Balanced Silverman Games on General Discrete Sets

Gerald A. Heuer

ISBN 10: 3540543724 / ISBN 13: 9783540543725

Published by Springer, Springer, 1991

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540543725

Bibliographic Details

• Title: Balanced Silverman Games on General Discrete Sets
• Publisher: Springer, Springer
• Publication Date: 1991
• Language: English
• ISBN 10: 3540543724
• ISBN 13: 9783540543725
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 242W x 170H x 9D millimeters 242 millimeters width by 170 millimeters height by 9 millimeters depth
• Weight: 273 grams

About this title

Synopsis

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.