Repeated games:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2015
|
| Series: | Econometric society monographs
55 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027674257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXVIII, 567 S. |
| ISBN: | 9781107030206 9781107662636 |
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MARC
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| 245 | 1 | 0 | |a Repeated games |c Jean-Francois Mertens ; Sylvain Sorin ; Shmuel Zamir |
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Record in the Search Index
| _version_ | 1819250113064730624 |
|---|---|
| adam_text | Contents
List of Figures page xiii
Foreword by Robert J. Aumann XV
Preface xxi
A ckno wl iedgmen ts xxiii
Presentation of the Content XXV
Part A: Background Material
I Basic Results on Normal Form Games 3
1.1 The Minmax Theorem 4
1.1 .a Definitions and Notations 4
1.1 .b A Basic Theorem 5
1.1.c Convexity 6
1.1 .d Mixed Strategies 6
1.1 .e Note on the Separation Theorem 9
Exercises 10
1.2 Complements to the Minmax Theorem 15
I.2.a The Topology on S 16
I.2.b Lack of Continuity: Regularization 16
I.2.c Lack of Compactness: Approximation 19
I.2.d Measurability: Symmetric Case 20
I.2.e Pure Optimal Strategies 23
Exercises 24
1.3 The Minmax Theorem for Ordered Fields 31
Exercises 32
IA Equilibrium Points 45
Exercises 45
vii
58
58
58
60
62
64
90
90
95
96
101
101
103
105
108
110
118
121
123
123
124
135
138
151
153
153
154
158
161
166
171
171
172
173
174
176
177
178
Contents
Basic Results on Extensive Form Games
11.1 The Extensive Form
II. 1.a Definitions
II. 1 .b The Finite Case
IIЛ.с A Measurable Setup
Exercises
11.2 Infinite Games
11.2. a Infinite Games with Perfect Information
11.2. b Remarks: Infinite Games without Perfect
Information
Exercises
И.З Correlated Equilibria and Extensions
11.3. а Correlated Equilibria
11.3. Ь Multistage Games, Extensive Form Correlated
Equilibria
11.3. C Communication Equilibria
11.3. d Finite Games
Exercises
II. 4 Vector Payoffs
Exercises
The Belief Space
III. ] The Universal Belief Space
III. 1 .a States of the World and Types
III. 1 .b Belief Subspaces
111.2 Consistency and Common Knowledge
111.3 An Approximation Theorem
111.4 Games with Incomplete Information
111.4. a The Model
111.4. b Two-Person Zero-Sum Case
111.4. C “Approachability” in One-Shot Games
111.4. d Concavification and Convex і fication
Exercises
General Model of Repeated Games
IV. 1 The Model
IV. 1 .a States, Signals, and Transitions
IV. 1 .b Strategies and Payoffs
IV. 1 .c Zero-Sum Case
IV. 1 d Non-Zero-Sum Case
IV. 1 .e Stochastic Games and Games with Incomplete
Information
Exercises
Contents
IX
IV.2 Equivalent Representations 178
IV.2.a Simple Transformations 178
IV,2.b A Deterministic Framework 180
IV.2.C A Combinatorial Form 182
IV.3 Recursive Structure 183
IV.3.a A Canonical Representation 183
IV.3.b The Recursive Formula 184
Exercises 187
IV.4 Supergames 190
IV.4.a Standard Signaling 190
IV.4.b Partial Monitoring 193
Exercises 201
1V.5 Recursive Games 205
Exercises 208
Part B: The Central Results
Full Information on One Side 215
V.I General Properties 215
V.2 Elementary Tools and the Full Monitoring Case 217
V.2.a Posterior Probabilities and Non-Revealing
Strategies 218
V.2.b iim vn(p) and vx(p) 222
V.2.c Approachability Strategy 224
V.3 The General Case 225
V.3.a Iim vn(p) and vx(p) 226
V.3.b The Non-Revealing Game 227
V.3.C Study of Voo(p) 230
V.3.d Optimal Strategy for the Uninformed Player 233
V.3.e Approachability 239
V.3.f The Errors E+ in the Approachability Theorem 248
v.3.g Implications of the Approachability Theorem 257
V.3.h A Continuum of Types 259
V.3.i Implications of the Approachability Theorem
(continued) 270
V.4 The Role of the Normal Distribution 279
V.4. a The Heuristics of the Result 282
V.4.b Proof of Theorem V.4.1 284
V.4.C More General Results 291
V.5 The Speed of Convergence of vn 294
V.5.a State-Independent Signaling 294
V.5.b State-Dependent Signaling 296
V.5.C Games with Error Term ~ (In n)/n 299
X
Contents
Exercises 302
V. 6 Appendix 316
VI Incomplete Information on Two Sides 326
VI. 1 Introduction 326
VI.2 General Preparations 326
VI.2,a Definitions and Notations 326
VI.2.b Preliminary Results 328
V1.2.C An Auxiliary Game 330
VI.2.d The Probabilistic Structure 331
VI.3 The Infinite Game 339
VI.3.a Minmax and Maxmin 339
VI. 3.b Approachability 345
VI.4 The Limit of vn(p) 357
VI.5 The Functional Equations: Existence and Uniqueness 362
VI.6 On the Speed of Convergence of vn 365
VI. 7 Examples 366
Exercises 379
VII Stochastic Games 392
VII. 1 Discounted Case 392
VII. 1.a Zero-Sum Case 393
VII. I.b Non-Zero-Sum Case (Finite) 395
VII. 1 .c Non-Zero-Sum Case (General) 396
VII.2 Asymptotic Analysis, Finite Case: The Algebraic Aspect 399
Vil.3 e-Optimal Strategies in the Undiscounted Game 401
VII.3.a The Theorem 401
VII.3.b Proof of the Theorem under H(Ly A, A, 8) 402
VII.3.C End of the Proof 404
VII.3.d Particular Cases (Finite Games, Two-Person
Zero-Sum) 407
VII.4 The Two-Person Non-Zero-Sum Undiscounted Case 410
VII.4.a An Example 410
VII. 4.b Games with Absorbing States 413
Exercises 416
VII. 5 Reminder about Dynamic Programming 424
Exercises 425
Part C: Further Developments
VIII Extensions and Further Results 431
VIII. 1 Incomplete Information: The Symmetric Case 431
VIII.2 Games with No Signals 433
VIII. 2.a Presentation 433
Contents
XI
Vili.2.b An Auxiliary Game 434
VIII.2.c Minmax and Maxmin 436
VIII.2.d lim vn and iim vx 443
VIII. 3 A Game with State-Dependent Signaling Matrices 446
VIII.3.a Introduction and Notation 446
VIII.3.b Minmax 447
VIIL3.C Maxmin 452
Vili.4 Stochastic Games with Incomplete Information 457
VIII.4.a A First Class 458
VIII. 4.b A Second Class 464
Vili.4.C Minmax: Two More Examples 469
Exercises 474
IX Non-Zero-Sum Games with Incomplete Information 481
IX. 1 Equilibria in Too 481
IX. La Existence 481
IX.l.b Characterization (Hart, 1985) 484
IX.2 Bi-Convexity and Bi-Martingales 492
IX.3 Correlated Equilibrium and Communication
Equilibrium 495
IX.3.a Communication Equilibrium 496
IX.3.b “Noisy Channels”; Characterization of D,
(0 r oc) 504
Exercises 507
Appendix A: Reminder about Analytic Sets 511
A.l Notation 511
A.2 Souslin Schemes 511
A.3 X-Analytic and X-Lusin Spaces 512
A.4 Capacities 513
A.5 Polish, Analytic, and Lusin Spaces 515
A.6 Blackwell Spaces and Standard Borei Spaces 517
A.7 Spaces of Subsets 518
A. 8 Some Harder Results 519
A.9 Complements to Measure Theory 520
АЛ0 *-Radon Spaces 522
Appendix B: Historical Notes 526
Chapter I 526
Chapter II 527
Chapter III 528
Chapter IV 529
Chapter V 529
Chapter VI 530
Contents
xii
Chapter VII 530
Chapter VIII 531
Chapter IX 531
Appendix C: Bibliography 533
Appendix D: Updates 548
D.l Complements and Advances 548
D.2 Complementary Bibliography 552
Author Index 561
Subject Index 564
|
| any_adam_object | 1 |
| author | Mertens, Jean-François 1946-2012 Sorin, Sylvain Zamir, Shemuʾel 1939- |
| author_GND | (DE-588)17005862X (DE-588)17070923X (DE-588)170839575 |
| author_facet | Mertens, Jean-François 1946-2012 Sorin, Sylvain Zamir, Shemuʾel 1939- |
| author_role | aut aut aut |
| author_sort | Mertens, Jean-François 1946-2012 |
| author_variant | j f m jfm s s ss s z sz |
| building | Verbundindex |
| bvnumber | BV042236037 |
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| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV042236037 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:05:30Z |
| institution | BVB |
| isbn | 9781107030206 9781107662636 |
| language | English |
| lccn | 2014006953 |
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| physical | XXVIII, 567 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Econometric society monographs |
| series2 | Econometric society monographs |
| spellingShingle | Mertens, Jean-François 1946-2012 Sorin, Sylvain Zamir, Shemuʾel 1939- Repeated games Econometric society monographs Spieltheorie (DE-588)4056243-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4057630-9 |
| title | Repeated games |
| title_auth | Repeated games |
| title_exact_search | Repeated games |
| title_full | Repeated games Jean-Francois Mertens ; Sylvain Sorin ; Shmuel Zamir |
| title_fullStr | Repeated games Jean-Francois Mertens ; Sylvain Sorin ; Shmuel Zamir |
| title_full_unstemmed | Repeated games Jean-Francois Mertens ; Sylvain Sorin ; Shmuel Zamir |
| title_short | Repeated games |
| title_sort | repeated games |
| topic | Spieltheorie (DE-588)4056243-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Spieltheorie Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027674257&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018129 |
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