An Introduction to Decision Theory (Cambridge Introductions to Philosophy) by Peterson, Martin -- Read -- Imperial Library of Trantor

Index

An Introduction to Decision Theory Title page Copyright page Contents Preface 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 formalisations

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 Randomised acts

4 Decisions under risk

4.1 Maximising what? 4.2 Why is it rational to maximise expected utility? 4.3 The axiomatic approach 4.4 Allais’ paradox 4.5 Ellsberg’s paradox 4.6 The St Petersburg paradox 4.7 The two-envelope paradox

5 Utility

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 Why should we accept the preference axioms?

8.1 Must a rational preference be transitive? 8.2 Must a rational preference be complete? 8.3 The multi-attribute approach 8.4 Must a rational preference satisfy the independence axiom? 8.5 Risk aversion

9 Causal vs. evidential decision theory

9.1 Newcomb’s problem 9.2 Causal decision theory 9.3 Evidential decision theory

10 Bayesian vs. non-Bayesian decision theory

10.1 What is Bayesianism? 10.2 Arguments for and against Bayesianism 10.3 Non-Bayesian approaches

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 A: Glossary Appendix B: Proof of the von Neumann–Morgenstern theorem Further reading Index