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Silverman’s Game

A Special Class of Two-Person Zero-Sum Games

  • Book
  • © 1995

Overview

Authors:
  1. Gerald A. Heuer

    1. Department of Mathematics and Computer Science, Concordia College, Moorhead, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Ulrike Leopold-Wildburger

    1. Department of Statistics, Econometrics and Operations Research, Karl-Franzens-University, Graz, Austria

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 424)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 1-8

  3. Silverman’s Game on Intervals: Preliminaries

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 9-19

  4. Intervals with Equal Left Endpoints or Equal Right Endpoints

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 20-55

  5. Intervals with No Common Endpoints

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 56-76

  6. Reduction by Dominance

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 77-91

  7. The Further Reduction of Semi-Reduced Games

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 92-132

  8. The Symmetric Discrete Game

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 133-155

  9. The Disjoint Discrete Game

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 156-184

  10. Irreducibility and Solutions of the Odd-Order Reduced Games

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 185-217

  11. Irreducibility and Solutions of the Even-Order Reduced Games

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 218-263

  12. Explicit Solutions

    • Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 264-278

  13. Back Matter

    Pages 279-286
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Computer Science, Concordia College, Moorhead, USA

    Gerald A. Heuer

  • Department of Statistics, Econometrics and Operations Research, Karl-Franzens-University, Graz, Austria

    Ulrike Leopold-Wildburger

Bibliographic Information

  • Book Title: Silverman’s Game

  • Book Subtitle: A Special Class of Two-Person Zero-Sum Games

  • Authors: Gerald A. Heuer, Ulrike Leopold-Wildburger

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-46819-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-59232-7Published: 20 June 1995

  • eBook ISBN: 978-3-642-46819-3Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: X, 283

  • Topics: Economic Theory/Quantitative Economics/Mathematical Methods

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