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Balanced Silverman Games on General Discrete Sets

  • Gerald A. Heuer
  • Ulrike Leopold-Wildburger

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 365)

Table of contents

  1. Front Matter
    Pages i-v
  2. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 1-4
  3. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 5-5
  4. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 6-7
  5. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 8-18
  6. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 19-28
  7. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 29-31
  8. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 32-33
  9. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 34-71
  10. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 72-113
  11. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 114-118
  12. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 119-125
  13. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 126-137
  14. Gerald A. Heuer, Ulrike Leopold-Wildburger
    Pages 138-139
  15. Back Matter
    Pages 140-142

About this book

Introduction

A Silverman game is a two-person zero-sum game defined in terms of two sets S I and S II of positive numbers, and two parameters, the threshold T > 1 and the penalty v > 0. Players I and II independently choose numbers from S I and S II, respectively. The higher number wins 1, unless it is at least T times as large as the other, in which case it loses v. Equal numbers tie. Such a game might be used to model various bidding or spending situations in which within some bounds the higher bidder or bigger spender wins, but loses if it is overdone. Such situations may include spending on armaments, advertising spending or sealed bids in an auction. Previous work has dealt mainly with special cases. In this work recent progress for arbitrary discrete sets S I and S II is presented. Under quite general conditions, these games reduce to finite matrix games. A large class of games are completely determined by the diagonal of the matrix, and it is shown how the great majority of these appear to have unique optimal strategies. The work is accessible to all who are familiar with basic noncooperative game theory.

Keywords

Bidding/Spending Models Noncooperative Game Theory Optimierungstheorie Optimization Theory Silvermanspiel Spieltheorie game theory

Authors and affiliations

  • Gerald A. Heuer
    • 1
  • Ulrike Leopold-Wildburger
    • 2
  1. 1.Concordia CollegeMoorheadUSA
  2. 2.University of GrazGrazAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-95663-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54372-5
  • Online ISBN 978-3-642-95663-8
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site