Ebook: Game Theory: A Multi-Leveled Approach

This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.

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This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.

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This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.

Content:
Front Matter....Pages i-xv
Introduction....Pages 1-18
Finite Two-Person Zero-Sum Games....Pages 21-29
Finite Two-Person Games....Pages 31-41
Finite Extensive Form Games....Pages 43-57
Finite Games with Incomplete Information....Pages 59-71
Noncooperative Games: Extensions....Pages 73-100
Repeated Games....Pages 101-110
An Introduction to Evolutionary Games....Pages 111-120
Cooperative Games with Transferable Utility....Pages 121-131
Cooperative Game Theory Models....Pages 133-150
Social Choice....Pages 151-160
Matrix Games....Pages 163-167
Finite Games....Pages 169-195
Extensive Form Games....Pages 197-212
Evolutionary Games....Pages 213-225
TU-Games: Domination, Stable Sets, and the Core....Pages 229-239
The Shapley Value....Pages 241-258
Core, Shapley Value, and Weber Set....Pages 259-269
The Nucleolus....Pages 271-284
Special Transferable Utility Games....Pages 285-295
Bargaining Problems....Pages 297-306
Tools....Pages 309-319
Back Matter....Pages 321-365

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This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.

Content:
Front Matter....Pages i-xv
Introduction....Pages 1-18
Finite Two-Person Zero-Sum Games....Pages 21-29
Finite Two-Person Games....Pages 31-41
Finite Extensive Form Games....Pages 43-57
Finite Games with Incomplete Information....Pages 59-71
Noncooperative Games: Extensions....Pages 73-100
Repeated Games....Pages 101-110
An Introduction to Evolutionary Games....Pages 111-120
Cooperative Games with Transferable Utility....Pages 121-131
Cooperative Game Theory Models....Pages 133-150
Social Choice....Pages 151-160
Matrix Games....Pages 163-167
Finite Games....Pages 169-195
Extensive Form Games....Pages 197-212
Evolutionary Games....Pages 213-225
TU-Games: Domination, Stable Sets, and the Core....Pages 229-239
The Shapley Value....Pages 241-258
Core, Shapley Value, and Weber Set....Pages 259-269
The Nucleolus....Pages 271-284
Special Transferable Utility Games....Pages 285-295
Bargaining Problems....Pages 297-306
Tools....Pages 309-319
Back Matter....Pages 321-365
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