An introductory course on mathematical game theory and applications:
Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. T...
Gespeichert in:
Hauptverfasser: | , , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2023]
|
Ausgabe: | Second edition |
Schriftenreihe: | Graduate studies in mathematics
238 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Zusammenfassung: | Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. In this second edition, the content on cooperative games is considerably strengthened, with a new chapter on applications of cooperative games and operations research, including some material on computational aspects and applications outside academia. |
Beschreibung: | Includes bibliographical references (pages 371-394) and index Preface:"The present book is an extended edition of A Introductory Course on Mathematiccal Game Theory..." |
Beschreibung: | xiv, 415 Seiten Diagramme |
ISBN: | 9781470467968 9781470475635 |
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490 | 1 | |a Graduate studies in mathematics |v 238 | |
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520 | 3 | |a Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. In this second edition, the content on cooperative games is considerably strengthened, with a new chapter on applications of cooperative games and operations research, including some material on computational aspects and applications outside academia. | |
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Datensatz im Suchindex
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adam_text |
Contents Preface Chapter 1. Introduction to Decision Theory xi 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 73 §2.11 . Correlated Equilibrium 76 §2.12 . On the Epistemic Foundations of the Different Solution Concepts for Strategic Games 81 vii
Contents viii §2.13 . Fixed-Point Theorems §2.14 . Extreme Points and Convex Sets: Krein-Milman Theorem Exercises of Chapter 2 Chapter 3. Extensive Games §3.1 . Introduction to Extensive Games 88 92 95 101 101 §3.2 . Strategies in Extensive Games: Mixed Strategies vs. Behavior Strategies 106 §3.3 . Nash Equilibrium in Extensive Games 112 §3.4 . Subgame Perfect Equilibrium 119 §3.5 . Sequential Equilibrium 127 §3.6 . Further Refinements 134 §3.7 . Repeated Games 148 Exercises of Chapter 3 160 Chapter 4. Games with Incomplete Information 165 §4.1 . Incomplete Information: Introduction and Modeling 165 §4.2 . Bayesian Games and Bayesian Nash Equilibrium 167 §4.3 . The Chain Store Paradox in Perspective 173 §4.4 . A First Application of Bayesian Games: Auctions 180 §4.5 . A Second Application of Bayesian Games: Mechanism Design and the Revelation Principle 188 §4.6 . Extensive Games with Incomplete Information: Multistage Games and Perfect Bayesian Equilibrium 192 §4.7 . An Outline of Harsanyi's Approach 199 Exercises of Chapter 4 202 Chapter 5. Fundamentals of Cooperative Games 205 §5.1 . Introduction to Cooperative Games 205 §5.2 . Nontransferable Utility Games 206 §5.3 . Bargaining 208 §5.4 . Transferable Utility Games 216 §5.5 . The Core and Related Concepts 219 §5.6 . The Shapley Value 228
Contents ix §5.7. Computation of the Shapley Value 233 §5.8. The Banzhaf Value 239 §5.9. Equal Division Values 242 §5.10. The Nucleolus 245 §5.11. The Core-Center 249 §5.12. Convex Games 253 §5.13. Games with Communication Graphs: The Myerson Value 256 §5.14. Games with A Priori Unions: The Owen Value 261 §5.15. Noncooperative Models in Cooperative Game Theory: Implementation Theory 265 Exercises of Chapter 5 Chapter 6. Applications of Cooperative Games 283 285 §6.1. Preliminaries 285 §6.2. Airport Problems and Airport Games 286 §6.3. Bankruptcy Problems and Bankruptcy Games 293 §6.4. Voting Problems and Voting Games: Power Indices 303 §6.5. Apportionments and Data Science 315 §6.6. Linear Production Games 320 §6.7. Maximum Flow Games 324 §6.8. Inventory Games 327 §6.9. Project Planning 333 §6.10. Assignment Games 339 §6.11. Cooperation on Minimum Cost Spanning Tree Problems 347 §6.12. Cooperation on Queueing Problems 358 §6.13. Cooperation on Sequencing Problems 363 Exercises of Chapter 6 367 Bibliography 371 Notations 395 Index of Authors 397 Index of Solution Concepts 403 Subject Index 405 |
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author | González-Díaz, Julio 1978- García-Jurado, Ignacio Fiestras-Janeiro, M. Gloria 1962- |
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author_sort | González-Díaz, Julio 1978- |
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building | Verbundindex |
bvnumber | BV049680587 |
classification_rvk | SK 860 |
ctrlnum | (OCoLC)1413201526 (DE-599)KXP1866089935 |
discipline | Mathematik |
edition | Second edition |
format | Book |
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spelling | González-Díaz, Julio 1978- Verfasser (DE-588)142122793 aut An introductory course on mathematical game theory and applications Julio González-Díaz, Ignacio García-Jurado, M. Gloria Fiestras-Janeiro Second edition Providence, Rhode Island American Mathematical Society [2023] xiv, 415 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 238 Includes bibliographical references (pages 371-394) and index Preface:"The present book is an extended edition of A Introductory Course on Mathematiccal Game Theory..." Game theory provides a mathematical setting for analyzing competition and cooperation in interactive situations. The theory has been famously applied in economics, but is relevant in many other sciences, such as psychology, computer science, artificial intelligence, biology, and political science. This book presents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field. The theory is illustrated through abundant examples, applications, and exercises. The style is distinctively concise, while offering motivations and interpretations of the theory to make the book accessible to a wide readership. The basic concepts and results of game theory are given a formal treatment, and the mathematical tools necessary to develop them are carefully presented. In this second edition, the content on cooperative games is considerably strengthened, with a new chapter on applications of cooperative games and operations research, including some material on computational aspects and applications outside academia. Spieltheorie (DE-588)4056243-8 gnd rswk-swf Game theory Game theory, economics, social and behavioral sciences -- Instructional exposition (textbooks, tutorial papers, etc.) Game theory, economics, social and behavioral sciences -- Game theory -- Noncooperative games Game theory, economics, social and behavioral sciences -- Game theory -- Cooperative games Game theory, economics, social and behavioral sciences -- Game theory -- Games in extensive form Game theory, economics, social and behavioral sciences -- Game theory -- Applications of game theory 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, 9781470475642 Graduate studies in mathematics 238 (DE-604)BV009739289 238 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035023395&sequence=000001&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 and applications Graduate studies in mathematics Spieltheorie (DE-588)4056243-8 gnd |
subject_GND | (DE-588)4056243-8 |
title | An introductory course on mathematical game theory and applications |
title_auth | An introductory course on mathematical game theory and applications |
title_exact_search | An introductory course on mathematical game theory and applications |
title_full | An introductory course on mathematical game theory and applications Julio González-Díaz, Ignacio García-Jurado, M. Gloria Fiestras-Janeiro |
title_fullStr | An introductory course on mathematical game theory and applications Julio González-Díaz, Ignacio García-Jurado, M. Gloria Fiestras-Janeiro |
title_full_unstemmed | An introductory course on mathematical game theory and applications Julio González-Díaz, Ignacio García-Jurado, M. Gloria Fiestras-Janeiro |
title_short | An introductory course on mathematical game theory and applications |
title_sort | an introductory course on mathematical game theory and applications |
topic | Spieltheorie (DE-588)4056243-8 gnd |
topic_facet | Spieltheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035023395&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV009739289 |
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