An introductory course on mathematical game theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc. [u.a.]
2010
Madrid |
| Series: | Graduate studies in mathematics
115 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 324 S. graph. Darst. |
| ISBN: | 9780821851517 |
Staff View
MARC
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| 100 | 1 | |a González-Díaz, Julio |d 1978- |e Verfasser |0 (DE-588)142122793 |4 aut | |
| 245 | 1 | 0 | |a An introductory course on mathematical game theory |c Julio González-Díaz ; Ignacio García-Jurado ; M. Gloria Fiestras-Janeiro |
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| 264 | 1 | |a Madrid | |
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Preface
xi
Chapter
1.
Introduction to Decision Theory
1
§1.1.
Preliminaries
1
§1.2.
Ordinal Utility
3
§1.3.
Linear Utility
6
Chapter
2.
Strategic Games
13
§2.1.
Introduction to Strategic Games
13
§2.2.
Nash Equilibrium in Strategic Games
18
§2.3.
Two-Player Zero-Sum Games
24
§2.4.
Mixed Strategies in Finite Games
28
§2.5.
Bimatrix Games
31
§2.6.
Matrix Games
37
§2.7.
Algorithms for Matrix Games
43
§2.8.
Matrix Games and Linear Programming
52
§2.9.
Refinements of Nash Equilibrium in Finite Games
59
§2.10.
A Basic Model of Knowledge
72
§2.11.
Correlated Equilibrium
75
§2.12.
On the
Epistemic
Foundations of the Different Solution
Concepts for Strategic Games
80
vii
viii Contents
§2.13.
Fixed-Point Theorems
87
§2.14.
On Extreme Points and Convex Sets: Krein-Milman Theorem
91
Exercises of Chapter
2 94
Chapter
3.
Extensive Games
99
§3.1.
Introduction to Extensive Games
99
§3.2.
Strategies in Extensive Games: Mixed Strategies vs. Behavior
Strategies
104
§3.3.
Nash Equilibrium in Extensive Games
110
§3.4.
Subgame
Perfect Equilibrium
117
§3.5.
Sequential Equilibrium
124
§3.6.
Further Refinements
132
§3.7.
Repeated Games
146
Exercises of Chapter
3 159
Chapter
4.
Games with Incomplete Information
163
§4.1.
Incomplete Information: Introduction and Modeling
163
§4.2.
Bayesian Games and Bayesian Nash Equilibrium
165
§4.3.
The Chain Store Paradox in Perspective
171
§4.4.
A First Application of Bayesian Games: Auctions
178
§4.5.
A Second Application of Bayesian Games: Mechanism Design
and the Revelation Principle
186
§4.6.
Extensive Games with Incomplete Information: Multistage
Games and Perfect Bayesian Equilibrium
190
§4.7.
An Outline of Harsanyi's Approach
197
Exercises of Chapter
4 200
Chapter
5.
Cooperative Games
203
§5.1.
Introduction to Cooperative Games
203
§5.2. Nontransferable
Utility Games
204
§5.3.
Bargaining
206
§5.4.
Transferable Utility Games
214
§5.5.
The Core and Related Concepts
217
§5.6.
The Shapley Value
226
Contents ix
§5.7.
The Nucleolus
231
§5.8.
Convex
Games 235
§5.9.
Noncooperative
Models in
Cooperative Game
Theory:
Implementation
Theory
238
§5.10. Airport Problems
and Airport Games
256
§5.11.
Bankruptcy Problems and Bankruptcy Games
261
§5.12.
Voting Problems and Voting Games: Power Indices
270
§5.13.
Cooperation in Operations Research Models
275
Exercises of Chapter
5 289
Bibliography
293
Notations
309
Index of Authors
311
Index of Solution Concepts
315
Subject Index
317 |
| any_adam_object | 1 |
| author | González-Díaz, Julio 1978- García-Jurado, Ignacio Fiestras-Janeiro, M. Gloria 1962- |
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| author_role | aut aut aut |
| author_sort | González-Díaz, Julio 1978- |
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| building | Verbundindex |
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| classification_tum | MAT 920f |
| ctrlnum | (OCoLC)695842244 (DE-599)GBV617208115 |
| 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 | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-07-31T00:23:06Z |
| institution | BVB |
| isbn | 9780821851517 |
| language | English |
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| publisher | American Math. Soc. [u.a.] |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | González-Díaz, Julio 1978- Verfasser (DE-588)142122793 aut An introductory course on mathematical game theory Julio González-Díaz ; Ignacio García-Jurado ; M. Gloria Fiestras-Janeiro Providence, RI American Math. Soc. [u.a.] 2010 Madrid XIII, 324 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 115 Spieltheorie (DE-588)4056243-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Spieltheorie (DE-588)4056243-8 s DE-604 García-Jurado, Ignacio Verfasser (DE-588)142299804 aut Fiestras-Janeiro, M. Gloria 1962- Verfasser (DE-588)171515188 aut Erscheint auch als Online-Ausgabe 978-1-4704-1177-0 Graduate studies in mathematics 115 (DE-604)BV009739289 115 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020480797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | González-Díaz, Julio 1978- García-Jurado, Ignacio Fiestras-Janeiro, M. Gloria 1962- An introductory course on mathematical game theory Graduate studies in mathematics Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4123623-3 |
| title | An introductory course on mathematical game theory |
| title_auth | An introductory course on mathematical game theory |
| title_exact_search | An introductory course on mathematical game theory |
| title_full | An introductory course on mathematical game theory Julio González-Díaz ; Ignacio García-Jurado ; M. Gloria Fiestras-Janeiro |
| title_fullStr | An introductory course on mathematical game theory Julio González-Díaz ; Ignacio García-Jurado ; M. Gloria Fiestras-Janeiro |
| title_full_unstemmed | An introductory course on mathematical game theory Julio González-Díaz ; Ignacio García-Jurado ; M. Gloria Fiestras-Janeiro |
| title_short | An introductory course on mathematical game theory |
| title_sort | an introductory course on mathematical game theory |
| topic | Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Spieltheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020480797&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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