PhD Programme 2009/2010 Period 3 – Jan/Feb Foundations of Utility, Risk and Decision Theory Professor: Enrico Diecidue Assistant: Melissa Wojciechowski [email protected] [email protected] PMLS 0.06 PMLS OSPA 0.02 Ext 4447 Ext 9296 Course Objectives The goal of this course is to present the foundations of decision theory. Summary of Course Content The focus is mainly on axiomatic theories of individual decision making under risk and uncertainty, i.e., the course discusses the basic models of decision theory that underlie economics and management. First the course will briefly explore utility theory under certainty and the notion of preferences and their representation. Then we will study in detail the classic theories of decision under risk and uncertainty: von Neumann and Morgenstern, Anscombe and Aumann, and Savage. Decision theory is tied to a constant interplay between formalization and empirical observations. Therefore, the interaction between models of choice and their formal testing underlies the course contents in a large part. Required or Recommended Textbook(s) We are going to discuss the theory and solve exercises from the following book available at the library. I assume you come to class having studied the assigned material. Kreps, David M. (1988), “Notes on the Theory of Choice.” Westview Press, Boulder, Colorado. Description of optional readings Supplementary readings will be made available. The Grading Scheme Homework: 30% Exam: 40% In class presentations: 30% Description of Examinations and Assignments TBA Outline of Class Sessions (tentative) Session 1: Introduction; From choices to preferences; Preferences and ordinal utility Main Readings: Kreps, Chapters 1-3 Optional Readings: Fishburn (1970), Chapters 2-3; Mas-Collel, Whinston, Green (MGW)(1995), Chapter 1. Problems: Kreps, Chapter 1, number 1 and 2; Chapter 2, number 1, 3, 4, Chapter 3, numbers 2, 3, 4, 5 and 6. Session 2: Choice under risk -- von Neumann-Morgenstern expected utility Main Readings: Kreps, Chapter 4, pp. 31-33 and Chapter 5. Optional Readings: Fishburn (1970), Chapters 8 and 10; MGW, Chapter 6.A-6.B. Background material: Jensen (1967), Fishburn and Wakker (1995), Herstein and Milnor (1953. Problems: Kreps, Chapter 5, numbers 1, 4 and 6. Session 3: Attitudes towards risk; risk-aversion and utility Main Readings: Kreps, Chapter 6; Rabin (2000), chapter 4 of Keeney and Raiffa (1976), Wakker on power utility Optional Readings: Gollier (2001), Chapter 2; Ross (1981); Yaari (1969); Pratt (1964); MGW, Chapter 6.C. Problems: Kreps, Chapter 6, numbers 1, 9, and give some thoughts to 13. Prove proposition 6.3 Session 4: The lottery-acts approach to expected utility -- Anscombe-Aumann Main Readings: Kreps, Chapter 7, A&A (1963), Sarin and Wakker (1997); Other Readings: Fishburn (1970), Chapter 13 Class presentation of AA Session 5: A fully subjective approach to expected utility -- Savage Main Readings: Kreps, Chapters 8-9, Fishburn (1970), Chapter 14 Other Readings: Savage (1972, 1954), Chapters 1-5; Class presentation of Savage Session 6: Expected Utility measurement Farquhar, Peter H. (1984), “Utility Assessment Methods,” Management Science 30, 1283–1300. Hershey, J. & Schoemaker, P. (1985). Probability versus Certainty Equivalence methods in utility measurement: are they equivalent? Management Science, 31, 1213-1231. McCord, M. & de Neufville, R. (1986). Lottery Equivalents: reduction of the certainty effect problem in utility assessment. Management Science, 32, 56-60. Wakker, Peter P. & Daniel Deneffe (1996), “Eliciting von Neumann-Morgenstern Utilities when Probabilities Are Distorted or Unknown,” Management Science 42, 1131–1150. Session 7: Multiattribute extension of Expected Utility Optional readings Fishburn, Peter C. (1970), "Utility Theory for Decision Making." Wiley, New York. Krantz, David H., R. Duncan Luce, Patrick Suppes, & Amos Tversky (1971), “Foundations of Measurement, Vol. I (Additive and Polynomial Representations).” Academic Press, New York. Savage, L.J. (1954), "The Foundations of Statistics." Wiley, New York. (Second edition 1972, Dover, New York.) Jensen, Niels-Erik (1967), “An Introduction to Bernoullian Utility Theory, I, II,” Swedish Journal of Economics 69, 163–183, 229–247. Herstein, Israel N. & John Milnor (1953), “An Axiomatic Approach to Measurable Utility,” Econometrica 21, 291–297. Fishburn, Peter C. & Peter P. Wakker (1995), “The Invention of the Independence Condition for Preferences,” Management Science 41, 1130–1144. Sarin, Rakesh K. & Peter P. Wakker (1997), “A Single-Stage Approach to Anscombe and Aumann’s Expected Utility,” Review of Economic Studies 64, 399–409. Anscombe, Frank J. & Robert J. Aumann (1963), “A Definition of Subjective Probability,” Annals of Mathematical Statistics 34, 199–205. Keeney, Ralph L. & Howard Raiffa (1976), “Decisions with Multiple Objectives.” Wiley, New York (2nd edition 1993, Cambridge University Press, Cambridge, UK). .