| |
| |
Preface | |
| |
| |
| |
Introduction | |
| |
| |
| |
Normative and descriptive decision theory | |
| |
| |
| |
Rational and right decisions | |
| |
| |
| |
Risk, ignorance and uncertainty | |
| |
| |
| |
Social choice theory and game theory | |
| |
| |
| |
A very brief history of decision theory | |
| |
| |
| |
The decision matrix | |
| |
| |
| |
States | |
| |
| |
| |
Outcomes | |
| |
| |
| |
Acts | |
| |
| |
| |
Rival formalisations | |
| |
| |
| |
Decisions under ignorance | |
| |
| |
| |
Dominance | |
| |
| |
| |
Maximin and leximin | |
| |
| |
| |
Maximax and the optimism-pessimism rule | |
| |
| |
| |
Minimax regret | |
| |
| |
| |
The principle of insufficient reason | |
| |
| |
| |
Randomised acts | |
| |
| |
| |
Decisions under risk | |
| |
| |
| |
Maximising what? | |
| |
| |
| |
Why is it rational to maximise expected utility? | |
| |
| |
| |
The axiomatic approach | |
| |
| |
| |
Allais' paradox | |
| |
| |
| |
Ellsberg's paradox | |
| |
| |
| |
The St Petersburg paradox | |
| |
| |
| |
The two-envelope paradox | |
| |
| |
| |
Utility | |
| |
| |
| |
How to construct an ordinal scale | |
| |
| |
| |
von Neumann and Morgenstern's interval scale | |
| |
| |
| |
Can utility be measured on a ratio scale? | |
| |
| |
| |
Can we define utility without being able to measure it? | |
| |
| |
| |
The mathematics of probability | |
| |
| |
| |
The probability calculus | |
| |
| |
| |
Conditional probability | |
| |
| |
| |
Bayes' theorem | |
| |
| |
| |
The problem of unknown priors | |
| |
| |
| |
The philosophy of probability | |
| |
| |
| |
The classical interpretation | |
| |
| |
| |
The frequency interpretation | |
| |
| |
| |
The propensity interpretation | |
| |
| |
| |
Logical and epistemic interpretations | |
| |
| |
| |
Subjective probability | |
| |
| |
| |
Why should we accept the preference axioms? | |
| |
| |
| |
Must a rational preference be transitive? | |
| |
| |
| |
Must a rational preference be complete? | |
| |
| |
| |
The multi-attribute approach | |
| |
| |
| |
Must a rational preference satisfy the independence axiom? | |
| |
| |
| |
Risk aversion | |
| |
| |
| |
Causal vs. evidential decision theory | |
| |
| |
| |
Newcomb's problem | |
| |
| |
| |
Causal decision theory | |
| |
| |
| |
Evidential decision theory | |
| |
| |
| |
Bayesian vs. non-Bayesian decision theory | |
| |
| |
| |
What is Bayesianism? | |
| |
| |
| |
Arguments for and against Bayesianism | |
| |
| |
| |
Non-Bayesian approaches | |
| |
| |
| |
Game theory I: Basic concepts and zero-sum games | |
| |
| |
| |
The prisoner's dilemma | |
| |
| |
| |
A taxonomy of games | |
| |
| |
| |
Common knowledge and dominance reasoning | |
| |
| |
| |
Two-person zero-sum games | |
| |
| |
| |
Mixed strategies and the minimax theorem | |
| |
| |
| |
Game theory II: Nonzero-sum and cooperative games | |
| |
| |
| |
The Nash equilibrium | |
| |
| |
| |
The battle of the sexes and chicken | |
| |
| |
| |
The bargaining problem | |
| |
| |
| |
Iterated games | |
| |
| |
| |
Game theory and evolution | |
| |
| |
| |
Game theory and ethics | |
| |
| |
| |
Social choice theory | |
| |
| |
| |
The social choice problem | |
| |
| |
| |
Arrow's impossibility theorem | |
| |
| |
| |
Sen on liberalism and the Pareto principle | |
| |
| |
| |
Harsanyi's utilitarian theorems | |
| |
| |
| |
Overview of descriptive decision theory | |
| |
| |
| |
Observed violations of the expected utility principle | |
| |
| |
| |
Prospect theory | |
| |
| |
| |
Violations of transitivity and completeness | |
| |
| |
| |
The relevance of descriptive decision theory | |
| |
| |
| |
Glossary | |
| |
| |
| |
Proof of the von Neumann-Morgenstern theorem | |
| |
| |
Further reading | |
| |
| |
Index | |