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Rapoport A. — N-person game theory: Concepts and Applications
Rapoport A. — N-person game theory: Concepts and Applications



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Название: N-person game theory: Concepts and Applications

Автор: Rapoport A.

Аннотация:

Game theory is properly a branch of mathematics. As such it is concerned with assertions which can be proved to be true if certain other assertions are true. This way of establishing truth by reference to assertions previously established as true would lead to infinite regress unless certain fundamental assertions were simply accepted as true (without proof). These basic assertions are called axioms. Assertions whose truth is derived by logical proof are called theorems. Game theory, like any other mathematical theory, is essentially a collection of theorems derived from axioms...


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 345

Добавлена в каталог: 04.12.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Game(s), dual      213
Game(s), dual-homogeneous      219
Game(s), essential (inessential)      83
Game(s), essential (inessential), characteristic function of      85
Game(s), essential (inessential), constant-sum      85 115
Game(s), homogeneous      218
Game(s), improper      211—212
Game(s), in extensive form      54 57 64 67—68
Game(s), in normal form      58—59 61 65 67 70 73
Game(s), logical structure of      63
Game(s), multiplication of      214
Game(s), N-person, constant-sum      138
Game(s), N-person, experiments in      254
Game(s), N-person, fundamental theorem of      n313
Game(s), N-person, solution of      95 172
Game(s), negotiated      161
Game(s), non-constant-sum      64—65 87 309
Game(s), non-cooperative      158
Game(s), non-zerosum      63—64 81 see constant-sum non-constant-sum" "Three-person" "Two-person"
Game(s), non-zerosum, symmetric zerosum      223
Game(s), non-zerosum, zerosum      60—61 63—64 66 68 165
Game(s), not "solvable"      65 n313
Game(s), not strong      218 n315
Game(s), null      210—211
Game(s), of chance      48 see
Game(s), of complete opposition      n312
Game(s), of strategy      45
Game(s), parlor      60 64 see etc."
Game(s), product      214
Game(s), pure bargaining      210—211 216
Game(s), quota      124 133 222 229 232 309
Game(s), quota, with even number of players      229
Game(s), rules of the      53—54 57—58 137
Game(s), settlements      67
Game(s), simple      207 213 227 289 309
Game(s), simple, as product game      218
Game(s), solution of      62 65 92 155 see "Solutions" "Von
Game(s), strategic structure of      84 294 309
Game(s), strategically equivalent      258
Game(s), strong      210 215 n315
Game(s), super      217
Game(s), symmetric      112 172 222 293 298 309
Game(s), terminal rule of      53 n312
Game(s), Three-person Prisoners Dilemma      148—149 153 176
Game(s), Three-person Prisoners Dilemma, solution of      151
Game(s), Three-person, characteristic function of      90
Game(s), Three-person, constant-sum      85—86 100 115 119 221
Game(s), Three-person, constant-sum in normalized form      99
Game(s), Three-person, constant-sum in partition function form      152
Game(s), Three-person, essential      86
Game(s), Three-person, non-constant-sum      106
Game(s), Three-person, solution of      102 120
Game(s), two-person      59 61 63 66 74 80 158
Game(s), Two-person, characteristic function of      169
Game(s), Two-person, constant-sum      76 179 305
Game(s), Two-person, cooperative      113 162
Game(s), Two-person, in characteristic function form      199
Game(s), Two-person, non-constant-sum      159
Game(s), Two-person, non-cooperative      176
Game(s), Two-person, Shapley value solution to      170
Game(s), Two-person, theory of      158
Game(s), unhomogeneous      218
Game(s), value of      33 38 66 77—78 147
Game(s), value of to coalition      40 83
Game(s), weighted majority in      217 243
Game(s), with (without) cores      309
Game(s), with more than two players      14
Game-theoretic analysis      45 124
Game-theoretic analysis, extra-game-theoretical considerations      122
Game-theoretic analysis, levels of      45—67
Game-theoretic analysis, non-game-theoretic specifications      285
Games, theory of, in characteristic function form      53 66—67 137
Games, theory of, in characteristic function form in extensive form      53
Games, theory of, in characteristic function form in normal form      53
Games, theory of, in characteristic function form normalized      86 99 102 111
Gamson, William      291—292 294—295 n316
Gelbaum, B.R.      n315
Generality, levels of      50
Geometry      13
Gillies, D.B.      n315
Group theory      52
Harsanyi, bargaining model      170 173 175—176 178—222 285 294
Harsanyi, J.C.      n315
Harsanyi, solution      179 286 291 305
Hausner, M.      271
Imputation(s)      92 97—100 119—120 137 142 285
Imputation(s) as basis of "reasonable outcome"      114
Imputation(s) as outcomes      96
Imputation(s) as payoff disbursement      150
Imputation(s) in a large market game      201 205
Imputation(s) in a small market game      187
Imputation(s) in Two-person zerosum game      93
Imputation(s), comparison of      146
Imputation(s), constraints on      92
Imputation(s), defined for games in partition function form      149
Imputation(s), egalitarian      135 205—206
Imputation(s), equally divided, stability of      120
Imputation(s), non-dominated      96
Imputation(s), ordering of      94
Imputation(s), set of      92
Imputation(s), simplexes      157
Imputation(s), stable      193 227 309
Imputation(s), stable set of      95
Imputation(s), weak ordering among      n312
Infinite regress      11
Infinitely divisible goods      196
Information sets      54
Information, available      68
Interests in conflict situations      96
Interests of players      64
Interests, collective      148 n316
Interests, conflicting      234 307
Interests, conflicts of, psychological aspects of      180
Interests, opposed      165
Interests, opposed diametrically      66 165
Interests, self-      117
International, politics      287
International, politics relations      45
Intersection (of sets)      18 20—21
Irrelevant alternatives, independence from      163 172
Jackson, Andrew      298
Jury (American)      210
Kalisch, G.K.      n316
Kannai, Y.      n312
Kernel      125 146 157 286
Knowledge about others' preferences      69 see
Left-Right game      73
Left-Right game in normal form      73
Left-Right game, characteristic function of      97
Left-Right game, core of      89
Legislature, a      185 207 211—212 see
Legislature, as a symmetric game      220
Legislature, improper      216
Legislature, simple      210
Legislature, state      211
Legislature, sum of      216
Legislature, weak      216
Lesser of two evils      70
Lieberman, B.      297 n316
Linear invariance      172
Lobbies      216
Logistics      304
Lucas, W.F.      7 156—157 n313—314
Luce, R.D.      7 111 168 194 245 n312—316
Magnitudes      28
Malan, D.W.      7
Management ability      301
Mann, Irwin      244 n315
Market with a monopolist      203
Market, as non-zerosum game      196
Market, classical      307
Market, large      185 196
Market, price      202
Market, small      185—186 204
Maschler, Michael      122—123 269 290 297 n313 n316
Mathematical concept      11
Mathematical concept, logic      6
Mathematical concept, mode of reasoning      14
Mathematical concept, notation      6 16 25 37
Mathematical concept, operations      32
Mathematical concept, proposition      11 13
Mathematical concept, symbols      12
Mathematical concept, term      11
Mathematical concept, theory      11
Maximin      28 61 242
Maximization of gain      308
Migrations      250
Military, alliances      234
Military, alliances proficiency      302
Milnor, J.W.      n316
minimax      61
Minimization of effort      308
Minimum (minimal) Power Theory      291 293—294
Minimum power, principle of      219
Minimum resources, principle of      219 289—290 294
Models      49
money      66 76 see
Morgenstem, O.      6 see
Moves      58
Nash's bargaining problem      168
Nash's bargaining problem, Nash — Zeuthen principle      170 172 n314
Nash's bargaining problem, procedure      162 164 168—169 170—172 178 n314
Nash, J.F.      271 n316
Observation(s)      12 97 285
Observation(s), suggested by game theory      308
One-person game paradigm      302
One-to-one correspondence      30 54
Operation(s)      15 18 23
Operation(s) of algebra      19
Operation(s) of arithmetic      51
Operation(s), binary      24
Operation(s), mathematical      32
Operation(s), routine      67
Operational notation      25
Order of preference      46
Ordered n-tuples      24
Ordered pairs      24
Ordering      29
Ordering, strong      29
Ordering, weak      29 94
Outcomes      53—54 57 63 70 124 308
Outcomes of mixed strategy choices      n312
Outcomes, control over      46
Outcomes, equilibrium      111 158—159
Outcomes, expected      56 87 n312
Outcomes, final      49
Outcomes, influence on by coalition      146
Outcomes, intermediate      46 49
Outcomes, intuitive notions about      219
Outcomes, not confined to imputations      115
Outcomes, not dominated by other outcomes      162
Outcomes, possible      94
Outcomes, predicted by $\psi$-stability model      264
Outcomes, predicted by Shapley value      260
Outcomes, range of      96
Outcomes, restrictions of      125
Outcomes, stable      193
Outcomes, unique      122 175
Outcomes, utilities of      301
Paradoxes      52
Pareto-optimal payoff      171
PARETO-optimality      306
Pareto-solution      305
Pariah      101
Partition function, representation of, value assigned by      147
Partitions      34
Partitions as strategy      238
Partitions, sets of      34
Party discipline      246 250
Payoff(s)      26 53 59 66 70 88 122 159 293
Payoff(s) of a single player      n315
Payoff(s), additive      26 n315
Payoff(s), apportionment      66 137 235 293
Payoff(s), deviating from bargaining set      268
Payoff(s), disbursement vector      89 90 119
Payoff(s), disbursements      29 37 89 92 113—114 134 143 146 149 237—238 303 305
Payoff(s), distribution of      134
Payoff(s), equal      134 225
Payoff(s), expected      63 163
Payoff(s), fixed      97—98 100—101
Payoff(s), individually rational configurations      116 120 128 194
Payoff(s), individually rational configurations, departures from      122
Payoff(s), less than value      88 91
Payoff(s), minimum expected      110
Payoff(s), not additive      162
Payoff(s), plane      162
Payoff(s), polygon      160
Payoff(s), pooling of      76
Payoff(s), space      174
Payoff(s), split      101
Payoff(s), stable pair      139
Payoff(s), transformation      86
Payoff(s), unique vector      180
Payoff(s), vector      88—89 111 117
Payoffs, apportionment of      286—287
Payoffs, division of      88 91 126 141 161
Payoffs, equal split of      103 221—222 292
Payoffs, guaranteed by syndicates      173
Payoffs, joint      76 97 147 161 n312
Payoffs, maximization of      82 162 179
Payoffs, minimum of      66 110
Payoffs, the sum of      33 64
Peleg, B.      n313
Personal characteristics, minimizing effects of      256
Pivot      243
Pivotal powers (of players)      294
Player(s)      26—27 54 69
Player(s) in coalition with himself      82 120 129 139
Player(s) in equilibrium      136
Player(s) in non-symmetric games      113
Player(s), "hopes"      127 133
Player(s), according to Von Neumann — Morgenstem, Harsanyi      180
Player(s), bargaining position of      132 170
Player(s), bargaining potential of      122 see
Player(s), cooperation of      81
Player(s), counter-objections      118—119 194
Player(s), dictator      212
Player(s), dummy      212
Player(s), expectations of      105 108
Player(s), irrelevance of personal characteristics      163
Player(s), joined in coalitions      34 see
Player(s), loyalty of      146
Player(s), number of      93
Player(s), objections of      117—119
Player(s), objections of, justified      119—121 124 130
Player(s), weak      230
Poker      60
Political, parties      234
Political, patronage      287
Political, process      287
positional notation      71
Power, gradients      251
Power, index      252 see
Power, redistribution      251
Preferences, knowledge about others'      69
Preferences, order of      196
Preferences, scale of      196 199
Preferred outcomes      64 see
Prescriptive behavior theory      136
Pressure groups      237 242—243 303
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