An Introduction to Decision Theory

Cover
Half-title page
Title page
Copyright page
Contents
Preface
Preface to the Second Edition
1 Introduction
	1.1 Normative and Descriptive Decision Theory
	1.2 Rational and Right Decisions
	1.3 Risk, Ignorance and Uncertainty
	1.4 Social Choice Theory and Game Theory
	1.5 A Very Brief History of Decision Theory
2 The Decision Matrix
	2.1 States
	2.2 Outcomes
	2.3 Acts
	2.4 Rival Formalizations
3 Decisions under Ignorance
	3.1 Dominance
	3.2 Maximin and Leximin
	3.3 Maximax and the Optimism–Pessimism Rule
	3.4 Minimax Regret
	3.5 The Principle of Insufficient Reason
	3.6 Randomized Acts
4 Decisions under Risk
	4.1 Maximizing What?
	4.2 Why is it Rational to Maximize Expected Utility?
	4.3 The Axiomatic Approach
	4.4 The Allais Paradox
	4.5 The Ellsberg Paradox
	4.6 The St. Petersburg Paradox
	4.7 The Pasadena Paradox
	4.8 The Two-Envelope Paradox
5 Utility
	5.1 How to Construct an Ordinal Scale
	5.2 Von Neumann and Morgenstern’s Interval Scale
	5.3 Can Utility be Measured on a Ratio Scale?
	5.4 Can We Define Utility Without Being Able to Measure It?
6 The Mathematics of Probability
	6.1 The Probability Calculus
	6.2 Conditional Probability
	6.3 Bayes’ Theorem
	6.4 The Problem of Unknown Priors
7 The Philosophy of Probability
	7.1 The Classical Interpretation
	7.2 The Frequency Interpretation
	7.3 The Propensity Interpretation
	7.4 Logical and Epistemic Interpretations
	7.5 Subjective Probability
8 Bayesianism and Pragmatic Arguments
	8.1 Why Should We Accept the Axioms?
	8.2 Must a Rational Preference be Transitive?
	8.3 Must a Rational Preference be Complete?
	8.4 Must a Rational Preference Satisfy the Independence Axiom?
	8.5 Can Bayesians be Money Pumped?
	8.6 Do Bayesians Put the Cart Before the Horse?
	8.7 Non-Bayesian Decision Theory
9 Causal vs. Evidential Decision Theory
	9.1 Newcomb’s Problem
	9.2 Causal Decision Theory
	9.3 Evidential Decision Theory
10 Risk Aversion
	10.1 Actuarial Risk Aversion
	10.2 Aversion Against Utility Risks
	10.3 Epistemic Risk Aversion
11 Game Theory I: Basic Concepts and Zero-sum Games
	11.1 The Prisoner’s Dilemma
	11.2 A Taxonomy of Games
	11.3 Common Knowledge and Dominance Reasoning
	11.4 Two-Person Zero-sum Games
	11.5 Mixed Strategies and the Minimax Theorem
12 Game Theory II: Nonzero-sum and Cooperative Games
	12.1 The Nash Equilibrium
	12.2 The Battle of the Sexes and Chicken
	12.3 The Bargaining Problem
	12.4 Iterated Games
	12.5 Game Theory and Evolution
	12.6 Game Theory and Ethics
13 Social Choice Theory
	13.1 The Social Choice Problem
	13.2 Arrow’s Impossibility Theorem
	13.3 Sen on Liberalism and the Pareto Principle
	13.4 Harsanyi’s Utilitarian Theorems
14 Overview of Descriptive Decision Theory
	14.1 Observed Violations of the Expected Utility Principle
	14.2 Prospect Theory
	14.3 Violations of Transitivity and Completeness
	14.4 The Relevance of Descriptive Decision Theory
Appendix: Glossary
Further Reading
Index