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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 365)
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About this book
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.
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
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Bibliographic Information
Book Title: Balanced Silverman Games on General Discrete Sets
Authors: Gerald A. Heuer, Ulrike Leopold-Wildburger
Series Title: Lecture Notes in Economics and Mathematical Systems
DOI: https://doi.org/10.1007/978-3-642-95663-8
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1991
Softcover ISBN: 978-3-540-54372-5Published: 11 September 1991
eBook ISBN: 978-3-642-95663-8Published: 06 December 2012
Series ISSN: 0075-8442
Series E-ISSN: 2196-9957
Edition Number: 1
Number of Pages: V, 140
Topics: Economic Theory/Quantitative Economics/Mathematical Methods, Operations Research/Decision Theory