BA 513 [STA 234]:  Ph.D. Seminar on Choice Theory
Professor Robert Nau
Spring Semester 2008

Schedule update:  this course will normally meet on Monday from 8:45 to 11:30am in Seminar Room C at Fuqua, throughout the Spring semester.  However, due to the MLK class shift for all Duke graduate courses, the first class meeting will be on Wednesday, January 9 (same time and place), the second class meeting will be on Monday, January 14, and the remaining classes will be on Mondays from January 28 to April 14.

Course description:  This seminar deals with the foundations and applications of the theory of rational choice, including Bayesian decision theory (i.e., subjective expected utility) as well as the theories of nonexpected utility, noncooperative games, competitive equilibrium, and asset pricing by arbitrage.  It will survey the classic literature in the field and discuss the interconnections among its branches; dissect a variety of paradoxes, puzzles, and pathologies; and discuss recent advances and controversies. The goal of this seminar is to equip students with an understanding of both the power and the limits of rational choice theory, so that they can construct as well as critically analyze rational choice applications in a wide variety of social science contexts.   It will also suggest some new directions for choice-theoretic research that involve a synthesis of ideas from competing paradigms.

Unplugged course description: This course will be a helicopter tour of the vast literature on foundations and applications of rational choice. By "rational choice" I mean the theory of the probability-assessing, expected-utility-maximizing, equilibrium-seeking individual that originated in statistical decision theory and economics and has spread to many other disciplines over the last six decades. We will fly fast over broad areas of terrain, but we will touch down periodically to drill some deep holes. More material will be handed out than you will be able to read, but you can explore the rest of it later according to your interests and needs. The course objectives will be to understand the origins and promise of rational choice theory as pioneered by von Neumann and Morgenstern, de Finetti, Savage, and Arrow; to probe deeply into the paradoxes and puzzles that have emerged over the last few decades;  to trace these issues back to their roots in the fundamental assumptions of the theory; to learn where rational choice models should or should not be expected to work; to learn the right and wrong ways to build them; and to speculate on what lies beyond the next paradigm shift.  You may already be familiar with violations of the axioms of expected utility theory demonstrated by Allais, Ellsberg, and Tversky & Kahneman--which we will touch on to some extent--but those are not the only problems nor necessarily the biggest ones. Although many of the readings will have significant mathematical content, the focus of the course will be on fundamental concepts and practical modeling issues rather than on theorem-proving. Undergraduate mathematics will suffice. If all goes well, we will have some lively arguments.

Who should be interested in this course: students and faculty who use models of boundedly or unboundedly rational decision makers in their research or  who otherwise use tools of statistical decision theory, game theory, and market theory.  Thus, the course should be of interest to those engaged in research in statistics, economics, finance, marketing, operations research, etc., who wish to gain a deeper understanding of foundational issues, historical developments, and current controversies in choice theory.  It should also be of interest to those pursuing research in management, political science, public policy, etc., who wish to gain a deeper understanding of  "economic" models of behavior.  In other words, everyone is welcome.

Readings: are described and discussed in the downloadable lecture notes available on this web page.   The current links in the course outline below are the notes from the previous offering of the course, and they will be updated and extended as the term progresses.  Hard copies of the updated versions will be handed out on a class-by-class basis.  (If you read them in advance, your comments are welcome.)  Meanwhile, here is a link to a rational choice reading list that includes some of the assigned readings and a great deal more.  Here's another link to a list of who's who and what's what in rational choice theory.

Grading basis: class participation and your choice of (a) a take-home essay test, or (b) a research or discussion paper that has significant choice-theoretic content.  The latter paper may be based on ongoing dissertation research and/or may overlap with work being performed in another course, with permission of both instructors.

1.  Introduction to rational choice (Arrow); history of utility theory (Stigler); review of consumer theory and competitive equilibrium; the arbitrage principle. Notes and  guide to readings.  HET notes on the marginalist revolution and the consumer.
 
2. Axioms of subjective probability, expected utility, and subjective expected utility (de Finetti, von Neumann and Morgenstern, Savage). Notes and guide to readings.  HET notes on choice under risk and uncertainty.   HET notes on subjective expected utility.
 
3. Fundamentals of utility theory:  risk aversion, properties of utility functions, preference aggregation, markets under uncertainty, state-preference theory, risk neutral probabilities (Pratt, Arrow, Raiffa, and others). Notes and guide to readings.   HET notes on risk aversion.   HET notes on state-preference theory.
 
4. Non-expected utility theory:  prospect theory, rank-dependent expected utility, Choquet expected utility, etc.  (Kahneman & Tversky, Machina, Schmeidler, Quiggin, Yaari, Wakker). Notes and guide to readings.  HET notes on alternative expected utility.
     

5. Non-expected utility, continued: incomplete preferences, second-order utilities and probabilities  (Rigotti and Shannon, Klibanoff et al., Nau)
   

*The on-line notes for this course are partially based on research supported by the National Science Foundation under grant 98-09225.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.