Ebook: The Consistent Preferences Approach to Deductive Reasoning in Games

During the last decade I have explored the consequences of what I have chosen to call the 'consistent preferences' approach to deductive reasoning in games. To a great extent this work has been done in coop­ eration with my co-authors Martin Dufwenberg, Andres Perea, and Ylva Sovik, and it has lead to a series of journal articles. This book presents the results of this research program. Since the present format permits a more extensive motivation for and presentation of the analysis, it is my hope that the content will be of interest to a wider audience than the corresponding journal articles can reach. In addition to active researcher in the field, it is intended for graduate students and others that wish to study epistemic conditions for equilibrium and rationalizability concepts in game theory. Structure of the book This book consists of twelve chapters. The main interactions between the chapters are illustrated in Table 0.1. As Table 0.1 indicates, the chapters can be organized into four dif­ ferent parts. Chapters 1 and 2 motivate the subsequent analysis by introducing the 'consistent preferences' approach, and by presenting ex­ amples and concepts that are revisited throughout the book. Chapters 3 and 4 present the decision-theoretic framework and the belief operators that are used in later chapters. Chapters 5, 6, 10, and 11 analyze games in the strategic form, while the remaining chapters-Chapters 7, 8, 9, and 12-are concerned with games in the extensive form.

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The Consistent Preferences Approach to Deductive Reasoning in Games presents, applies, and synthesizes what my co-authors and I have called the 'consistent preferences' approach to deductive reasoning in games. Briefly described, this means that the object of the analysis is the ranking by each player of his own strategies, rather than his choice. The ranking can be required to be consistent (in different senses) with his beliefs about the opponent's ranking of her strategies. This can be contrasted to the usual `rational choice' approach where a player's strategy choice is (in different senses) rational given his beliefs about the opponent's strategy choice. Our approach has turned out to be fruitful for providing epistemic conditions for backward and forward induction, and for defining or characterizing concepts like proper, quasi-perfect and sequential rationalizability. It also facilitates the integration of game theory and epistemic analysis with the underlying decision-theoretic foundation.

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The Consistent Preferences Approach to Deductive Reasoning in Games presents, applies, and synthesizes what my co-authors and I have called the 'consistent preferences' approach to deductive reasoning in games. Briefly described, this means that the object of the analysis is the ranking by each player of his own strategies, rather than his choice. The ranking can be required to be consistent (in different senses) with his beliefs about the opponent's ranking of her strategies. This can be contrasted to the usual `rational choice' approach where a player's strategy choice is (in different senses) rational given his beliefs about the opponent's strategy choice. Our approach has turned out to be fruitful for providing epistemic conditions for backward and forward induction, and for defining or characterizing concepts like proper, quasi-perfect and sequential rationalizability. It also facilitates the integration of game theory and epistemic analysis with the underlying decision-theoretic foundation.

Content:
Front Matter....Pages i-xix
Introduction....Pages 1-10
Motivating Examples....Pages 11-20
Decision-Theoretic Framework....Pages 21-36
Belief Operators....Pages 37-51
Basic Characterizations....Pages 53-67
Relaxing Completeness....Pages 69-78
Backward Induction....Pages 79-97
Sequentiality....Pages 99-114
Quasi-Perfectness....Pages 115-119
Properness....Pages 121-132
Capturing forward Induction through Full Permissibility....Pages 133-154
Applying Full Permissibility to Extensive Games....Pages 155-174
Back Matter....Pages 175-202

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The Consistent Preferences Approach to Deductive Reasoning in Games presents, applies, and synthesizes what my co-authors and I have called the 'consistent preferences' approach to deductive reasoning in games. Briefly described, this means that the object of the analysis is the ranking by each player of his own strategies, rather than his choice. The ranking can be required to be consistent (in different senses) with his beliefs about the opponent's ranking of her strategies. This can be contrasted to the usual `rational choice' approach where a player's strategy choice is (in different senses) rational given his beliefs about the opponent's strategy choice. Our approach has turned out to be fruitful for providing epistemic conditions for backward and forward induction, and for defining or characterizing concepts like proper, quasi-perfect and sequential rationalizability. It also facilitates the integration of game theory and epistemic analysis with the underlying decision-theoretic foundation.

Content:
Front Matter....Pages i-xix
Introduction....Pages 1-10
Motivating Examples....Pages 11-20
Decision-Theoretic Framework....Pages 21-36
Belief Operators....Pages 37-51
Basic Characterizations....Pages 53-67
Relaxing Completeness....Pages 69-78
Backward Induction....Pages 79-97
Sequentiality....Pages 99-114
Quasi-Perfectness....Pages 115-119
Properness....Pages 121-132
Capturing forward Induction through Full Permissibility....Pages 133-154
Applying Full Permissibility to Extensive Games....Pages 155-174
Back Matter....Pages 175-202
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