Balanced Silverman Games on General Discrete Sets:
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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1991
|
| Edition: | 1st ed. 1991 |
| Series: | Lecture Notes in Economics and Mathematical Systems
365 |
| Subjects: | |
| Online Access: | BTU01 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (V, 140 p) |
| ISBN: | 9783642956638 |
| DOI: | 10.1007/978-3-642-95663-8 |
Staff View
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| spelling | Heuer, Gerald A. Verfasser aut Balanced Silverman Games on General Discrete Sets by Gerald A. Heuer, Ulrike Leopold-Wildburger 1st ed. 1991 Berlin, Heidelberg Springer Berlin Heidelberg 1991 1 Online-Ressource (V, 140 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 365 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 Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Spieltheorie (DE-588)4056243-8 gnd rswk-swf Silverman-Spiel (DE-588)4273072-7 gnd rswk-swf Silverman-Spiel (DE-588)4273072-7 s DE-604 Spieltheorie (DE-588)4056243-8 s Leopold-Wildburger, Ulrike aut Erscheint auch als Druck-Ausgabe 9783540543725 Erscheint auch als Druck-Ausgabe 9783642956645 https://doi.org/10.1007/978-3-642-95663-8 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Heuer, Gerald A. Leopold-Wildburger, Ulrike Balanced Silverman Games on General Discrete Sets Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Spieltheorie (DE-588)4056243-8 gnd Silverman-Spiel (DE-588)4273072-7 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4273072-7 |
| title | Balanced Silverman Games on General Discrete Sets |
| title_auth | Balanced Silverman Games on General Discrete Sets |
| title_exact_search | Balanced Silverman Games on General Discrete Sets |
| title_exact_search_txtP | Balanced Silverman Games on General Discrete Sets |
| title_full | Balanced Silverman Games on General Discrete Sets by Gerald A. Heuer, Ulrike Leopold-Wildburger |
| title_fullStr | Balanced Silverman Games on General Discrete Sets by Gerald A. Heuer, Ulrike Leopold-Wildburger |
| title_full_unstemmed | Balanced Silverman Games on General Discrete Sets by Gerald A. Heuer, Ulrike Leopold-Wildburger |
| title_short | Balanced Silverman Games on General Discrete Sets |
| title_sort | balanced silverman games on general discrete sets |
| topic | Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Spieltheorie (DE-588)4056243-8 gnd Silverman-Spiel (DE-588)4273072-7 gnd |
| topic_facet | Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Spieltheorie Silverman-Spiel |
| url | https://doi.org/10.1007/978-3-642-95663-8 |
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