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| Aubin J.- P., Wilson S. — Optima and Equilibria: An Introduction to Nonlinear Analysis |
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| Ïðåäìåòíûé óêàçàòåëü |
Accepted, multilosses 198 218
Accepted, multistrategies 197
Action game 216
Affine 21
Aggressive strategy 112
allocation 169
Approximate minimisation 15
Arrow — Debreu — Nash Theorem 192
Asymptotic, centre 315 364—365
Asymptotic, cone 51
Atomicity axiom 219 231 302
Average fitness 207
Average gain 208
Balanced, family 166 198
Balanced, game 199 227
Balanced, growth 180
Balancing 166 202 227
Banach 34
Banach — Picard Fixed-point Theorem 18 417
Barrier cone 51—52 408
Battle of the sexes 115
Behaviour, non-cooperative 189—190
Behaviour, profile 213
Behavioural quantity 213
Best approximation theorem 28
Best compromise solution 195
Biconjugate 36 37
Biloss mapping 107
Bistrategy 102
Bistrategy, consistent 103
Broad Separation Theorem 31
Brouwer's fixed-point theorem 104 141 143 162 418
Canonical decision rule 108 192
Caratheodory's theorem 243
Caristi's Fixed-point Theorem 17
Change function 173
Clarke differentiable 88
Coalition 196—197 211
Coalition, equilibrium 216
Coalition, fuzzy 212
Coalition, generalised 213
Coalition, social 214
Collective, Budgetary rule 174
Collective, stability 109
Commodity 168 179
Complement (of a toll set) 53
Completeness 15
Concave 21
Cone, asymptotic 51
Cone, barrier 51—52 408
Cone, contingent 274
Cone, negative polar 48 317
Cone, normal 60 70—73 97—98 411—413
Cone, tangent 60 70—73 97—98 332 380—383 411—413
Conjugate function 37 43—48 247—256 406—407
Conservative, strategy 110—111 126 130—134 194
Conservative, vector 111
Consistent 189
Consistent, bistrategy 103
Consistent, multistrategies 189
Constraints 80—82 99 192
consumption 168
Contingent, cone 274
Contingent, epiderivative 271
Continuous partition of unity 135—137 141
Continuously differentiable 88
Contraction 18
Convex function 21—34 242—247 403 405—406
Convexification strategy 105—106
Cooperative game 197—209 211—233 299—302
Coordination game 115
Core 197 198 223 224 226—233
Core (of a toll set) 53
Cournot's Duopoly 116—123
Cournot's equilibrium 119
Cyclically monotone set-valued map 260
Debreu — Gale — Nikaido theorem 148—149
Decentralisation, price 82—84 167 173
Decentralised, price 169
Decision rule 102—104 120 189
Decision rule, canonical 108 192
Decision rule, optimal 137—142
Decision rule, Stackelberg 121
Demand map 170 346 400
Derivative, Clarke directional 87
Derivative, right 62 88 410
Differentiable, Frechet 88 92
Differentiable, Gateaux 62 92
Dirac measures 53
Disjunct 33
Domain 10 403
Domain (of a toll set) 53
Dual problems 36 77
Duality 325 374
Duality interval 126
Economic equilibrium 167—179 287—291
Efficiency axiom 219 231 302
Eigen — Schuster's hypercycle 208
Ekeland's Theorem 15
Epigraph 10—11 403
Equilibrium of replicator systems 206
Equilibrium, coalition 216
Equilibrium, Cournot 119
Equilibrium, economic 167—179 287—291
Equilibrium, Nash 108 190
Equilibrium, non-cooperative 108 119 190
Equilibrium, social 192
Equilibrium, Stackelberg 121—123
Equilibrium, state 216
Equilibrium, static 102
Equilibrium, Walrasian 170 346 399
Euler — Lagrange inclusion 78
Evaluation function 106
Evolutionary stable equilibrium 206
Exchange economy 168
Existence of zeros of set-valued map 150—152 417—422
Extremal point 255
Fenchel's Theorem 39—43 321 370
Fermat 57
Fermat's rule 58 76—80 99 329 377
Finite game 112—116
Fisher — Wright — Haldane's model 207
Fitness matrix 207
Fixed-point theorem 154—155
Fixed-point theorem, Banach — Picard 18 417
Fixed-point Theorem, Brouwer's 104 141 143 162 418
Fixed-point theorem, Caristi 17
Fixed-point theorem, Kakutani 154
Fixed-point theorem, Kakutani — Fan 155
Frechet differentiable 88 92
Function, change 173
Function, conjugate 37 43—48 247—256 406—407
Function, convex 21—34 242—247 403 405—406
Function, evaluation 106
Function, gamma-convex 318 368
Function, indicator 10 404
Function, locally Lipschitz 87—99 270—277 403
Function, loss 106
Function, lower semi-compact 13—15 403
Function, lower semi-continuous 11—13 37—39 403
Function, marginal 240 305 352
Function, support 36 48—52 407—409
Function, upper semi-continuous 12
Function, utility 106
Function, worst-loss 110
Fuzzy, coalition 212
Fuzzy, game 211—233 299—302
Fuzzy, set 212
Gale — Nikai'do — Debreu Theorem 340 391 418
Game, action 216
| Game, balanced 199 227
Game, Chicken 114
Game, cooperative 197—209 211—233 299—302
Game, coordination 115
Game, finite 112—116
Game, fuzzy 211—233 299—302
Game, inessential 301
Game, market 224
Game, n-person 189—209 292—299
Game, non-cooperative 192—193
Game, regular 220
Game, simple 233
Game, subadditive 222
Game, two-person 101—123 415—417
Game, two-person zero-sum 125—142 277—281
Game, weighting 221
Gamma-convex function 318 368
Gateaux differentiable 62 88 92 410
Gaussian toll sets 55
Generalised gradient 270
Generalised, coalition 213
Generalised, gradient 87—99 223
Gradient 62 88
Gradient, generalised 87—99 223 270
Graph 18 145 303
Growth rate 180
Hamiltonian system 78
inclusion 75 76 143—166 282—287
Indicator function 10 404
Indicators 53
Individual stability 108
Inequality, Ky Fan's 140 277—281 339 390—391
Inequality, quasi-variational 160—162
Inequality, Variational 157—159 344
Inessential game 301
Inf-compact 13
Inf-convolution 45 239
Inner semicontinuous 147
Inverse of set-valued map 145
Kakutani — Fan Fixed-point Theorem 155
Kakutani's Fixed-point Theorem 154
Knaster — Kuratowski — Mazurkiewicz lemma 163 418
Ky Fan's inequality 140 277—281 339 390—391
Ky Fan's theorem 277—281
Lagrange multipliers 78 83—84 97 272
Legendre transformation 64
Leray — Schauder theorem 159—160 419
Locally Lipschitz function 87—99 270—277 403
Loss function 106
Lotka — Volterra equation 208
Lower section 11
Lower semi-compact function 13—15 403
Lower semi-continuous function 11—13 37—39 403
Lower semi-continuous set-valued map 146 417—422
Maintenon (marquess of) 101
Marginal function 240 305 352
Marginal properties 75—86 263—270
Market game 224
Maynard — Smith' dynamic game 208
Measure Maslov 56
membership 212
Membership cost functions 53
Mere (Antoine Gombaud, chevalier de) 101
Metagame 192—193
Minimax theorem 134 279 337—339 388—390
Minimax theorem, Ky Fan 140 277—281 339 390—391
Minimax theorem, von Neumann 277—281
Minimisation problem 9—19 35—56 75—86 99 237—302 413—415
Minimising sequence 237
Minimum, virtual 110 194
Minkowski 34 36
Mixed strategy 105 134
Monotone set-valued map 344 397
Moreau transform 55
Multilosses, accepted 198 218
Multistrategies, accepted 197
Multistrategies, consistent 189
N-person game 189—209 292—299
Nash equilibrium 108 190
Nash's theorem 191
Negative polar cone 48 317
Non-cooperative, behaviour 189—190
Non-cooperative, equilibrium 108 119 190
Non-cooperative, game 192—193
Nonlinear equations 143—166 282—287
Normal cone 60 70—73 97—98 411—413
Normal form (of game) 106—108 190—191
Open covering 135
Open image theorem 313 362—364
Optimal decision rule 137—142
Optimisation 413—415
Orthogonal, projector 317 367—369
Orthogonal, subspace 48
Outer semicontinuous 147
Pareto optima 108—110 193—195
Partial order 107
Participation 212
Partition of unity, continuous 135—137
Peaceable strategy 112
Penalisation 84—86 414
Perron — Frobenius theorem 184—186 422
Population genetics 207
Prebiotic evolution 208
Price, decentralisation 82—84 167 173
Price, decentralised 169
Price, simplex 169
Prisoner's Dilemma 112—113
Probability simplex 205
Projector of best approximation 28 407
Proper mapping 319 369—370
Proximation Theorem 27—31 84
Pseudo convex 276
Quasi-convex 22
Quasi-variational inequality 160—162
Re-entrant 154 418
Redundant-players axiom 220 231 302
Regular game 220
Regularisation 84—86 414
Replicator system 205
Replicator systems for linear growth rates 207
Restriction 10
Right derivative 62 88 410
Saddle point 125—130 134 415
Salient 154 418
Scarf's Theorem 199
Section 11 403
Separation theorem 31
Separation Theorem, Broad 31
Set-valued map 144 303—305 349—352
Set-valued map, cyclically monotone 260
Set-valued map, existence of zeros 150—152 417—422
Set-valued map, inverse 145
Set-valued map, lower semi-continuous 146 417—422
Set-valued map, monotone 344 397
Set-valued map, upper hemi-continuous 145 417—422
Set-valued map, upper semi-continuous 145 303 417—422
Shapley, (K-K-M-S)Theorem 162—166
Shapley, value 220 229 232
Share-out rule 219
Side payments 218—226
Simple game 233
Slater condition 251
Smith, Adam 167
Social, coalition 214
Social, equilibrium 192
Solution (of the game) 223
Stability, collective 109
Stability, individual 108
Stackelberg, decision rule 121
Stackelberg, disequilibrium 123
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