Some Cinderella Ruckle Type Games - Search Theory: A Game Theoretic Perspective - page 97

readers who relish
the more esoteric problems may like to investigate problems in the topology arising
from the distance function d

In addition to problems in the topology given by || x − y || p ,

n
i = 1

p where 0

( x , y )= ∑ | x i − y i | < p < 1; in this topology

the closed ball in R 2 is not convex.

6.9 Conclusions

In this chapter we have investigated only a few of the games proposed by Ruckle
in his topic but they indicate how the apparently simple games there can provide a
challenge in themselves or the foundation for significant generalisations. A common
thread running through most of the games is that there are optimal strategies which
involve, in some way, coverings of the set the game is played on. Research problems
are the lifeblood of any mathematical discipline and it is hoped that it has been
shown that Ruckle's problems are in rude health. However one can also expect the
games to evolve in different directions. With the current global financial crisis there
is a much greater questioning as to whether projects are affordable so a natural
direction would be to incorporate costs into many of Ruckle's games. For instance
the several intervals game has been interpreted as a game in which a defender puts
detecting devices (intervals) across a channel in an attempt to detect an infiltrator
but little interest has so far been shown in creating scenarios in which the defender
has a limited budget and the more efficient the device (the larger the length of the
interval) the greater the cost of deployment. Be that as it may, the important aspect
of Ruckle's games from my viewpoint is that they provide one with intellectual fun.
His topic even includes a game on a Möbius band; definitely a game that people
don't play.

References

1. S. Alpern and M. Asic: The Search Value of a Network. Networks 15 229-238 (1985).
2. S. Alpern and S. Gal: The Theory of Search Games and Rendezvous. Kluwer, Boston (2003).
3. V. J. Baston, F.A. Bostock and T. S. Ferguson: The Numbers Hides Game , Proc. American
Math. Soc. 107 437-447 (1989).
4. W. H. Ruckle: Geometric Games and Their Applications. Pitman, Boston (1983).
5. I. Woodward, I: Cable Laying Ambush Games, Ph.D. thesis, University of Southampton (2002).
6. P. Zoroa, N. Zoroa and J. M. Ruiz: Juego de Intersección de Intervalos Finitos , Revista de la
Real Academia de Ciencias Exactas, Fisicas y Naturales, Madrid, Spain, 82 469-481 (1988).
7. N. Zoroa, M. J. Fernández-Sáez and P. Zoroa: A Game Related to the Number Hides Game ,
JOTA ( 103 ) 457-473 (1999).
8. N. Zoroa, M. J. Fernández-Sáez, M. J., and P. Zoroa: Search and Ambush Games with Capaci-
ties ,JOTA( 123 ) 431-450 (2004).