Silverman's game on discrete sets

In a symmetric Silverman game each of the two players chooses a number from a set S⊂(0,∞). The player with the larger number wins 1, unless the larger is at least T times as large as the other, in which case he loses v. Such games are investigated for discrete S, for T>1 and v>0. Except for v...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 166; pp. 217 - 235
Main Authors Evans, Ronald J., Heuer, Gerald A.
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 15.03.1992
Elsevier Science
Subjects
Applied sciences
Exact sciences and technology
Game theory
Operational research and scientific management
Operational research. Management science
Two person game
Game theory
Optimal strategy
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Summary:In a symmetric Silverman game each of the two players chooses a number from a set S⊂(0,∞). The player with the larger number wins 1, unless the larger is at least T times as large as the other, in which case he loses v. Such games are investigated for discrete S, for T>1 and v>0. Except for v too near zero, where there is a proliferation of cases, explicit solutions are obtained. These are of finite type and, except at certain boundary cases, unique.
ISSN:0024-3795
1873-1856
DOI:10.1016/0024-3795(92)90279-J