De Bruin Explaining Games

The Epistemic Programme in Game Theory
1. Auflage 2010
ISBN: 978-1-4020-9906-9
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 346, 185 Seiten

Reihe: Synthese Library

Does game theory - the mathematical theory of strategic interaction - provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory - the first monograph on the philosophy of game theory - is a bold attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. De Bruin proves new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and he explores in detail the logical form of game theory as it is used in explanatory and normative contexts. He argues that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, De Bruin argues, has been rather successful in achieving this aim.

Boudewijn de Bruin is assistant professor of philosophy in the Faculty of Philosophy of the University of Groningen. He obtained his Ph.D. in philosophy from the Institute for Logic, Language and Computation in Amsterdam. His dissertation was awarded several prizes including a Research Prize from the Praemium Erasmianum Foundation. De Bruin did undergraduate work in musical composition at Enschede, and studied mathematics and philosophy at Amsterdam, Berkeley and Harvard. His research interests include epistemology, moral and political philosophy and philosophy of science. Receiver of several prestigious research grants, De Bruin is published widely in such journals as Ethical Theory and Moral Practice, Journal of Political Philosophy, Studies in History and Philosophy of Science and Synthese.

Autoren/Hrsg.

De Bruin, Boudewijn

Inhaltsverzeichnis

1;Contents;8
2;Acknowledgements;11
3;Introduction;13
4;1 Preliminaries;17
4.1;1.1 The Logic of Game Theory;17
4.1.1;1.1.1 Decision Theory and Game Theory;18
4.1.1.1;1.1.1.1 The Ban on Exogenous Information;18
4.1.1.2;1.1.1.2 Epistemic Characterisation Theorems;19
4.1.2;1.1.2 Normal Form Games;22
4.1.3;1.1.3 Extensive Games: The One-Shot Interpretation;27
4.1.4;1.1.4 Extensive Games: The Many-Moment Interpretation;30
4.1.4.1;1.1.4.1 Identity Over Time;34
4.2;1.2 A Logic for Game Theory;35
4.2.1;1.2.1 A Logic for Normal form Games;36
4.2.2;1.2.2 A Logic for Extensive Games;39
4.2.2.1;1.2.2.1 The One-Shot Interpretation;40
4.2.2.2;1.2.2.2 The Many-Moment Interpretation;41
5;Part I Epistemic Logic;42
5.1;2 Normal Form Games;43
5.1.1;2.1 The Nash Equilibrium;44
5.1.1.1;2.1.1 The Epistemic Characterisation Theorems;44
5.1.1.1.1;2.1.1.1 An Explicit Formalisation of Rationality;44
5.1.1.2;2.1.2 Discussion;48
5.1.1.2.1;2.1.2.1 The Axiom of Truth;48
5.1.1.2.2;2.1.2.2 The Rational Equilibration of Beliefs;50
5.1.1.2.3;2.1.2.3 The Ban on Exogenous Information;52
5.1.2;2.2 Iterated Strict Dominance;53
5.1.2.1;2.2.1 The Epistemic Characterisation Theorem;53
5.1.2.1.1;2.2.1.1 An Implicit, Inductive Formalisation of Rationality;54
5.1.2.2;2.2.2 Discussion;57
5.1.2.2.1;2.2.2.1 Axioms T and K, and the Rule of Necessitation;57
5.1.2.2.2;2.2.2.2 Motivation of the Axioms;59
5.1.2.2.3;2.2.2.3 Variants;60
5.1.2.2.4;2.2.2.4 More than Two Players;63
5.1.2.2.5;2.2.2.5 Stalnaker's Game Models Approach;64
5.1.3;2.3 The Dekel--Fudenberg Procedure;67
5.1.3.1;2.3.1 The Epistemic Characterisation Theorem;67
5.1.3.1.1;2.3.1.1 An Implicit, Inductive Formalisation of Perfect Rationality;68
5.1.3.2;2.3.2 Discussion;70
5.1.3.2.1;2.3.2.1 Stalnaker's Game Models Approach;70
5.1.3.2.2;2.3.2.2 Motivation of the Axioms;74
5.1.4;2.4 Mixed Iterated Strict Weak Dominance;76
5.1.4.1;2.4.1 The Epistemic Characterisation Theorem;76
5.1.4.2;2.4.2 Discussion;84
5.1.4.2.1;2.4.2.1 Comparison with the Literature;85
5.1.4.2.2;2.4.2.2 Motivation of the Axioms;86
5.1.4.2.3;2.4.2.3 The Ban on Exogenous Information;89
5.2;3 Extensive Games;91
5.2.1;3.1 The One-Shot Interpretation;92
5.2.1.1;3.1.1 The Epistemic Characterisation Result;92
5.2.1.1.1;3.1.1.1 An Explicit Formalisation of Rationality;94
5.2.1.1.2;3.1.1.2 An Implicit, Inductive Formalisation of Rationality;96
5.2.1.2;3.1.2 Discussion;99
5.2.2;3.2 The Many-Moment Interpretation;100
5.2.2.1;3.2.1 The Inconsistency Result;100
5.2.2.1.1;3.2.1.1 An Explicit Formalisation of Rationality;102
5.2.2.2;3.2.2 Discussion;106
6;Part II Epistemology;109
6.1;4 Applications of Game Theory;110
6.1.1;4.1 Logical Form;111
6.1.1.1;4.1.1 Rationality;111
6.1.1.1.1;4.1.1.1 Max Weber and John Stuart Mill;112
6.1.1.1.2;4.1.1.2 Decision and Game Theory;114
6.1.1.2;4.1.2 Decision Theory;116
6.1.1.2.1;4.1.2.1 Explanatory Use;116
6.1.1.2.2;4.1.2.2 Normative Use;119
6.1.1.3;4.1.3 Game Theory;122
6.1.1.3.1;4.1.3.1 Explanatory Use;122
6.1.1.3.2;4.1.3.2 Normative Use;124
6.1.2;4.2 Game Theory as an Explanatory Theory;126
6.1.2.1;4.2.1 The Reduction;126
6.1.2.2;4.2.2 The Ban on Exogenous Information;127
6.1.2.2.1;4.2.2.1 A Narrow Epistemology;127
6.1.2.2.2;4.2.2.2 The Correlated Equilibrium;129
6.1.3;4.3 Game Theory as a Normative Theory;132
6.1.3.1;4.3.1 Collective Advice;132
6.1.3.2;4.3.2 Individual Advice;133
6.1.3.2.1;4.3.2.1 Actuality;134
6.1.3.2.2;4.3.2.2 Probability;135
6.1.3.2.3;4.3.2.3 Possibility;135
6.2;5 The Methodology of Game Theory;137
6.2.1;5.1 Truth in the Abstract;140
6.2.1.1;5.1.1 The Methodology;140
6.2.1.1.1;5.1.1.1 John Stuart Mill;140
6.2.1.1.2;5.1.1.2 Robert Aumann and Ariel Rubinstein;141
6.2.1.2;5.1.2 The Research Habits;143
6.2.1.2.1;5.1.2.1 Overmathematisation;144
6.2.1.2.2;5.1.2.2 Introversion;144
6.2.1.2.3;5.1.2.3 Model-Tinkering;145
6.2.2;5.2 A Case Study: Refining the Nash Equilibrium;146
6.2.2.1;5.2.1 The Nash Equilibrium Refinement Programme;147
6.2.2.1.1;5.2.1.1 The Nash Equilibrium;147
6.2.2.1.2;5.2.1.2 The Subgame-Perfect Equilibrium;149
6.2.2.1.3;5.2.1.3 The Perfect Equilibrium;151
6.2.2.1.4;5.2.1.4 The Proper Equilibrium;153
6.2.2.2;5.2.2 Mathematics-Driven Mathematisation in the Nash Equilibrium Refinement Programme;154
6.2.2.3;5.2.3 Application-Driven Mathematisation in the Epistemic Programme;159
6.3;Conclusion;162
6.4;A Notation, Definitions, Theorems;166
6.4.1;A.1 Decision Theory;166
6.4.2;A.2 Normal Form Games;167
6.4.3;A.3 Extensive Games;168
6.5;Bibliography;170
6.6;Index;177