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Aubin J.- P., Wilson S. — Optima and Equilibria: An Introduction to Nonlinear Analysis
Aubin J.- P., Wilson S. — Optima and Equilibria: An Introduction to Nonlinear Analysis



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Íàçâàíèå: Optima and Equilibria: An Introduction to Nonlinear Analysis

Àâòîðû: Aubin J.- P., Wilson S.

Àííîòàöèÿ:

Advances in game theory and economic theory have proceeded hand in hand with that of nonlinear analysis and in particular, convex analysis. These theories motivated mathematicians to provide mathematical tools to deal with optima and equilibria. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its applications to economics and game theory, has written a rigorous and concise - yet still elementary and self-contained - text-book to present mathematical tools needed to solve problems motivated by economics, management sciences, operations research, cooperative and noncooperative games, fuzzy games, etc. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: 2nd edition

Ãîä èçäàíèÿ: 1998

Êîëè÷åñòâî ñòðàíèö: 460

Äîáàâëåíà â êàòàëîã: 05.04.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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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