**BA 513 [STA 234]: Ph.D. Seminar on Choice
Theory**

**Professor Robert
Nau
**Spring Semester
2010

**Class schedule: **Fridays from 3:00-6:00 in the DeSanctis seminar room at Fuqua throughout the Spring
semester (January 15 through April 16)

**Course description: **This seminar deals with the
mathematical 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. 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*.

**Relations with other courses:** this course is a complement rather than a substitute for courses that focus on applications of statistical decision theory or game theory or market theory that arise in particular fields of study. It will deal more with broad theoretical issues that link the models used in all these areas, it will discuss competing points of view as well as the current orthodoxy. In terms of sequencing, it could taken either before or after the more field-specific courses.

**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.
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: **general class participation, plus (i) presentation and discussion of a journal article or working paper (written by someone else) during the last few weeks of class, and (ii) your choice between a take-home exam or a term paper that has significant
choice-theoretic content. The term paper could involve mathematical modeling or it could be a review and discussion of the literature on a topic of interest to you (beyond what has been covered in class). The paper may be based on
ongoing
dissertation research and/or may overlap with work being performed in
another
course, with permission of both instructors.

- 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.
- 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.
- 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.
- 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.
- Non-expected utility, continued: incomplete preferences, second-order utilities and probabilities (Rigotti and Shannon, Klibanoff et al., Nau)
- Fundamentals of noncooperative game theory: a bestiary of solution concepts (Nash, Selten, et al.) Notes and guide to readings.
- Game theory, continued: common knowledge, the common prior assumption (Harsanyi), correlated equilibrium (Aumann), joint coherence (Nau/McCardle) Notes and guide to readings.
- Game theory, continued
- Social choice: Harsanyi's aggregation theorem, Arrow's impossibility theorem, paradoxes of voting. Notes and guide to readings.
- Asset pricing theory. Notes and guide to readings. HET notes on general equilibrium under uncertainty.
- Auction theory: Notes and guide to readings.
- TBA + student presentations
- TBA + student presentations
- TBA + student presentations

Additional legacy notes:

Problems with subjective expected utility: criticism by Ellsberg, Aumann, Shafer. Notes and guide to readings.

Problems with game theory: criticism by Kadane and Larkey, Sugden, and others. Notes and guide to readings.

"Pathologies of rational choice": criticism by Green and Shapiro, rebuttals and rejoinders. Guide to readings.

Alternative perspectives on choice theory: radical subjectivism, Austrian economics, bounded rationality, evolutionary psychology, and cognitive neuroscience. Notes and guide to readings.