Theory of Decision under Uncertainty

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories.

Itzhak Gilboa (Author)

9780521517324, Cambridge University Press

Hardback, published 16 March 2009

230 pages
22.9 x 15.2 x 1.8 cm, 0.43 kg

'[Gilboa] provides a textbook, but mathematically sophisticated, treatment of the recent developments in Choquet expected utility theory, prospect theory, and maxmin expected utility theory.' History of Economic Thought and Policy

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.

1. Preface
2. Motivating examples
3. Free will and determinism
4. The principle of indifference
5. Relative frequencies
6. Subjective probabilities
7. A case study
8. The role of theories
9. Von Neumann and Morgenstern's theorem
10. De Finetti's theorem
11. Savage's theorem
12. The definition of states
13. A critique of Savage
14. Objectivity and rationality
15. Anscombe-Aumann's theorem
16. Choquet expected utility
17. Prospect theory
18. Maxmin expected utility
19. Case-based qualitative beliefs
20. Frequentism revisited
21. Future research.

Subject Areas: Probability & statistics [PBT], Economic statistics [KCHS], Econometrics [KCH]