Balanced Silverman games on general discrete sets

Bibliographic Information

Balanced Silverman games on general discrete sets

Gerald A. Heuer, Ulrike Leopold-Wildburger

(Lecture notes in economics and mathematical systems, 365)

Springer-Verlag, c1991

  • : gw
  • : us

Other Title

Silverman games on general discrete sets

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Note

Includes bibliographical references

Description and Table of Contents

Description

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.

Table of Contents

1. Introduction.- 2. Games with saddle points.- 3. The 2 by 2 games.- 4. Some games which reduce to 2 by 2 when ? ? 1.- 5. Reduction by dominance.- 6. Balanced 3 by 3 games.- 7. Balanced 5 by 5 games.- 8. Reduction of balanced games to odd order.- 9. Reduction of balanced games to even order.- 10. Games with +/-1 as central diagonal element.- 11. Further reduction to 2 by 2 when ? = 1.- 12. Explicit solutions for certain classes.- 13. Concluding remarks on irreducibility.- References.

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Details

  • NCID
    BA13011659
  • ISBN
    • 3540543724
    • 0387543724
  • LCCN
    91026729
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin ; Tokyo
  • Pages/Volumes
    139 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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