Mathematical game theory and applications:
"Provides introductory material to game theory, including bargaining, parlour games, sport, networking games and dynamic games"..
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chichester
Wiley
2014
|
| Ausgabe: | 1. publ. |
| Schlagwörter: | |
| Links: | http://catalogimages.wiley.com/images/db/jimages/9781118899625.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027514002&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | "Provides introductory material to game theory, including bargaining, parlour games, sport, networking games and dynamic games".. |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | XIV, 414 S. graph. Darst. |
| ISBN: | 9781118899625 |
Internformat
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| 245 | 1 | 0 | |a Mathematical game theory and applications |c Vladimir Mazalov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2014 | |
| 300 | |a XIV, 414 S. |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references and index | ||
| 520 | |a "Provides introductory material to game theory, including bargaining, parlour games, sport, networking games and dynamic games".. | ||
| 650 | 7 | |a MATHEMATICS / Game Theory |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Applied |2 bisacsh | |
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| 650 | 4 | |a MATHEMATICS / Game Theory | |
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Datensatz im Suchindex
| _version_ | 1819352862812012544 |
|---|---|
| adam_text | Titel: Mathematical game theory and applications
Autor: Mazalov, Vladimir V
Jahr: 2014
Contents
Preface xi
Introduction xiii
1 Strategie-Form Two-Player Games 1
Introduction 1
1.1 The Coumot Duopoly 2
1.2 Continuous Improvement Procedure 3
1.3 The Bertrand Duopoly 4
1.4 The Hotelling Duopoly 5
1.5 The Hotelling Duopoly in 2D Space 6
1.6 The Stackelberg Duopoly 8
1.7 Convex Games 9
1.8 Some Examples of Bimatrix Games 12
1.9 Randomization 13
1.10 Games 2 X 2 16
1.11 Games 2 Xn and mx 2 18
1.12 The Hotelling Duopoly in 2D Space with Non-Uniform Distribution
of Buyers 20
1.13 Location Problem in 2D Space 25
Exercises 26
2 Zero-Sum Games 28
Introduction 28
2.1 Minimax and Maximin 29
2.2 Randomization 31
2.3 Games with Discontinuous Payoff Functions 34
2.4 Convex-Concave and Linear-Convex Games 37
2.5 Convex Games 39
2.6 Arbitration Procedures 42
2.7 Two-Point Discrete Arbitration Procedures 48
2.8 Three-Point Discrete Arbitration Procedures with Interval Constraint 53
vi CONTENTS
2.9 General Discrete Arbitration Procedures 56
Exercises 62
3 Non-Cooperative Strategie-Form /(-Player Games 64
Introduction 64
3.1 Convex Games. The Cournot Oligopoly 65
3.2 Polymatrix Games 66
3.3 Potential Games 69
3.4 Congestion Games 73
3.5 Player-Specific Congestion Games 75
3.6 Auctions 78
3.7 Wars of Attrition 82
3.8 Duels, Truels, and Other Shooting Accuracy Contests 85
3.9 Prediction Games 88
Exercises 93
4 Extensive-Form «-Player Games 96
Introduction 96
4.1 Equilibrium in Games with Complete Information 97
4.2 Indifferent Equilibrium 99
4.3 Games with Incomplete Information 101
4.4 Total Memory Games 105
Exercises 108
111
111
112
113
116
118
118
122
127
129
130
132
134
136
136
137
139
145
145
147
152
5 Parlor Games and Sport Games
Introduction
5.1 Poker. A Game-Theoretic Model
5.1.1 Optimal Strategies
5.1.2 Some Features of Optimal Behavior in Poker
5.2 The Poker Model with Variable Bets
5.2.1 The Poker Model with Two Bets
5.2.2 The Poker Model with n Bets
5.2.3 The Asymptotic Properties of Strategies in the Poker Model with
Variable Bets
5.3 Preference. A Game-Theoretic Model
5.3.1 Strategies and Payoff Function
5.3.2 Equilibrium in the Case of ^A~B
M B+C ~ 2(A+C)
5.3.3 Equilibrium in the Case of
n 2(A+C) B+C
5.3.4 Some Features of Optimal Behavior in Preference
5.4 The Preference Model with Cards Play
5.4.1 The Preference Model with Simultaneous Moves
5.4.2 The Preference Model with Sequential Moves
5.5 Twenty-One. A Game-Theoretic Model
5.5.1 Strategies and Payoff Functions
5.6 Soccer. A Game-Theoretic Model of Resource Allocation
Exercises
CONTENTS vii
6 Negotiation Models 155
Introduction 155
6.1 Models of Resource Allocation 155
6.1.1 Cake Cutting 155
6.1.2 Principles of Fair Cake Cutting 157
6.1.3 Cake Cutting with Subjective Estimates by Players 158
6.1.4 Fair Equal Negotiations 160
6.1.5 Strategy-Proofness 161
6.1.6 Solution with the Absence of Envy 161
6.1.7 Sequential Negotiations 163
6.2 Negotiations of Time and Place of a Meeting 166
6.2.1 Sequential Negotiations of Two Players 166
6.2.2 Three Players 168
6.2.3 Sequential Negotiations. The General Case 170
6.3 Stochastic Design in the Cake Cutting Problem 171
6.3.1 The Cake Cutting Problem with Three Players 172
6.3.2 Negotiations of Three Players with Non-Uniform Distribution 176
6.3.3 Negotiations of n Players 178
6.3.4 Negotiations of n Players. Complete Consent 181
6.4 Models of Tournaments 182
6.4.1 A Game-Theoretic Model of Tournament Organization 182
6.4.2 Tournament for Two Projects with the Gaussian Distribution 184
6.4.3 The Correlation Effect 186
6.4.4 The Model of a Tournament with Three Players and
Non-Zero Sum 187
6.5 Bargaining Models with Incomplete Information 190
6.5.1 Transactions with Incomplete Information 190
6.5.2 Honest Negotiations in Conclusion of Transactions 193
6.5.3 Transactions with Unequal Forces of Players 195
6.5.4 The Offer-Counteroffer Transaction Model 196
6.5.5 The Correlation Effect 197
6.5.6 Transactions with Non-Uniform Distribution of
Reservation Prices 199
6.5.7 Transactions with Non-Linear Strategies 202
6.5.8 Transactions with Fixed Prices 207
6.5.9 Equilibrium Among n-Threshold Strategies 210
6.5.10 Two-Stage Transactions with Arbitrator 218
6.6 Reputation in Negotiations 221
6.6.1 The Notion of Consensus in Negotiations 221
6.6.2 The Matrix Form of Dynamics in the Reputation Model 222
6.6.3 Information Warfare 223
6.6.4 The Influence of Reputation in Arbitration Committee.
Conventional Arbitration 224
6.6.5 The Influence of Reputation in Arbitration Committee.
Final-Offer Arbitration 225
6.6.6 The Influence of Reputation on Tournament Results 226
Exercises 228
viii CONTENTS
7 Optimal Stopping Games 230
Introduction 230
7.1 Optimal Stopping Game: The Case of Two Observations 231
7.2 Optimal Stopping Game: The Case of Independent Observations 234
7.3 The Game rN(G) Under N 3 237
7.4 Optimal Stopping Game with Random Walks 241
7.4.1 Spectra of Strategies: Some Properties 243
7.4.2 Equilibrium Construction 245
7.5 Best Choice Games 250
7.6 Best Choice Game with Stopping Before Opponent 254
7.7 Best Choice Game with Rank Criterion. Lottery 259
7.8 Best Choice Game with Rank Criterion. Voting 264
7.8.1 Solution in the Case of Three Players 265
7.8.2 Solution in the Case of m Players 268
7.9 Best Mutual Choice Game 269
7.9.1 The Two-Shot Model of Mutual Choice 270
7.9.2 The Multi-Shot Model of Mutual Choice 272
Exercises 276
8 Cooperative Games 278
Introduction 278
8.1 Equivalence of Cooperative Games 278
8.2 Imputations and Core 281
8.2.1 The Core of the Jazz Band Game 282
8.2.2 The Core of the Glove Market Game 283
8.2.3 The Core of the Scheduling Game 284
8.3 Balanced Games 285
8.3.1 The Balance Condition for Three-Player Games 286
8.4 The r-Value of a Cooperative Game 286
8.4.1 The r-Value of the Jazz Band Game 289
8.5 Nucleolus 289
8.5.1 The Nucleolus of the Road Construction Game 291
8.6 The Bankruptcy Game 293
8.7 The Shapley Vector 298
8.7.1 The Shapley Vector in the Road Construction Game 299
8.7.2 Shapley s Axioms for the Vector 300
8.8 Voting Games. The Shapley-Shubik Power Index and the Banzhaf Power
Index 302
8.8.1 The Shapley-Shubik Power Index for Influence Evaluation in the
14th Bundestag 305
8.8.2 The Banzhaf Power Index for Influence Evaluation in the 3rd State
Duma 307
8.8.3 The Holler Power Index and the Deegan-Packel Power Index for
Influence Evaluation in the National Diet (1998) 309
8.9 The Mutual Influence of Players. The Hoede-Bakker Index 309
Exercises 312
CONTENTS
9 Network Games 314
Introduction 314
9.1 The KP-Model of Optimal Routing with Indivisible Traffic. The Price
of Anarchy 315
9.2 Pure Strategy Equilibrium. Braess s Paradox 316
9.3 Completely Mixed Equilibrium in the Optimal Routing Problem with
Inhomogeneous Users and Homogeneous Channels 319
9.4 Completely Mixed Equilibrium in the Optimal Routing Problem with
Homogeneous Users and Inhomogeneous Channels 320
9.5 Completely Mixed Equilibrium: The General Case 322
9.6 The Price of Anarchy in the Model with Parallel Channels and
Indivisible Traffic 324
9.7 The Price of Anarchy in the Optimal Routing Model with Linear Social
Costs and Indivisible Traffic for an Arbitrary Network 328
9.8 The Mixed Price of Anarchy in the Optimal Routing Model with Linear
Social Costs and Indivisible Traffic for an Arbitrary Network 332
9.9 The Price of Anarchy in the Optimal Routing Model with Maximal
Social Costs and Indivisible Traffic for an Arbitrary Network 335
9.10 The Wardrop Optimal Routing Model with Divisible Traffic 337
9.11 The Optimal Routing Model with Parallel Channels. The Pigou Model.
Braess s Paradox 340
9.12 Potential in the Optimal Routing Model with Indivisible Traffic for an
Arbitrary Network 341
9.13 Social Costs in the Optimal Routing Model with Divisible Traffic for
Convex Latency Functions 343
9.14 The Price of Anarchy in the Optimal Routing Model with Divisible
Traffic for Linear Latency Functions 344
9.15 Potential in the Wardrop Model with Parallel Channels for
Player-Specific Linear Latency Functions 346
9.16 The Price of Anarchy in an Arbitrary Network for Player-Specific Linear
Latency Functions 349
Exercises 351
10 Dynamic Games 352
Introduction 352
10.1 Discrete-Time Dynamic Games 353
10.1.1 Nash Equilibrium in the Dynamic Game 353
10.1.2 Cooperative Equilibrium in the Dynamic Game 356
10.2 Some Solution Methods for Optimal Control Problems with
One Player 358
10.2.1 The Hamilton-Jacobi-Bellman Equation 358
10.2.2 Pontryagin s Maximum Principle 361
10.3 The Maximum Principle and the Bellman Equation in Discrete- and
Continuous-Time Games of N Players 368
10.4 The Linear-Quadratic Problem on Finite and Infinite Horizons 375
X CONTENTS
10.5 Dynamic Games in Bioresource Management Problems. The Case of
Finite Horizon 378
10.5.1 Nash-Optimal Solution 379
10.5.2 Stackelberg-Optimal Solution 381
10.6 Dynamic Games in Bioresource Management Problems. The Case of
Infinite Horizon 383
10.6.1 Nash-Optimal Solution 1 383
10.6.2 Stackelberg-Optimal Solution 385
10.7 Time-Consistent Imputation Distribution Procedure 388
10.7.1 Characteristic Function Construction and Imputation
Distribution Procedure 390
10.7.2 Fish Wars. Model without Information 393
10.7.3 The Shapley Vector and Imputation Distribution Procedure 398
10.7.4 The Model with Informed Players 399
Exercises 402
References 405
Index
411
|
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| illustrated | Illustrated |
| indexdate | 2024-12-20T17:01:33Z |
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| isbn | 9781118899625 |
| language | English |
| lccn | 014019649 |
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| physical | XIV, 414 S. graph. Darst. |
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| subject_GND | (DE-588)4056243-8 |
| title | Mathematical game theory and applications |
| title_auth | Mathematical game theory and applications |
| title_exact_search | Mathematical game theory and applications |
| title_full | Mathematical game theory and applications Vladimir Mazalov |
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| title_short | Mathematical game theory and applications |
| title_sort | mathematical game theory and applications |
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