Twenty lectures on algorithmic game theory:
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
[2016]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 341 Seiten Diagramme |
| ISBN: | 9781107172661 9781316624791 |
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Contents
Preface xi
1 Introduction and Examples 1
l.J The Science of Rule-Making 1
1.2 When Is Selfish Behavior Near-Optimal? 3
1.3 Can Strategic Players Learn an Equilibrium? 6
Notes, Problems, and Exercises 9
2 Mechanism Design Basics 11
2.1 Single-Item Auctions 11
2.2 Sealed-Bid Auctions 12
2.3 First-Price Auctions 12
2.4 Second-Price Auctions and Dominant Strategies 13
2.5 Ideal Auctions 15
2.6 Case Study: Sponsored Search Auctions 16
Notes, Problems, and Exercises 20
3 Myerson’s Lemma 24
3.1 Single-Parameter Environments 24
3.2 Allocation and Payment Rules 26
3.3 Statement of Myerson’s Lemma 26
*3.4 Proof of Myerson’s Lemma 28
3.5 Applying the Payment Formula 31
Notes, Problems, and Exercises 34
4 Algorithmic Mechanism Design 39
4.1 Knapsack Auctions 39
4.2 Algorithmic Mechanism Design 42
4.3 The Revelation Principle 46
Notes, Problems, and Exercises 49
vii
Contents
vm
5 Revenue-Maximizing Auctions
5.1 The Challenge of Revenue Maximization
5.2 Characterization of Optimal DSIC Mechanisms
5.3 Case Study: Reserve Prices in Sponsored Search
*5.4 Proof of Lemma 5.1
Notes, Problems, and Exercises
6 Simple Near-Optimal Auctions
6.1 Optimal Auctions Can Be Complex
6.2 The Prophet Inequality
6.3 Simple Single-Item Auctions
6.4 Prior-Independent Mechanisms
Notes, Problems, and Exercises
7 Multi-Parameter Mechanism Design
7.1 General Mechanism Design Environments
7.2 The VCG Mechanism
7.3 Practical Considerations
Notes, Problems, and Exercises
8 Spectrum Auctions
8.1 Indirect Mechanisms
8.2 Selling Items Separately
8.3 Case Study: Simultaneous Ascending Auctions
8.4 Package Bidding
8.5 Case Study: The 2016 FCC Incentive Auction
Notes, Problems, and Exercises
9 Mechanism Design with Payment Constraints
9.1 Budget Constraints
9.2 The Uniform-Price Multi-Unit Auction
9.3 The Clinching Auction
9.4 Mechanism Design without Money
Notes, Problems, and Exercises
10 Kidney Exchange and Stable Matching
10.1 Case Study: Kidney Exchange
10.2 Stable Matching
*10-3 Further Properties
55
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139
Contents
IX
Notes, Problems, and Exercises 142
11 Selfish Routing and the Price of Anarchy 145
11.1 Selfish Routing: Examples 145
11.2 Main Result: Informal Statement 147
11.3 Main Result: Formal Statement 149
11.4 Technical Preliminaries 152
*11.5 Proof of Theorem 11.2 153
Notes, Problems, and Exercises 156
12 Over-Provisioning and Atomic Selfish Routing 159
12.1 Case Study: Network Over-Provisioning 159
12.2 A Resource Augmentation Bound 161
*12.3 Proof of Theorem 12.1 162
12.4 Atomic Selfish Routing 163
*12.5 Proof of Theorem 12.3 165
Notes, Problems, and Exercises 169
13 Equilibria: Definitions, Examples, and Existence 173
13.1 A Hierarchy of Equilibrium Concepts 173
13.2 Existence of Pure Nash Equilibria 179
13.3 Potential Games 181
Notes, Problems, and Exercises 183
14 Robust Price-of-Anarchy Bounds in Smooth Games 187
*14.1 A Recipe for POA Bounds 187
*14.2 A Location Game 188
*14.3 Smooth Games 194
*14.4 Robust POA Bounds in Smooth Games 195
Notes, Problems, and Exercises 199
15 Best-Case and Strong Nash Equilibria 202
15.1 Network Cost-Sharing Games 202
15.2 The Price of Stability 205
15.3 The POA of Strong Nash Equilibria 208
*15.4 Proof of Theorem 15.3 210
Notes, Problems, and Exercises 213
16 Best-Response Dynamics 216
16.1 Best-Response Dynamics in Potential Games 216
X
Contents
16.2 Approximate PNE in Selfish Routing Games 219
*16.3 Proof of Theorem 16.3 221
*16.4 Low-Cost Outcomes in Smooth Potential Gann's 223
Notes, Problems, and Exercises 226
17 No-Regret Dynamics 230
17.1 Online Decision Making 230
17.2 The Multiplicative Weights Algorithm 234
*17.3 Proof of Theorem 17.6 236
17.4 No Regret and Coarse Correlated Equilibria 239
Notes, Problems, and Exercises 242
18 Swap Regret and the Minimax Theorem 247
18.1 Swap Regret and Correlated Equilibria, 247
*18.2 Proof of Theorem 18.5 249
18.3 The Minimax Theorem for Zero-Sum Games 253
*18.4 Proof of Theorem 18.7 255
Notes, Problems, and Exercises 258
19 Pure Nash Equilibria and VCompleteness 261
19.1 When Are Equilibrium Concepts Tractable? 261
19.2 Local Search Problems 264
19.3 Computing a PNE of a Congestion Game 271
Notes, Problems, and Exercises 276
20 Mixed Nash Equilibria and Completeness 279
20.1 Computing a MNE of a Bimatrix Game 279
20.2 Total MV Search Problems 280
*20.3 WAV: A Syntactic Subclass of 285
*20.4 A Canonical WAV Problem: Sperner’s Lemma 288
*20.5 MNE and WAV 290
20.6 Discussion 293
Notes, Problems, and Exercises 294
The Top 10 List 299
Hints to Selected Exercises and Problems 301
Bibliography 3Q9
Index
329 |
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| spelling | Roughgarden, Tim 1975- (DE-588)1117167275 aut Twenty lectures on algorithmic game theory Tim Roughgarden, Stanford University, California Cambridge Cambridge University Press [2016] © 2016 xiii, 341 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Algorithmische Spieltheorie (DE-588)1133091814 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algorithmische Spieltheorie (DE-588)1133091814 s DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029247642&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Twenty lectures on algorithmic game theory |
| title_auth | Twenty lectures on algorithmic game theory |
| title_exact_search | Twenty lectures on algorithmic game theory |
| title_full | Twenty lectures on algorithmic game theory Tim Roughgarden, Stanford University, California |
| title_fullStr | Twenty lectures on algorithmic game theory Tim Roughgarden, Stanford University, California |
| title_full_unstemmed | Twenty lectures on algorithmic game theory Tim Roughgarden, Stanford University, California |
| title_short | Twenty lectures on algorithmic game theory |
| title_sort | twenty lectures on algorithmic game theory |
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| topic_facet | Algorithmische Spieltheorie Einführung |
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