, 1965.

    MATH  Google Scholar 

  12. J. H. Reijnierse and J. A. M. Potters, Search games with immobile hider, Int. J. Game Theory 21 (1993), 385–394.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. I. Zeliken On a differential game with incomplete information, Soviet Math. Doklady 13 (1973), 228–231.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. London School of Economics, Houghton Street, WC2A 2AE, UK, London

    Steve Alpern

  2. Delft Institute of Applied Mathematics, Delft University, Delft, GA, 5031, 2600, The Netherlands

    Robbert Fokkink

  3. Faculty of Economics and Business Administration, Tilburg University, Tilburg, LE, 90153, 5000, The Netherlands

    Roy Lindelauf

  4. Delft Institute of Applied Mathematics, Delft University, Delft, GA, 5031, 2600, The Netherlands

    Geert Jan Olsder

Authors
  1. Steve Alpern
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robbert Fokkink
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roy Lindelauf
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Geert Jan Olsder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steve Alpern .

Editor information

Editors and Affiliations

    Rights and permissions

    Reprints and permissions

    Copyright information

    © 2009 Birkhäuser Boston

    About this chapter

    Cite this chapter

    Alpern, S., Fokkink, R., Lindelauf, R., Olsder, G.J. (2009). A Numerical Approach to the ‘Princess and Monster’ Game on an Interval. In: Pourtallier, O., Gaitsgory, V., Bernhard, P. (eds) Advances in Dynamic Games and Their Applications. Annals of the International Society of Dynamic Games, vol 10. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4834-3_9

    Download citation

    Publish with us

    Policies and ethics

    Search

    Navigation