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

**Professor Robert Nau
**

**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.

**Course
outline and downloadable lecture notes: **The following week-by-week
sequence of topics is provisional. The "notes and guides to
readings" that are currently linked below will be revised and expanded as
the course progresses. I am in the process of writing a book on
"Arbitrage and Rational Choice" and will use some of its completed
chapters. The additional "HET notes" links refer to pages on the
History of Economic Thought website at New School University, an ambitious work-in-progress
written by Goncalo L. Fonseca. They provide excellent supplementary
reading, although somewhat heavier on mathematical formalism than will be
necessary for our purposes.

- 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.

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.