Silverman’s Game

A Special Class of Two-Person Zero-Sum Games

Häftad, Engelska, 1995

Av Gerald A. Heuer, Ulrike Leopold-Wildburger, Gerald Heuer

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This book brings together in an efficient and unified way virtually all that has been learned about this intriguing class of games since its appearance on the scene in 1979. The game on discrete sets is reduced to minimal strategy sets on which the payoff matrix has a canonical structure, and the game on intervals is analyzed for all possible pairs of intervals. For most cases, optimal strategies and game value can be explicitly obtained.

Produktinformation

Utgivningsdatum1995-06-20
Mått155 x 235 x 17 mm
Vikt458 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Economics and Mathematical Systems
Antal sidor283
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540592327

Tillhör följande kategorier

1. Introduction.- Survey of prior work.- The payoff function and expected payoffs.- The sequences {pk} and {vk}.- The sequences {Vk} and {Uk}.- Equivalent variations.- 2. Silverman’s game on intervals: preliminaries.- The key mixed strategies.- 3. Intervals with equal left endpoints or equal right endpoints.- The regions LAn, and equal right endpoints.- Case 1. [(1, B)] × [(1, B)].- Case 2. [(1, B)] × [(1, D)],1 < B < D.- Case 3. [(1, B)] × [(A, B)], 1 < A < B.- 4. Intervals with no common endpoints.- Case 4. [(1, B)] × [(A, D)], 1 < A < B < D.- Case 5. [(1, D)] × [(A, B)], 1 < A < B < D.- Case 6. [(1, B)] × [(A, D)], 1 < B ? A < D.- Appendix. Multisimilar distributions.- 5. Reduction by dominance.- Type A dominance.- Type B dominance.- Type C dominance.- Type D dominance.- Semi-reduced games.- 6. The further reduction of semi-reduced games.- Games with |M| = 1. (Reduction to 2 × 2.).- Games with M = 0 which reduce to odd order.- Games with M = 0 which reduce to even order.- 7. The symmetric discrete game.- The symmetric game with v ? 1.- The symmetric game with v < v(n).- 8. The disjoint discrete game.- The disjoint game with v ? 1.- The disjoint game with v < 1.- 9. Irreducibility and solutions of the odd-order reduced games.- The reduced game matrix A and the associated matrix B.- The polynomial sequences.- The odd-order game of type (i).- The odd-order game of type (ii).- The odd-order game of type (iii).- The odd-order game of type (iv).- 10. Irreducibility and solutions of the even-order reduced games.- The reduced game matrix A and the associated matrix B.- Further polynomial identities.- The even-order game of type (i).- The even-order games of types (ii) and (iii).- The even-order game of type (iv).- 11. Explicit solutions.- The game onintervals.- The symmetric discrete game.- The disjoint discrete game.- The reduced discrete game.- Semi-reduced balanced discrete games with no changes of sign on the diagonal.- Maximally eccentric games.- References.