Mathematical methods and theory in games, programming and economics. Volume II, The theory of infinite games / by Samuel Karlin.
Mathematical Methods and Theory in Games, Programming, and Economics.
Saved in:
| Online Access: |
Full Text (via ScienceDirect) |
|---|---|
| Main Author: | |
| Other title: | Theory of infinite games. |
| Format: | eBook |
| Language: | English |
| Published: |
London :
Pergamon Press : Addison-Wesley,
1959.
|
| Series: | Addison-Wesley series in statistics.
|
| Subjects: |
Table of Contents:
- Front Cover; Mathematical Methods and Theory in Games, Programming, and Economics; Copyright Page; Table of Contents; CHAPTER 1. THE DEFINITION OF A GAME AND THE MIN-MAX THEOREM; 1.1 Introduction. Games in normal form; 1.2 Examples; 1.3 Choice of strategies; 1.4 The min-max theorem for finite matrix games; 1.5 General min-max theorem; 1.6 Problems; Notes and references; CHAPTER 2. THE NATURE AND STRUCTURE OF INFINITE GAMES; 2.1 Introduction; 2.2 Games on the unit square; 2.3 Classes of games on the unit square; 2.4 Infinite games whose strategy spaces are known function spaces.
- 2.5 How to solve infinite games2.6 Problems; Notes and references; CHAPTER 3. SEPARABLE AND POLYNOMIAL GAMES; 3.1 General finite convex games; 3.2 The fixed-point method for finite convex games; 3.3 Dimension relations for solutions of finite convex games; 3.4 The method of dual cones; 3.5 Structure of solution sets of separable games; 3.6 General remarks on convex sets in En; 3.7 The reduced moment spaces; 3.8 Polynomial games; 3.9 Problems; Notes and references; CHAPTER 4. GAMES WITH CONVEX KERNELS AND GENERALIZED CONVEX KERNELS; 4.1 Introduction; 4.2 Convex continuous games.
- 4.3 Generalized convex games4.4 Games with convex pay-off in En; 4.5 A theorem on convex functions; 4.6 Problems; Notes and references; CHAPTER 5. GAMES OF TIMING OF ONE ACTION FOR EACH PLAYER; 5.1 Examples of games of timing; 5.2 The integral equations of games of timing and their solutions; 5.3 Integral equations with positive kernels; 5.4 Existence proofs; 5.5 The silent duel with general accuracy functions; 5.6 Problems; Notes and references; CHAPTER 6. GAMES OF TIMING (CONTINUED); 6.1 Games of timing of class I; 6.2 Examples; 6.3 Proof of Theorem 6.1.1.
- 6.4 Games of timing involving several actions6.5 Butterfly-shaped kernels; 6.6 Problems; Notes and references; CHAPTER 7. MISCELLANEOUS GAMES; 7.1 Games with analytic kernels; 7.2 Bell-shaped kernels T; 7.3 Bell-shaped games; 7.4 Other types of continuous games; 7.5 Invariant games; 7.6 Problems; Notes and references; CHAPTER 8. INFINITE CLASSICAL GAMES NOT PLAYED OVER THE UNIT SQUARE ; 8.1 Preliminary results (the Neyman-Pearson lemma); 8.2 Application of the Neyman-Pearson lemma to a variational problem; 8.3 The fighter-bomber duel; 8.4 Solution of the fighter-bomber duel.
- 8.5 The two-machine-gun duel8.6 Problems; Notes and references; CHAPTER 9. POKE R AND GENERAL PARLOR GAMES; 9.1 A simplified blackjack game; 9.2 A poker model with one round of betting and one size of bet; 9.3 A poker model with several sizes of bet; 9.4 Poker model with two rounds of betting; 9.5 Poker model with kraises; 9.6 Poker with simultaneous moves; 9.7 The Le Her Game; 9.8 High hand wins
- 9.9 Problems; Notes and references; SOLUTIONS TO PROBLEMS; APPENDIX A. VECTOR SPACES AND MATRICES; A.1 Euclidean and unitary spaces.