Simple adaptive strategies: from regret-matching to uncoupled dynamics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ
World Scientific
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | (Hardback) |
| Beschreibung: | XXXVIII, 296 S. |
| ISBN: | 9789814390699 |
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| 245 | 1 | 0 | |a Simple adaptive strategies |b from regret-matching to uncoupled dynamics |c by Sergiu Hart & Andreu Mas-Colell |
| 264 | 1 | |a Hackensack, NJ |b World Scientific |c 2013 | |
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Datensatz im Suchindex
| _version_ | 1804149102066270208 |
|---|---|
| adam_text | CONTENTS
Foreword
vii
Eric
Maskin
Introduction
xvii
Sergiu
Hart
and Andreu
Mas-Colell
Part I Correlated Equilibria
1
Chapter
1.
Existence of Correlated Equilibria
3
Sergiu Hart and David Schmeidler
1
Introduction
.......................... 3
2
Finite Games
......................... 4
3
Infinitely Many Players
.................... 7
4
Infinitely Many Players and Strategies
........... 11
References
.............................. 14
Part II Regret Matching
15
Chapter
2.
A Simple Adaptive Procedure Leading
to Correlated Equilibrium
17
Sergiu Hart and
Andreu Mas-Colell
1
Introduction
.......................... 17
2
The Model and Main Result
................. 20
3
No Regret and
Blackwell
Approachabiłity..........
24
4
Discussion
........................... 30
Appendix. Proof of the Main Theorem
.............. 36
References
.............................. 45
IX
χ
Contents
Chapter
3-
A Generał
Class of Adaptive Strategies
47
Sergiu Hart and
Andreu
Mas-Colell
1
Introduction
.......................... 47
2
The Approachability Problem
................ 49
2.1
Model and Main Theorem
.............. 49
2.2
Proof of Theorem
2.1................. 55
2.3
Counterexamples
................... 59
3
Regrets
............................. 63
3.1
Model and preliminary results
............ 63
3.2
Regret-based strategies
................ 65
3.3
Counterexamples
................... 67
4
Fictitious Play and Better Play
............... 68
4.1
Fictitious play and smooth fictitious play
...... 68
4.2
Better play
....................... 70
5
Discussion and Extensions
.................. 73
5.1
Conditional regrets
.................. 73
5.2
Variable game
..................... 74
5.3
Unknown game
.................... 75
References
.............................. 75
Chapter
4.
A Reinforcement Procedure Leading
to Correlated Equilibrium
77
Sergiu Hart and
Andreu Mas-Colell
1
Introduction
.......................... 77
2
Model and Results
...................... 79
3
Discussion
........................... 84
4
Proof
.............................. 86
References
.............................. 98
Chapter
5.
Regret-Based Continuous-Time Dynamics
99
Sergiu Hart and
Andreu Mas-Colell
1
Introduction
.......................... 99
2
Model
............................. 100
2.1
Preliminaries
...................... 100
2.2
Dynamics
........................ 101
3
Regret-Based Strategies
.................... 102
3.1
Regrets and the
Hannán
set
............. 102
Contents xi
3.2 Potential
functions ..................
102
3.3
Regret-based strategies
................ 103
4
Nash Equilibria
........................ 105
4.1
Two-person zero-sum games
............. 106
4.2
Two-person potential games
............. 106
4.3
Other classes of games
................ 110
5
Correlated Equilibria
..................... 110
6
Remarks
............................ 114
Appendix A. Discrete-Time Dynamics for Potential Games
... 114
Appendix B. Continuous-Time Markov Processes
........ 120
Appendix C. Continuous-Time Approachability
......... 123
References
.............................. 124
Chapter
6.
General Procedures Leading
to Correlated Equilibria
125
Amotz Cahn
1
Introduction
.......................... 125
1.1
Correlated equilibria
................. 126
1.2
Regrets
......................... 127
2
Preliminaries
.......................... 128
2.1
The Hart-Mas-Colell simple procedure
....... 128
2.2
Approachable sets
................... 130
3
Consistency of the
Hart-Mas-Cołełl
Strategy
........ 130
3.1
Introduction
...................... 130
3.2
Main results of this section
.............. 131
3.3
Proof of theorem
.................... 132
3.3.1
Remarks
................... 132
3.3.2
Lemma
.................... 133
3.3.3
Proof of Theorem
3.1............ 134
3.4
Counterexample
.................... 137
4
A General Class of Simple Adaptive Procedures
...... 140
4.1
Introduction
...................... 140
4.2
The model
....................... 141
4.3
Proof of Theorem
4.1................. 143
4.3.1
Steps of the proof
.............. 144
4.4
Proof of Theorem
4.2................. 146
4.5
Conditional smooth fictitious play
.......... 148
References
.............................. 149
xii Contents
Part III Uncoupled Dynamics
151
Chapter
7.
Uncoupled Dynamics Do Not Lead
to Nash Equilibrium
153
Sergm Hart and
Andreu Mas-Colell
1
The Model
........................... 154
2
An Example with a Continuum of Strategies
........ 156
3
An Example with Finitely
Alany
Strategies
......... 158
4
Discussion
........................... 160
Appendix
............................... 162
References
.............................. 162
Chapter
8.
Stochastic Uncoupled Dynamics
and Nash Equilibrium
165
Sergiu Hart and
Andreu Mas-Colell
1
Introduction
.......................... 165
2
The Setting
.......................... 167
3
Pure Equilibria
........................ 168
4
Mixed Equilibria
....................... 173
5
Discussion and Comments
.................. 179
Appendix A. Proof of Theorem
5 ................. 182
References
.............................. 188
Chapter
9.
Uncoupled Automata and Pure
Nash Equilibria
191
Yakov Babichenko
1
Introduction
.......................... 191
2
The Model
........................... 192
2.1
The game
........................ 192
2.2
The dynamic setup
.................. 193
2.3
Automata
....................... 193
2.4
Strategy mappings
................... 194
2.5
The results
....................... 195
3
Two-Player Games
...................... 196
3.1
Stochastic transitions and mixed actions
...... 196
3.2
Stochastic transitions and pure actions
....... 199
3.3
Deterministic transitions and mixed actions
.... 200
Contents xiii
3.4
Deterministic transitions and pure actions
..... 200
4
η
-Player Games {n
> 3)................... 200
4.1
Stochastic transitions, and pure or mixed
actions
......................... 200
4.2
Deterministic transitions and mixed actions
.... 204
4.3
Deterministic transitions and pure actions
..... 205
Appendix A. Proof of Theorem.
6 ................. 209
Appendix B. Proof of Theorem
7.................. 212
References
.............................. 214
Chapter
10.
How Long to Equilibrium?
The Communication Complexity of Uncoupled
Equilibrium Procedures
215
Sergiu Hart and Yishay
Åimisow
1
Introduction
.......................... 215
2
Preliminaries
.......................... 218
2.1
Game-theoretic setting
................ 218
2.2
Communication complexity background
....... 219
2.3
Nash equilibrium procedures
............. 220
3
Pure Equilibria
........................ 222
3.1
Reductions
....................... 223
3.2
Matching Pennies reduction
............. 223
4
Pure Equilibria in a Bayesian Setting·
............ 224
5
Mixed Equilibria
....................... 228
6
Upper Bounds
......................... 232
7
Correlated Equilibria
..................... 233
8
Extensions
........................... 235
8.1
Stochastic procedures
................. 23-5
8.2
Larger action spaces
.................. 236
8.3
Nash approximate equilibria
............. 236
Appendix A. Potential Game Reduction
..............
23T
Appendix B. Correlated Equilibria
................. 243
B.I Modified Jordan games
............. 244
B.2 Bayesian setting
................. 244
B.3 Correlated approximate equilibria
....... 246
References
.............................. 247
xiv Contents
Part IV
Dynamics
and Equilibria
251
Chapter
11.
Adaptive Heuristics
253
Sergiu Hart
1
Introduction
.......................... 253
2
A Rational Classification of Dynamics
........... 254
2.1
Learning dynamics
.................. 254
2.2
Evolutionary dynamics
................ 255
2.3
Adaptive heuristics
.................. 256
2.4
Degrees of rationality
................. 256
3
Preliminaries
.......................... 257
4
Regret Matching
........................ 258
4.1
Joint distribution of play
............... 261
5
Behavioral Aspects
...................... 262
6
Correlated Equilibria
..................... 263
7
Generalized Regret Matching
................. 266
8
Uncoupled Dynamics
..................... 267
9
Summary
............................ 269
9.1
Directions of research
................. 270
10
Additional Results
...................... 271
10.1
Hannán
consistency and the
Hannán
set
...... 271
10.2
Regret eigenvector strategies
............. 273
10.3
Generalized regret matching strategies
....... 274
10.4
Fictitious play and variants
.............. 275
10.5
The case of the unknown game
............ 275
10.6
Continuous time
.................... 276
10.7
Computing regrets
................... 276
10.8
Convergence
...................... 277
10.9
A summary of strategies
............... 277
10.10
Variable game
..................... 279
10.11
The set of correlated equilibria
............ 279
Appendix. Approachability
..................... 279
References
.............................. 283
Chapter
12.
Nash Equilibrium and Dynamics
289
S&rgmt Hart
1
Nash Equilibrium
....................... 289
2
Non-cooperative Games
.................... 289
Contents xv
3
The Nash
Program .....................
290
4
The Mass-Action Interpretation
.............. 290
5
The Rational Interpretation
................ 291
6
Dynamics
........................... 291
7
Correlated Equilibrium
.................... 292
8
Summary
............................ 292
References
.............................. 293
Index
295
|
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| author | Hart, Sergiu Mas-Colell, Andreu 1944- |
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| id | DE-604.BV040135597 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:17:41Z |
| institution | BVB |
| isbn | 9789814390699 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024992667 |
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| physical | XXXVIII, 296 S. |
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| spelling | Hart, Sergiu Verfasser (DE-588)170007529 aut Simple adaptive strategies from regret-matching to uncoupled dynamics by Sergiu Hart & Andreu Mas-Colell Hackensack, NJ World Scientific 2013 XXXVIII, 296 S. txt rdacontent n rdamedia nc rdacarrier (Hardback) Spieltheorie (DE-588)4056243-8 gnd rswk-swf Adaptives Verfahren (DE-588)4310560-9 gnd rswk-swf Nash-Gleichgewicht (DE-588)4171190-7 gnd rswk-swf Gleichgewicht (DE-588)4121372-5 gnd rswk-swf Gleichgewicht (DE-588)4121372-5 s Spieltheorie (DE-588)4056243-8 s Adaptives Verfahren (DE-588)4310560-9 s DE-604 Nash-Gleichgewicht (DE-588)4171190-7 s Mas-Colell, Andreu 1944- Verfasser (DE-588)130591297 aut Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024992667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hart, Sergiu Mas-Colell, Andreu 1944- Simple adaptive strategies from regret-matching to uncoupled dynamics Spieltheorie (DE-588)4056243-8 gnd Adaptives Verfahren (DE-588)4310560-9 gnd Nash-Gleichgewicht (DE-588)4171190-7 gnd Gleichgewicht (DE-588)4121372-5 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4310560-9 (DE-588)4171190-7 (DE-588)4121372-5 |
| title | Simple adaptive strategies from regret-matching to uncoupled dynamics |
| title_auth | Simple adaptive strategies from regret-matching to uncoupled dynamics |
| title_exact_search | Simple adaptive strategies from regret-matching to uncoupled dynamics |
| title_full | Simple adaptive strategies from regret-matching to uncoupled dynamics by Sergiu Hart & Andreu Mas-Colell |
| title_fullStr | Simple adaptive strategies from regret-matching to uncoupled dynamics by Sergiu Hart & Andreu Mas-Colell |
| title_full_unstemmed | Simple adaptive strategies from regret-matching to uncoupled dynamics by Sergiu Hart & Andreu Mas-Colell |
| title_short | Simple adaptive strategies |
| title_sort | simple adaptive strategies from regret matching to uncoupled dynamics |
| title_sub | from regret-matching to uncoupled dynamics |
| topic | Spieltheorie (DE-588)4056243-8 gnd Adaptives Verfahren (DE-588)4310560-9 gnd Nash-Gleichgewicht (DE-588)4171190-7 gnd Gleichgewicht (DE-588)4121372-5 gnd |
| topic_facet | Spieltheorie Adaptives Verfahren Nash-Gleichgewicht Gleichgewicht |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024992667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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