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.

  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)
  6. Fundamentals of noncooperative game theory:  a bestiary of solution concepts (Nash, Selten, et al.) Notes and guide to readings.
  7. Game theory, continued: common knowledge, the common prior assumption (Harsanyi), correlated equilibrium (Aumann), joint coherence (Nau/McCardle)  Notes and guide to readings.
  8. Game theory, continued
  9. Social choice:  Harsanyi's aggregation theorem, Arrow's impossibility theorem, paradoxes of voting.  Notes and guide to readings. 
  10. Asset pricing theory.  Notes and guide to readings.   HET notes on general equilibrium under uncertainty.
  11. 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.