Some Cinderella Ruckle Type Games - Search Theory: A Game Theoretic Perspective - page 79

Chapter 6
Some Cinderella Ruckle Type Games
Vic Baston
Abstract Nearly 30 years have elapsed since Ruckle's pioneering topic (Ruckle
WH (1983) Geometric games and their applications. Pitman, Boston) on geometric
games was published; it was pioneering in the sense that it did not seek to detail
a theory but dealt with a host of two-person zero-sum games which were easy to
state and understandable to an intelligent layperson. Attractive features were the
“toy” examples giving very idealized applications of the games and the list of open
problems at the end of most chapters. Although many of the games had quite a lot
in common, the professed aim was to provide “usable solutions” rather than a uni-
fied treatment. In fact Gal's topic (Gal S (1980) Search games. Academic Press,
New York) which developed a theory of search games had already appeared when
Ruckle's topic was published but, in the main, Ruckle's games fell outside its scope.
Although there has been considerable activity in the theory of search games since
then (see [ 2 ]andChap. 9 of the topic), the main emphasis has been on the devel-
opment of the aspects covered in Gal's topic. The aim of this chapter is to draw
attention to some Ruckle games which the writer feels have not received the atten-
tion they deserve; hence the Cinderella in the title.
6.1 Introduction
Fraenkel divides games into two types, games people play (i.e. games that people
buy and play) and games that mathematicians play or, in Peter Winkler's words,
games people don't play. The selection of the games here fall very definitely into
the latter category and the hope is that these games will lead to the development of