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TABLE OF CONTETNS
1 GAME, STRATEGY, AND SADDLE-POINT, 1
1. introduction, 1
2. description of a game of strategy, 2
3. illustrative examples, 3
4. relations among expections, 10
5. saddle-points, 12
6. games with perfect information, 14
2 THE FUNDAMENTAL THEOREM, 16
1. preliminaries, 16
2. games without saddle-points, 17
3. mixed strategies, 18
4. graphical representation of mixed strategies, 20
5. the minimax theorem, 21
6. optimal mixed strategies, 22
7. graphical representation of minimax theorem, 23
8. proof of the minimax theorem, 24
3 PROPERTIES OF OPTIMAL STRATEGIES, 36
1. many optimal strategies, 36
2. some properties of an optimal strategy, 36
3. convex set of optimal strategies, 39
4. operations on games, 39
5. dominated strategies, 40
6. all strategies active, 42
7. optimal strategies as extreme points, 43
8. extreme point which yields submatrix, 44
9. submatrix which yields extreme points, 46
10. determing the sets of optimal strategies, 49
11. geometry of solutions, 51
12. target selection-for attack and defense, 54
13. solution of the game "le Her", 59
14. solution of the game of "Morra," 60
15. reconnaissance as a game of strategy, 61
16. application of structure theorems to reconnaissance, 65
17. attack on hidden-object, 68
18. selecton a particular optimal strategy, 71
4 GAMES IN EXTENSIVE FORM, 74
1. representation of games, 74
2. games with perfect information-saddle-points, 76
5 METHODS OF SOLVING GAMES, 79
1. solving for optimal strategies, 79
2. guess and verify, 80
3. examination of submatrices, 81
4. successive approminations, 82
5. graphical solution of 3X3 games, 85
6. mapping method for solving games with constraints, 88
7. mappong method for solving games, 91
8. solution of reconnaissance game by mapping method, 92
6 GAMES WITH INFINITE NUMBER OF STRATEGIES, 97
1. introduction, 97
2. description of continuous games, 97
3. mixed strategy-distribution fuction, 98
4. expectation-stieltjes integral, 100
5. stieltjes integral for continuous function, 101
6. stieltjes integral and Riemann integral, 104
7. stieltjes integral with respect to a step-functuin, 104
8. some properties of stieltjes integral, 105
7 SOLUTION OF INFINITE GAMES, 107
1. optimal mixed strategy, 107
2. existence of optimal strategies, 108
3. properties of optimal strategies, 109
4. delayed firing, 111
5. example of game without solution, 115
8 GAMES WITH CONVEX PAYOFF FUNCTIONS, 117
1. convex payoff functions, 117
2. optimal pure stategy for Red, 118
3. value of game is min max M(x,y),118
4. Red's optimal pure strategy, 119
5. Blue's optimal strategies, 119
6. concave paoff functions, 121
7. general convex payoff, 122
8. defense of two targets against attack, 123
9. defense of many targets of different values, 124
9 GAMES OF TIMING-DUELS, 128
1. dule as a fmae of timing, 128
2. noisy duel : one bullet each duelist, 128
3. noisy duel : one bullet each dyelist, without saddle-point, 131
4. noisy duel : many bullets, equal accuracies, 133
5. noisy duel : one bullet, arvitraty accuracies, 134
6. silent duel: one bullet each duelist, equal accuracies, 134
7. silent-noisy duel: one bullet each duelist, 147
8. silent duel: one bullet versus two, equal accuracies, 137
9. silent duel: positive initial accuracy, 140
10. silent duel : m bullets each duelist, 140
11. silent duel : strictily monotonic accuracies, 141
12. silent duel : continuous fire, 142
13. target prediction, 143
10 TACTICAL AIR-WAR GAME, 145
1. introduction, 145
2. formulation of tactiocal game, 145
3. payoff of tactical game, 147
4. two tasks-counter air and ground support, 147
5. optimal tactics for two tasks, 148
6. optimal tactics for three tasks, 151
11 INFINITE GAMES WITH SEPARABLE PAYOFF FUNCTIONS, 157
1. introduction, 157
2. definition, 157
3. moments, 158
4. equivalence of F(x) and points of cinvex set R, 158
5. bilinear game over a convex set, 159
6. distribution function F(x) and points of convex set R, 160
7. number of steps in step-function solution of game, 161
8. solution of separable games, 161
9. lacal defense of targets of equal value, 165
10. solution of polynomial games, 170
11. tactical reconnaissance-single mission, 175
BIBLIOGRAPHY, 179
INDEX, 181
PUBLISHED RAND RESEARCH, 185
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출판사 책소개
This classic work, originally published in 1961, was written by Melvin Dresher, a RAND research mathematician, during the heyday of game theory research at RAND. The book introduces readers to the basic concepts of game theory and its applications for military, economic, and political problems, as well as its usefulness in decisionmaking in business, operations research, and behavioral science. This is a reprint of the original 1961 edition. Classic work from 1961 discusses basic concepts of game theory and its applications for military, economic, and political problems, as well as its usefulness in decisionmaking in business, operations research, and behavioral science.
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