Skip to main content

Open Problems on Search Games

  • Chapter
  • First Online:
Search Theory

Abstract

We discuss two classic search games: Isaacs’ princess and monster game, and Dresher’s high-low guessing game. Despite the fact that these games were introduced decades ago, there are still numerous open problems around them.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

References

  1. S. Alpern, Search for point in interval, with high-low feedback, Math. Proc. Camb. Phil. Soc. 98 (1985), 569–578.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Alpern, R. Fokkink, R. Lindelauf, and G. J. Olsder. Numerical Approaches to the ‘Princess and Monster’ Game on the Interval, Annals Soc. Dynamic Games 10 (2009), 1–9.

    MathSciNet  Google Scholar 

  3. B. Bollobás, The art of mathematics, coffee time in Memphis, Cambridge University Press, 2006.

    Book  MATH  Google Scholar 

  4. A. Bonato, R.J. Nowakowski, The game of cops and robbers on graphs, American Mathematical Society, 2011.

    Google Scholar 

  5. M. Dresher, Games of Strategy: theory and application, Prentice Hall, 1961.

    Google Scholar 

  6. T.S.Ferguson, A problem of minimax estimation with directional information, Statistics and Probability Letters 26 (1996), 205–211.

    Article  MathSciNet  MATH  Google Scholar 

  7. R.J. Fokkink, Tossing coins to guess a secret number, Amer. Math. Monthly 119 no. 4 (2012), 337–339.

    Article  MathSciNet  MATH  Google Scholar 

  8. R.J. Fokkink, M. Stassen, An asymptotic solution of Dresher’s guessing game, Gamesec 2011, LNCS 7037 (2011), 104–116.

    Google Scholar 

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

    MATH  Google Scholar 

  10. L. Geupel, The ‘Princess and Monster’ Game on an Interval, BSc thesis, TU München (2011), http://en.wikipedia.org/wiki/Princess_and_monster_game

  11. R. Isaacs, Differential games, John Wiley and Sons, New York, 1965.

    MATH  Google Scholar 

  12. Gilbert, E.: Games of identification and convergence, SIAM Rev., vol. 4 (1), 16–24 (1962).

    Article  Google Scholar 

  13. S. Johnson, A search game, in Advances in Game Theory, M. Dresher, L.S. Shapley, A.W. Tucker (eds), Princeton University press, Princeton 1964, 39–48.

    Google Scholar 

  14. J.E. Littlewood, A mathematician’s miscellany, ed. B. Bollobás, Cambridge University Press, 1986.

    Google Scholar 

  15. A. Pelc, Searching games with errors - fifty years of coping with liars, Theoretical Computer Science 270 (2002), 71–109.

    Article  MathSciNet  MATH  Google Scholar 

  16. S. Ulam, Adventures of a Mathematician, Scribner, New York, 1976.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robbert Fokkink .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Fokkink, R., Geupel, L., Kikuta, K. (2013). Open Problems on Search Games. In: Alpern, S., Fokkink, R., Gąsieniec, L., Lindelauf, R., Subrahmanian, V. (eds) Search Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6825-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-6825-7_5

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6824-0

  • Online ISBN: 978-1-4614-6825-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics