Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Expected utility
- Part II Nonexpected utility for Risk
- Part III Nonexpected utility for uncertainty
- 13 Conclusion
- Appendices
- Appendix A Models never hold perfectly: how to handle their deficiencies?
- Appendix B Choosing from multiple prospects and binary choice: the principles of revealed preference
- Appendix C Dynamic decisions
- Appendix D Applications other than decision under uncertainty
- Appendix E Bisymmetry-based preference conditions
- Appendix F Nonmonotonic rank-dependent models and the Fehr–Schmidt model of welfare evaluation
- Appendix G Extensions of finite-dimensional results to infinite-dimensional results: a meta-theorem
- Appendix H Measure theory
- Appendix I Related textbooks and surveys
- Appendix J Elaborations of exercises
- Appendix K Skipping parts and interdependencies between sections
- References
- Author index
- Subject index
Appendix J - Elaborations of exercises
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Expected utility
- Part II Nonexpected utility for Risk
- Part III Nonexpected utility for uncertainty
- 13 Conclusion
- Appendices
- Appendix A Models never hold perfectly: how to handle their deficiencies?
- Appendix B Choosing from multiple prospects and binary choice: the principles of revealed preference
- Appendix C Dynamic decisions
- Appendix D Applications other than decision under uncertainty
- Appendix E Bisymmetry-based preference conditions
- Appendix F Nonmonotonic rank-dependent models and the Fehr–Schmidt model of welfare evaluation
- Appendix G Extensions of finite-dimensional results to infinite-dimensional results: a meta-theorem
- Appendix H Measure theory
- Appendix I Related textbooks and surveys
- Appendix J Elaborations of exercises
- Appendix K Skipping parts and interdependencies between sections
- References
- Author index
- Subject index
Summary
If you do not know how to solve an exercise, then it is not yet time to inspect the elaborations provided here. It is better then to restudy the preceding theory so as to find out what is missing in your knowledge. Such searches for lacks in knowledge comprise the most fruitful part of learning new ideas.
Exercise 1.1.1.
(a) A: {Bil}; B: {Bill, no-one}; C: {Bill, Jane, Kate}; D: {Jane, Kate}; E: {Jane, Kate}. Note that D = E.
(b) x: (Bill: n, Jane: α, Kate: α, no-one: α); y: (Bill: n, Jane: n, Kate: α, no-one: n); z: (Bill: α, Jane: n, Kate: n, no-one: n).
(c) 24 = 16, being the number of ways to assign either an apple or nothing to each element of S.
(d) Two exist, being α and n. It is allowed to denote constant prospects just by their outcome, as we did. We can also write them as (Bill: α, Jane: α, Kate: α, no-one: α) and (Bill: n, Jane: n, Kate: n, no-one: n). □
Exercise 1.1.2. The anwer is no. Because only one state of nature is true, s1 and s2 cannot both happen, and s1∩s2 = Ø. Indeed, it is not possible that both horses win. P(s1∩s2) = 0 ≠ 1/8 = P(s1) × P(s2). Stochastic independence is typically interesting for repeated observations. Decision theory as in this book focuses on single decisions, where a true state of nature obtains only one time. The horse race takes place only once.
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- Chapter
- Information
- Prospect TheoryFor Risk and Ambiguity, pp. 399 - 454Publisher: Cambridge University PressPrint publication year: 2010