Game theory with applications to economics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Oxford Univ. Press
1991
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 322 S. graph. Darst. |
| ISBN: | 0195063554 0195070534 |
Internformat
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| 100 | 1 | |a Friedman, James W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Game theory with applications to economics |c James W. Friedman |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 1991 | |
| 300 | |a XXII, 322 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text | Contents
List of Figures xxi
List of Tables xxiii
1 Introduction to games 3
1 Examples of games 4
1.1 A three-firm market for computers, 4
1.2 Two political election games, 5
1.3 Labor—management: A cooperative game example, 7
2 Forms in which games are presented 8
2.1 The extensive form and some basic concepts applying to all games, 9
2.1.1 A game in extensive form, 10
2.1.2 Complete information, perfect information, and perfect recall, 11
2.1.3 The rules of the game, common knowledge, binding agreements,
and commitments, 13
2.2 The strategic form, 14
2.3 The coalitional, or characteristic function, form, 17
3 Outline of the book 19
3.1 Noncooperative games, 19
3.2 Cooperative games, 22
3.3 Application to economics and political science, 23
4 A note on the exposition 23
2 Finite noncooperative games 24
1 The structure of finite extensive form games 25
1.1 The game tree, 25
1.2 Extensive form games, 26
1.3 Classifying games in terms of information, 28
1.4 Pure, mixed, and behavior strategies, 30
1.4.1 Pure strategies, 31
1.4.2 Mixed strategies, 33
1.4.3 Behavior strategies, 34
xiv Contents
2 The strategic form derived from the extensive form 35
3 Some basic topics and results on finite games 36
3.1 The definition of noncooperative equilibrium, 37
3.2 Dominant strategies, dominated strategies, and dominant strategy
equilibria, 39
3.3 Pure strategy equilibria in games of perfect information, 40
3.4 Behavior strategies in games of perfect recall, 41
3.5 Two-person zero-sum games, 42
4 Subgames 43
5 Refinements of noncooperative equilibrium 44
5.1 Overview of refinements, 45
5.2 Subgame perfection, 46
5.3 Perfect equilibrium points, 49
5.3.1 The basics of perfect equilibrium, 50
5.3.2 Perfect equilibrium in finite extensive form games with perfect
recall, 52
5.3.3 Perfect equilibrium in finite extensive and strategic form games, 52
5.3.4 e-perfect equilibrium and perfect equilibrium, 54
5.4 Sequential equilibrium, 55
5.5 Proper equilibrium, 58
6 Concluding comments 60
Exercises 61
Notes 62
3 Noncooperative games in strategic form 63
/ 1 Basic concepts for noncooperative games 64
2 Existence of equilibrium points for n-person noncooperative
games 68
2.1 Best-reply mappings and their relationship to equilibrium points, 69
2.2 Fixed points of functions and correspondences, 70
2.3 Continuity properties of the best-reply mapping, 72
2.4 Existence of an equilibrium point, 72
2.5 Examples of and comments on computing equilibrium points, 73
2.6 Other results on existence of equilibrium, 75
2.6.1 Equilibrium in pseudogames, 75
2.6.2 Other existence theorems for games, 77
3 Strictly competitive two-person games 78
3.1 Properties of equilibrium points for strictly competitive games, 78
3.2 Equilibrium characteristics of strictly competitive games that do not
generalize, 80
3.3 Strictly competitive games without quasiconcavity, 81
4 Uniqueness of equilibrium points 83
4.1 Some additional restrictions needed to ensure uniqueness, 83
4.2 Uniqueness of equilibrium: the contraction mapping approach, 84
4.3 Uniqueness of equilibrium: the univalent mapping approach, 85
4.4 Examples of games with unique equilibrium points, 87
Contents xv
5 Noncooperative games under incomplete information 88
5.1 Definition of a game of incomplete information, 89
5.2 Consistency of players subjective beliefs, 90
5.3 A complete information companion game, 90
5.4 Existence of equilibrium points for incomplete information games, 91
5.5 A numerical example, 93
6 Applications of noncooperative games, 95
6.1 Cournot oligopoly, 95
6.2 General competitive exchange equilibrium, 97
6.3 The free rider problem, 100
7 Concluding comments 104
Exercises 105
Notes 106
4 Multiperiod noncooperative games without time
dependence 108
1 Introduction 108
1.1 The repeated prisoners dilemma, 109
1.2 Trigger strategy equilibria and the folk theorem for repeated games, 110
1.3 Outline of the chapter, 111
2 The formulation of repeated games, subgame perfection, and simple
strategy combinations 112
2.1 Repeated game definitions and the anti-folk theorem, 113
2.1.1 Information flow over time and the anti-folk theorem, 113
2.1.2 Strategies and strategy spaces for repeated games, 115
2.1.3 A note on discount parameters and continuation probabilities, 117
2.2 Subgames and subgame perfection, 118
2.3 The sufficiency of simple strategies, 120
2.3.1 Simple strategy combinations, 120
2.3.2 Optimal penal codes, 121
2.3.3 Supporting attainable outcomes, 122
3 Equilibria in infinite-horizon repeated games 124
3.1 Trigger strategy equilibria in repeated games with discounting, 124
3.1.1 Characterizing grim trigger and finite reversion trigger strategy
combinations, 124
3.1.2 An example of a cooperative outcome supported by noncooperative
equilibrium strategies, 125
3.1.3 Conditions for subgame perfect trigger strategy equilibria, 126
3.2 The folk theorem for repeated games without discounting and its extension
to subgame perfection, 131
3.3 Extending the folk theorem to games with discounting, 133
3.4 Trigger strategy equilibria in supergames with discounting, 137
4 Finite horizon repeated games 138
4.1 The finitely repeated game model, 138
4.2 Trigger strategy equilibria, 139
4.3 Extending the folk theorem to finitely repeated games, 143
4.4 2^«7on-equilibria in finite horizon games using trigger strategies, 144
xvi Contents
5 A comparison between trigger strategy equilibria and folk theorem
equilibria 148
6 Applications of repeated games 149
6.1 A model of differentiated products oligopoly, 149
6.2 Oligopoly for large and increasing n, 151
6.3 Trigger strategy equilibria when firms cannot observe prices, 152
6.4 Altruism and repeated games, 154
7 Concluding comments 156
Exercises 157
Notes 158
5 Time-dependent supergames, limited information, and bounded
rationality 159
1 Time-dependent supergames, 160
1.1 The stationary model, 161
1.1.1 Definition of stationary time-dependent supergames and existence
of open-loop equilibria, 161
1.1.2 On the interpretation of a time-dependent supergame as a sequence
of one-shot games, 162
1.2 Existence and stability of a steady-state equilibrium, 164
1.2.1 Existence of a unique steady-state equilibrium, 164
1.2.2 Stability of open-loop equilibria, 165
1.3 Nonstationary supergames and trigger strategy equilibria, 167
1.4 State variables and the partitioned states model, 168
2 A modification of the folk theorem for time-dependent
supergames 170
2.1 The structure of minimax paths, 170
2.2 The level of the per period average minimax payoff, 172
2.3 An additional assumption on the model, 174
2.4 The folk theorem modified for time-dependent games, 175
3 Stochastic games 178
3.1 The transition mechanism and the conditions defining a stochastic game,
178
3.2 Existence of equilibrium, 179
3.2.1 Policies, strategies, and Blackwell s lemma, 179
3.2.2 Transition probabilities and the payoff function when players use
policies, 180
3.2.3 The decision problem of a single player, 181
3.2.4 Equilibrium in the stochastic game, 181
4 Supergames with incomplete information 183
4.1 Description of the game, 183
4.1.1 Assumptions of the model, 184
4.1.2 Information conditions and the players beliefs, 184
4.1.3 Players strategies and the payoff function, 185
4.1.4 Defining the game, 186
4.2 Existence of equilibrium, 187
4.2.1 Markovian beliefs and the definition of a Markovian equilibrium,
187
4.2.2 The existence of a Markovian equilibrium, 188
Contents xvn
4.3 Comments on the model, 189
4.3.1 Extensions, 189
4.3.2 Comparison to Harsanyi s incomplete information model, 189
5 Reputations, rationality, and Nash equilibrium 190
5.1 Selten s chain store paradox, 190
5.1.1 Formulation of the chain store example, 190
5.1.2 Escaping the paradox via incomplete information, 192
5.2 Another view of beneficial irrational behavior, 193
6 Assorted topics relating to noncooperative games 194
6.1 Some restrictions on equilibrium points, 195
6.2 Iterated dominance and rationalizability, 196
7 Applications of time-dependent supergames 197
7.1 A model of oligopoly with capital, 197
7.2 A model of oligopoly with advertising, 200
8 Concluding comments 202
Exercises 203
Notes 203
6 Two-person cooperative games 205
1 Introduction to cooperative games 205
1.1 Comparison of cooperative and noncooperative games, 205
1.2 The various kinds of cooperative games, 207
1.3 Outline of the chapter, 208
2 Fixed threat bargaining: The models of Edgeworth and Nash 209
2.1 Edgeworth two-person bargaining and the core, 209
2.2 The Nash fixed-threat bargaining model, 211
2.2.1 The game and conditions defining the Nash bargaining solution,
212
2.2.2 Characterization and existence of the Nash solution, 214
2.2.3 Zeuthen s anticipation of the Nash solution, 216
3 Other approaches to fixed-threat bargaining 217
3.1 The Raiffa-Kalai-Smorodinsky solution, 217
3.1.1 A description of the Raiffa-Kalai-Smorodinsky solution, 218
3.1.2 Existence of the Raiffa-Kalai-Smorodinsky solution, 221
3.1.3 A comparison of the Raiffa—Kalai-Smorodinsky and Nash
solutions, 223
3.2 Bargaining solutions based on invariance with respect to a reference point,
223
3.2.1 Conditions defining a class of reference points, 223
3.2.2 Existence and uniqueness of solutions to games based on reference
points, 224
3.2.3 Comparison of different solutions by example, 225
3.2.4 Comparison of cooperative solutions with noncooperative games,
227
4 Bargaining over time 228
4.1 The strategy spaces and payoff functions, 228
4.2 Equilibrium and perfect equilibrium outcomes, 229
4.3 Examples of the model of bargaining over time, 232
xviii Contents
5 Variable threat games 234
6 Applications of two-person cooperative games 236
6.1 Labor—management: An example of bilateral monopoly, 236
6.2 An arms race, 237
7 Concluding comments 239
Exercises 240
Notes 240
7 n-person cooperative games with transferable utility 242
1 An overview of the chapter 242
2 Basic concepts for cooperative games 243
2.1 Coalitions, 243
2.2 Characteristic functions, 244
2.2.1 The a and ft characteristic functions, 244
2.2.2 The characteristic function form, 246
2.3 Imputations and essential games, 246
2.4 Domination, 247
3 The core and the £-core 247
3.1 Edgeworth and the core, 247
3.2 The core, 248
3.2.1 Two examples illustrating empty and nonempty cores, 248
3.2.2 Existence of the core, 249
3.3 The e-core, 250
3.4 Simple games and the zero—one normalized form, 251
3.4.1 The zero-one normalized form, 251
3.4.2 Simple games, 252
4 The stable set 254
5 The bargaining set, the kernel, and the nucleolus 255
5.1 The bargaining set, 256
5.1.1 Coalition structures and payoff configurations, 256
5.1.2 Objections and counterobjections, 257
5.1.3 Definition of the bargaining set, 258
5.2 The kernel, 260
5.2.1 Basic definitions of the kernel, 260
5.2.2 The relationship between the kernel and the bargaining set, 261
5.3 The nucleolus, 262
5.3.1 Definition of the nucleolus, 262
5.3.2 Existence and uniqueness of the nucleolus, 263
5.3.3 The nucleolus is contained in the kernel, 264
5.3.4 The nucleolus of ^-equivalent games, 265
5.4 Examples, 266
6 The Shapley value and the Banzhaf index 266
6.1 Description of the Shapley value, 267
6.2 Existence of the Shapley value, 268
6.2.1 The Shapley value for simple games, 268
6.2.2 The Shapley value for superadditive games, 269
6.3 The Banzhaf power index, 270
Contents xjx
7 An application to power in government 271
8 Concluding comments 273
Exercises 274
Notes 274
8 n-person cooperative games without transferable utility 275
1 Introduction to nontransferable utility games 275
1.1 A brief comparison between transferable and nontransferable utility, 275
1.2 Overview of the chapter, 276
2 The characteristic function and other basic tools 276
2.1 Imputations, domination, and the characteristic function, 276
2.2 Balanced games, 278
3 The core 279
3.1 The assumptions and the definition of the core, 279
3.2 The core for a finite-cornered game, 280
3.2.1 A two-matrix representation of finite-cornered games, 281
3.2.2 Defining a basis for each matrix, 283
3.2.3 Scarfs algorithm, 284
3.2.4 Preliminary results, 284
3.2.5 Existence of a nonempty core, 286
3.3 The core of a balanced game, 288
4 The stable set 289
5 The bargaining set, the kernel, and the nucleolus 289
6 Extending the Shapley value to games without transferable
utility 289
6.1 The assumptions of the model and the A-transfer value, 290
6.2 Existence of the A-transfer value, 292
6.3 An example, 293
7 Applications of the core 294
7.1 A model of general economic equilibrium with trade, 294
7.2 Group decision and the core, 297
8 Concluding comments 301
Exercises 302
Notes 302
Appendix: Mathematical notation, definitions, and theorems 304
Answers to exercises 307
References 311
Index 317
|
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV004573607 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:14:30Z |
| institution | BVB |
| isbn | 0195063554 0195070534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002813551 |
| oclc_num | 26260256 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM DE-20 DE-521 DE-634 DE-473 DE-BY-UBG |
| owner_facet | DE-384 DE-19 DE-BY-UBM DE-20 DE-521 DE-634 DE-473 DE-BY-UBG |
| physical | XXII, 322 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Friedman, James W. Verfasser aut Game theory with applications to economics James W. Friedman 2. ed. New York [u.a.] Oxford Univ. Press 1991 XXII, 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Economics, Mathematical Game theory Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Wirtschaftswissenschaften (DE-588)4066528-8 gnd rswk-swf Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Spieltheorie (DE-588)4056243-8 s Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Wirtschaftswissenschaften (DE-588)4066528-8 s 2\p DE-604 Wirtschaftstheorie (DE-588)4079351-5 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002813551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Friedman, James W. Game theory with applications to economics Economics, Mathematical Game theory Wirtschaftsmathematik (DE-588)4066472-7 gnd Spieltheorie (DE-588)4056243-8 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4056243-8 (DE-588)4066528-8 (DE-588)4079351-5 (DE-588)4151278-9 |
| title | Game theory with applications to economics |
| title_auth | Game theory with applications to economics |
| title_exact_search | Game theory with applications to economics |
| title_full | Game theory with applications to economics James W. Friedman |
| title_fullStr | Game theory with applications to economics James W. Friedman |
| title_full_unstemmed | Game theory with applications to economics James W. Friedman |
| title_short | Game theory with applications to economics |
| title_sort | game theory with applications to economics |
| topic | Economics, Mathematical Game theory Wirtschaftsmathematik (DE-588)4066472-7 gnd Spieltheorie (DE-588)4056243-8 gnd Wirtschaftswissenschaften (DE-588)4066528-8 gnd Wirtschaftstheorie (DE-588)4079351-5 gnd |
| topic_facet | Economics, Mathematical Game theory Wirtschaftsmathematik Spieltheorie Wirtschaftswissenschaften Wirtschaftstheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002813551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT friedmanjamesw gametheorywithapplicationstoeconomics |