Theory of Decision under Uncertainty

ISBN-10: 0521741238
ISBN-13: 9780521741231
Edition: 2009
Authors: Itzhak Gilboa
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Book details

List price: $56.95
Copyright year: 2009
Publisher: Cambridge University Press
Publication date: 3/16/2009
Binding: Paperback
Pages: 230
Size: 6.00" wide x 8.75" long x 0.50" tall
Weight: 1.012
Language: English

Robert Dunham founded the Institute for Generative Leadership and the consulting company Enterprise Performance.Itzhak Gilboa is Professor of Economics and Decision Sciences at HEC (�cole des Hautes �tudes Commerciales), Paris, and Professor of Economics at Berglas School of Economics, Tel Aviv University. He is the coauthor (with David Schmeidler) of Theory of Case-Based Decisions and the author of Theory of Decision under Uncertainty.

Preface
Intuitive Definitions
Motivating Examples
Free Will and Determinism
Can Free Choice Be Predicted?
Is the World Deterministic?
Is Free Will Observable?
The Problem of Free Will
A Rational Illusion
Free Will and the Decision Matrix
The Principle of Indifference
Will a Canonical Space Help?
The Canonical State Space
Difficulties with a Uniform Prior on [0, 1]
Conclusion
What's Special about the Coin?
Symmetry
Smooth Beliefs
Relative Frequencies
The Law of Large Numbers
The Problem of Induction
Hume's Critique
Goodman's Grue-Bleen Paradox
Kolmogorov Complexity and Its Dependence of Language
Grue-Bleen Again
Evolutionary Explanations
Problems with the Frequentist Approach
Subjective Probabilities
Linda the Bank Teller
Pascal's Wager
Classical versus Bayesian Statistics
Basic Definitions
The Gambler Fallacy
Exchangeability
Confidence Is Not Probability
Classical Statistics Can Be Ridiculous
Different Methods for Different Goals
Behavioral Definitions
A Case Study
A Characterization Theorem for Maximization of Utility
Proof
Interpretations
A Few Definitions
A Meta-Scientific Interpretation
A Normative Interpretation
A Descriptive Interpretation
Limitations
Semiorders
Other Ways to Measure Utility
The Role of Theories
Theories Are Always Wrong
Theories and Conceptual Frameworks
Logical Positivism as a Metaphor
Von Neumann-Morgenstern's Theorem
Background
The Theorem
Proofs
The Algebraic Approach
A Geometric Approach
A Separation Argument
The Three Interpretations
De Finetti's Theorem
Motivation
The Theorem
A Proof
The Three Interpretations
Savage's Theorem
Background
States, Outcomes, and Acts
Axioms
P1
P2
Notation
Null Events
P3
P4
P5
P6
P7
The Result for a Finite Outcome Set
Finitely Additive Measures
Nonatomic Measures
The Theorem
The Case of a General Outcome Set
Interpretations
The Proof and Qualitative Probabilities
The Definition of States
Causality
Newcomb's Paradox
States as Functions from Acts to Outcomes
A Problem
Hempel's Paradox of Confirmation
Are All Ravens Black?
A State-Space Formulation
What Is a Confirmation?
A Resolution
Good's Variation
What Do We Learn from This?
Monty Hall Three-Door Game
A Critique of Savage
Criticizing Critiques
An Example
The General Lesson
Critique of P3 and P4
Example
Defense
State-Dependent Utility
The Definition of Subjective Probability
When Is State Dependence Necessary?
Critique of P1 and P2
The Basic Problem
Reasoned Choice versus Raw Preferences
Schmeidler's Critique and Ellsberg's Paradox
Observability of States
Problems of Complexity
Objectivity and Rationality
Subjectivity and Objectivity
Objective and Subjective Rationality
Anscombe-Aumann's Theorem
Alternative Behavioral Theories
Choquet Expected Utility
Schmeidler's Intuition
Choquet Integral
Comonotonicity
Axioms and Result
Prospect Theory
Background
Gain-Loss Asymmetry
Distortion of Probabilities
Rank-Dependent Probabilities and Choquet Integration
Maxmin Expected Utility
Convex Games
A Cognitive Interpretation of CEU
Axioms and Result
Interpretation of MMEU
Generalizations and Variations
Bewley's Alternative Approach
Combining Objective and Subjective Rationality
Applications
Cognitive Origins
Case-Based Qualitative Beliefs
Axioms and Result
Four Known Techniques
The Combination Axiom in General Analogical Reasoning
Violations of the Combination Axiom
Frequentism Revisited
Similarity-Weighted Empirical Frequencies
Intuition
Axiomatization
Empirical Similarity and Objective Probabilities
Future Research
References
Index

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