Search Games and Other Applications of Game TheorySpringer Science & Business Media, 6 mai 2000 - 150 pages This book is on applications of game theory. The title of this book is not "Game Theory and its Applications" because it does not construct a general theory for considered games. The book contains a lot of examples of applica tion of game theory together with the background of those games considered and a list of unsolved problems. Also we consider only the game where the optimal strategies of the players are found in closed form. This book is an attempt to carryon the approach developed in nice books "Search Games" by Gal and "Geometric Games and their Applications" by Ruckle. The first chapter of this book supplies the required definitions and theorems from game theory. The second chapter deals with discrete search games where both players act simultaneously: the games of protection of a channel from infiltration of a submarine, the submarine versus helicopter game, the matrix search games and others. The third chapter considers the game where the players allocate their contin uous efforts. In these games players face up an alternative either not to come into contest if the cost of efforts seems too high, or come into it. In the last case the player have to decide how much resources they can afford to spend. The allocation models of search, antiballistic protection and marketing are investigated. |
Table des matières
Preliminary Results from Game Theory | 1 |
12 Nonzerosum Games | 4 |
Ambush Games | 5 |
22 An Infiltration Game with Two Cables | 6 |
23 Further Reading | 13 |
24 Number Hides Game | 14 |
25 Matrix Search Games | 16 |
26 Helicopter Versus Submarine Game | 20 |
47 Game Without Safe Zone | 74 |
48 Further Reading | 79 |
Problems | 80 |
Games of Timing | 81 |
52 Nonzero Sum Noisy Duel | 88 |
53 Nonzero Sum SilentNoisy Duel | 90 |
54 A Duel with Random Termination Time | 92 |
541 Uniqueness of Nash Equilibria | 95 |
Problems | 23 |
Allocation Games | 25 |
32 OneSided Allocation Game with Search Cost | 26 |
33 Further Reading | 29 |
34 TwoSided Allocation Game Without Search Cost | 31 |
341 Optimal Strategies of the Game | 33 |
35 TwoSided Allocation Game with Search Cost | 34 |
36 A NonZero Sum TwoSided Allocation Game | 37 |
37 One Person Search Game | 40 |
38 Marketing Games Without Taking into Acount Expenses | 41 |
39 Marketing Games Taking into Acount Expenses | 46 |
Problems | 50 |
Dynamic Infiltration and Inspection Games | 53 |
411 Auxiliary Results | 55 |
412 The Main Resuls | 58 |
42 A Multi Stage Customs and Smuggler Game | 61 |
421 The Main Result on Two Boats Game | 63 |
43 Further Reading | 64 |
44 Inspection Game | 65 |
45 Game with a Safe Zone I | 67 |
46 Game with a Safe Zone II | 72 |
55 A Noisy Duel with Random Termination Time | 101 |
56 A SilentNoisy Duel with Random Termination Time | 102 |
57 A Duel over a Cake | 104 |
571 Properties of Nash Equilibrium | 105 |
572 A Generalization of the Duel over a Cake | 109 |
58 R D Game | 110 |
581 Formulation of the Game | 112 |
582 Auxilary Results | 113 |
583 The Main Results | 117 |
584 Disscussion of the Results | 118 |
Problems | 120 |
Parlour Games | 121 |
62 Exchange Games | 124 |
63 Poker Games | 129 |
632 Second Setup of Poker Game | 130 |
633 Third Setup of Poker Game | 132 |
634 Forth Setup of Poker Game | 133 |
64 OnePerson Games with a Threshold | 134 |
65 TwoPerson Games | 136 |
141 | |
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Expressions et termes fréquents
assume C₁ C₂ choose with equal completes the proof Consider continuous Customs and Smuggler denoted equal probability equation F₁ F₁(x F₂ F2 is constant Fi(x Game Theory Garnaev given as follows Hence holds implies inequalities Infiltration Game Infiltrator and Guard integer interval K₁(a Lemma m₁ M₁(x m₂ mathematical induction matrix game noisy duel non-negative non-zero sum optimal mixed strategy optimal strategies otherwise patrol payoff matrix payoff to player payoff to Searcher payoff vector N1 payoffs are given probability vector Proof Let F1 proof of Lemma pure strategy respectively result follows Safe Zone Sakaguchi search game Searcher and Hider sensitive zone shoot strategies of Searcher strategy of Guard strategy of Infiltrator strategy of player strategy x strictly increasing Submarine game supp Theorem uniform distribution unique Nash equilibrium unique root v₁ variant Wait-and-Run strategy y₁ zero-sum game