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| Anatol Rapoport — Two-Person Game Theory. the Essential Ideas |
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| Ïðåäìåòíûé óêàçàòåëü |
Actuarial computations 36
Adler, C. 9
Agreement(s), binding 130
Agreement(s), broken 129 131
Agreement(s), enforceable 136
Agreement(s), incentives for keeping 129
Agreement(s), negotiated 94
Agreement(s), tacit 127 131
Agreement(s), unenforceable 129
Alphonse — Gaston result 97
Applied science 186 192 193
Arbitration 210 n216 “Game negotiated”)
Arbitration, theories of 99
Asymmetrical assumption 141
Atkinson, R. C. n218 b221
Automata 151
Balance of Power 59 68
Bargaining problem 104—22
Bargaining problem, general 106—22
Bargaining problem, special 104—6 121
Bargaining, ability 104
Bargaining, advantage (leverage, power) 103 111 211
Bargaining, principles 210 n216
Bargaining, theories of 99 (see also “Arbitration”)
Behavioral science 144
Behavioral scientists 6
Behavioral theory 206
Best of the worst 58 68 “Minimax”)
Best reply (answer) 135 138 141
Best strategy 62 78 “Strategy optimal”)
Betrayal 209
Bets 192
biology 15
Blackmail 127
Bona fide player 20
Braithwaite, R. B. 119 188 b220
Braithwaite’s solution (of the negotiated game) 119—20
Brinkmanship 112
Business decisions 189
Chammah, A. n217 b221
Chance (as a player) 19 20 21 62 214
Chance events n214
Choice(s), among bets 192
Choice(s), between lottery tickets 32—37
Choice(s), consequence of 16
Choice(s), consistency of 34
Choice(s), contingent on those of the other 99
Choice(s), coordination of 94 99—100(see coordination
Choice(s), equiprobable 58 67 70
Choice(s), independent (simultaneous) 46 47 49 71
Choice(s), preference 16
Choice(s), randomized 70 73 160
Clausewitz, Karl von 190 191
Collective interest 130
Common sense grounds 135 137
Communication 95 131 214
Competition 6 204
Competitive component (of a nonzero sum game) 115
Conditional probability of response 156 210(see
Conditional propensities 152 207 209
Conditionality of response 210
Conflict 5—6 145 201 205 214
conflict resolution 212
Constraints of the game 74
Contingencies 44—45
Controlled experiments 206
Convex body n215
Convex hull 100
Convex polygon 100
Cooperation 101 152 156 209 211
Cooperation, feinting 135
Cooperation, unilateral 131 209
Cooperative component (of a nonzero-sum game) 105
Counter-threat n215
Cybernetic devices 189
de M r, Chevalier 13
Decision problem under risk or uncertainty 17
Decision theory 9 16—21 188
Deductive reasoning 143 146
Deferring decisions 44
Degree of belief 201
Deterrence 132
Dimensionless units 209
Diplo-military policy 190
Distrust 157 209
Dominating strategy 54—62 82 84 85 125 133
Dummy player 21
Dynamic models of games 145—57 178—84
Efficiency 201
Einstein, A. 77
Electronic computers 189
End effect 160
Environment 144
Equilibrium(a) 59 126—30 137—39 142—43 150 151 177—78 184
Equilibrium(a) of a nonnegotiable game 137 210
Equilibrium(a), as a generalized minimax 137
Equilibrium(a), deviations (departures) from 154 177 210
Equilibrium(a), preferred 138
Equilibrium(a), stable 154 177
Equilibrium(a), strategies 127 137 140 153
Equilibrium(a), unstable 181 210
Equiprobability of choices 67(see also “Choices equiprobable”)
equity 103 119 210 211 n216 n217
Equity, multi-ordinal meaning of 210
Events, chance n214
Events, chance, determinate 195
Events, chance, nonrepeatable 199
Events, chance, probability of 198
Events, chance, repeated 200
Events, chance, universe of 198 200
Existence theorem 77
Existence theorem, on two-person zero-sum games 78—79
Expected gains (payoffs, utilities) 31 35—37 71—73 82 89 113—14 130 139 153—55 165—66 177 184 188 206 209 n214 n218
Expected gains (payoffs, utilities), guaranteed 73 79 108(see
Expected gains (payoffs, utilities), maximization of 74 146 153—56 193(see optimal”)
Experimental sciences 209
flexibility 43—44
Flood, M. M. n218
Gallo, P. S. n217
Game matrix 47—52
Game tree 47—52 65 193 in
games of chance n214
Games, against nature 164 n214
Games, artificial 48
Games, Backgammon 19
Games, Baseball 200
Games, Battle-of-the — Sexes 96—122
Games, Button — Button 65—73 79—89 95
Games, card 19 20
Games, Checkers 19
Games, Chess 14 18 19 21 62 63 69 145 212
Games, Chicken 138—44
Games, classification of 15 17 55
Games, competitive 116
Games, essential features of 18—21
Games, Go 19
Games, in extensive form 48—49
Games, in normal form 46—48 51 62 66 133 162
Games, Inspector — Evader 158—84
Games, Kriegspiel 19 63
Games, Morra 89—93
Games, negotiated (negotiable) 94—121 126 136 210 212 213
Games, Nim 39
Games, nonnegotiable 123—44 176—84
Games, nonzero-sum 95 101 115 119 126 169—85
Games, of perfect information 62
Games, of skill n214
Games, one-person n214 (see also “Games against
Games, parlor 13 47 193
Games, played a known number of times 131—32
| Games, Poker 62
Games, Prisoner’s Dilemma 128—44 137 138 141—42 209 n218
Games, Race-to-Twenty 39—46
Games, saddle point, with 59—62 n216
Games, saddle point, without 68—74 146 156 164 194 197 n216
games, Solitaire 21
Games, Square-the-Diagonal 48—53 63—64
Games, tic-tac-toe 19 20 21 40 41 48 62
Games, value of 80—81 90
Games, zero-sum 8 77 115 142 161 175 192 194 201 204 211 212
Gamesmanship 6
Gaming theory 9
Geometry 16 23
Greatest good for the greatest number 211
Guesses 127
Harsanyi, J. C. 139 210 n216 b221
Heuristic 213
Honor 213
incentives 129 141
Independence from irrelevant alternatives 106
Inductive method (reasoning) 146 150 151 209
Inductive theory of games 144—57
Infinite regress 143
Insight 203
Interests (of players) 38 95 125 132 189
Interval scale 26—31 38 105 161
Irrational opponent 70
Joint payoff 104 113
Joint payoff, improved 136
Joint payoff, largest 57
Knowledge, of each other’s payoffs 125
Knowledge, of game matrix 156
Knowledge, of other player’s motive 129
Labor-management disputes 213
Law enforcement 167
Linear transformation 27 31 38 116 117 n217
Lottery tickets 30 32—37 195
Luce, R. D. 8 96 n219 b220 b221
Malevolent opponent 211
Martyrdom 208
Mass behavior 203
Mathematical conclusions 24
Mathematical conclusions, functions 27
Mathematical conclusions, ideas 7
Mathematical conclusions, models 207 209
Mathematical conclusions, notation 7 8
Mathematical physics 146
Mathematics 7 8 16 189
Maximin 59 119 124 142 n215
Maximin, 136 156 n217
Maximin, departures from 69 92 deviations
Maximin, existence theorem 77 193
Maximin, principle 60 61 68
minimax 59—61 69 82 119
Move (of a game) 8
Nash, J. 104 106 111 128
Nash, J., 129 210 b221
Nash’s axioms 109
Nash’s solution (of the bargaining problem or of the negotiable game) 104—6 111—15 120 121 125 175—76 211
Natural sciences 146 147
Nature (as a player) 114 (see also “Games against
Negotiated solution (agreement, settlement) 94 101 111 172 211 212 “Nash’s” “Raiffa’s” “Shapley’s
Negotiation set 101—4 106
Negotiation set, 110 112 124 175
Negotiation set, equation of 118
Negotiations 94 126—27 130 136 n216
Negotiations, absence of 127—130 138
Negotiations, often impossible 130
Negotiations, purpose of 95
Negotiations, reduced to sequence of moves 130
Negotiations, results of 106 107
No sale 107 (see also “Status quo point”)
Normative theory 32
Nuclear exchange 190
One-criterion decision 33
Operations research 201 n214
Optimal strategy see “Strategy optimal”
Optimization problems 201
Ordered set 14
Ordinal scale 25—28
Outcome(s) 5 17—18 23 28 34 36 45—46 60 94 96 105 129 131 137—39 152 161 163 169
Outcome(s), as lottery tickets 195
Outcome(s), determined by a single decision-maker 201
Outcome(s), equilibrium 125—26 142
Outcome(s), in absence of negotiation 125
Outcome(s), inaccessible 139
Outcome(s), mixtures of 109 124
Outcome(s), preferred 105
Outcome(s), preferred by both players 94
Outcome(s), risky 32 34 36 146 198
Outcome(s), special 136
Paradoxes 128 142 143 209
Parameters 75 156 171
Parameters, assignment of values to 207
Parameters, interpretation of 207—9
Parameters, psychological 206—7
Pascal, B. 13
Payoff(s) 20—38 47 95 100 104 114 129 130 152 161—64 208
Payoff(s), additive 162 182
Payoff(s), as utilities 28—38
Payoff(s), average 150
Payoff(s), expected see “Expected gains (payoff utilities)”
Payoff(s), ignorance of each other’s 125 148
Payoff(s), interchange of 104
Payoff(s), joint 104 113
Payoff(s), jointly improved 136
Payoff(s), jointly largest 115
Payoff(s), largest 57
Payoff(s), largest average 57
Payoff(s), linear transformation of 105 116
Payoff(s), minimal guaranteed 58 119
Payoff(s), monetary 37
Payoff(s), multiplied by a constant 110 119
Payoff(s), normalized 118 (see also “Braith Waite’s solution” “Raiffa’s
Payoff(s), opponent’s 211
Payoff(s), polygon 100—106 112 124 171—72
Payoff(s), relations among 206
Payoff(s), restrictions on 118
Payoff(s), scale of 96 116
Payoff(s), space of 99 106
Payoff(s), units of 119
Phase space 150 n218
Physics 192
Play of a game 20
Player(s), bona fide 20
Player(s), dummy 21
Player(s), psychological characteristics of n217
Player(s), psychologically indistinguishable 126
Player(s), rationality of see “Rational player” “Rational opponent” “Rationality mutual
Policy making 6
Positive monotone transformation 27
Power struggle 189
Preference(s) 5 16 30 36 195
Preference(s), assignment of 196
Preference(s), consistent 34
Preference(s), order of 17 146 169
Preference(s), scale 28
Preference(s), transitive n214
Prescription (s), (prescriptive theory) 62 142—43 147 159 194 203 213
Probabilistic inspection 181—84
Probability theory 13 17 188—89 192 199 n214
Probability(ies) 57 189 192 197—98 201
Probability(ies), estimation of 198 200
Prominence (prominent solution) 128 140 n217
Prudence 112 139
Prudent policy (strategy) 92 131 “Maximin” “Minimax” “Security
Prudent policy (strategy), notions 157
Prudent policy (strategy), overtones 103
Prudent policy (strategy), parameters 206—11
Psychological characteristics of players n217
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