Ebook: Silverman’s Game: A Special Class of Two-Person Zero-Sum Games

The structure of a Silverman game can be explained very quickly: Each of two players independently selects a number out of a prede­ termined set, not necessarily the same one for both of them. The higher number wins unless it is at least k times as high as the other one; if this is the case the lower number wins. The game ends in a draw if both numbers are equal. k is a constant greater than 1. The simplicity of the rules stimulates the curiosity of the the­ orist. Admittedly, Silverman games do not seem to have a direct applied significance, but nevertheless much can be learnt from their study. This book succeeds to give an almost complete overview over the structure of optimal strategies and it reveals a surprising wealth of interesting detail. A field like game theory does not only need research on broad questions and fundamental issues, but also specialized work on re­ stricted topics. Even if not many readers are interested in the subject matter, those who are will appreciate this monograph.

---

This book brings together in an efficient and unified way virtually all that has been learned about this intriguing class of games since its appearance on the scene in 1979. The game on discrete sets is reduced to minimal strategy sets on which the payoff matrix has a canonical structure, and the game on intervals is analyzed for all possible pairs of intervals. For most cases, optimal strategies and game value can be explicitly obtained.