Games of strategy: theory and applications

Title page......Page 1
1. Introduction......Page 11
2. Description of a game of strategy......Page 12
3. Illustrative examples......Page 13
4. Relations among expectations......Page 20
5. Saddle-points......Page 22
6. Games with perfect information......Page 24
1. Preliminaries......Page 26
2. Games without saddle-points......Page 27
3. Mixed strategies......Page 28
4. Graphical representation of mixed strategies......Page 30
5. The minimax theorem......Page 31
6. Optimal mixed strategies......Page 32
7. Graphical representation of minimax theorem......Page 33
8. Proof of the minimax theorem......Page 34
2. Some properties of an optimal strategy......Page 46
4. Operations on games......Page 49
5. Dominated strategies......Page 50
6. All strategies active......Page 52
7. Optimal strategies as extreme points......Page 53
8. Extreme point which yields submatrix......Page 54
9. Submatrix which yields extreme points......Page 56
10. Determining the sets of optimal strategies......Page 59
11. Geometry of solutions......Page 61
12. Target selection-for attack and defense......Page 64
13. Solution of the game "le Her"......Page 69
14. Solution of the game of "Morra"......Page 70
15. Reconnaissance as a game of strategy......Page 71
16. Application of structure theorems to reconnaissance......Page 75
17. Attack on hidden-object......Page 78
18. Selecting a particular optimal strategy......Page 81
1. Representation of games......Page 84
2. Games with perfect information-saddle-points......Page 86
1. Solving for optimal strategies......Page 89
2. Guess and verify......Page 90
3. Examination of submatrices......Page 91
4. Successive approximations......Page 92
5. Graphical solution of 3 X 3 games......Page 95
6. Mapping method for solving games with constraints......Page 98
7. Mapping method for solving games......Page 101
8. Solution of reconnaissance game by mapping method......Page 102
2. Description of continuous games......Page 107
3. Mixed strategy-distribution function......Page 108
4. Expectation--8tieltjes integral......Page 110
5. Stieltjes integral for continuous function......Page 111
7. Stieltjes integral with respect to a step-function......Page 114
8. Some properties of Stieltjes integral......Page 115
1. Optimal mixed strategy......Page 117
2. Existence of optimal strategies......Page 118
3. Properties of optimal strategies......Page 119
4. Delayed firing......Page 121
5. Example of game without solution......Page 125
1. Convex payoff functions......Page 127
3. Value of game is min_y max_x M(x,y)......Page 128
5. Blue!s optimal strategies......Page 129
6. Concave payoff functions......Page 131
7. General convex payoff......Page 132
8. Defense of two targets against attack......Page 133
9. Defense of many targets of different values......Page 134
2. Noisy duel: one bullet each duelist......Page 138
3. Noisy duel: one bullet each duelist, without saddle-point......Page 141
4. Noisy duel: many bullets, equal accuracies......Page 143
6. Silent duel: one bullet each duelist, equal accuracies......Page 144
8. Silent duel: one bullet versus two, equal accuracies......Page 147
10. Silent duel: m bullets each duelist......Page 150
11. Silent duel: strictly monotonic accuracies......Page 151
12. Silent duel: continuous fire......Page 152
13. Target prediction......Page 153
2. Formulation of tactical game......Page 155
4. Two tasks-counter air and ground support......Page 157
5. Optimal tactics for two tasks......Page 158
6. Optimal tactics for three tasks......Page 161
2. Definition......Page 167
4. Equivalence of F(x) and points of convex set R......Page 168
5. Bilinear game over a convex set......Page 169
6. Distribution function F(x) and points of convex set R......Page 170
8. Solution of separable games......Page 171
9. Local defense of targets of equal value......Page 175
10. Solution of polynomial games......Page 180
11. Tactical reconnaissance--single mission......Page 185
BIBLIOGRAPHY......Page 189
INDEX......Page 191