This is an advanced PhD course with two unrelated focuses: information economics and game theory. The topic diversity is intended to open up a broad swath of theory for your use and possible future work.
The information economics course explores how Bayesian rational people behave under uncertainty, largely in dynamic matching and learning environments. The topics revolve around my past and current research in information theory, social learning, and frictional matching models.
Module 1: Monotone Methods in Economics
- Supermodularity and Quasi-supermodularity
– Donald Topkis, Supermodularity and Complementarity, Princeton University Press, 1998.
Sudhakar Dharmadhikari and Kumar Joag-dev, Unimodality, Convexity, and Applications, Academic Press, 1988.
– Paul Milgrom and Chris Shannon (1994), ”Monotone Comparative Statics”, Econometrica, 57: 157-180.
- Stochastic Dominance
– Moshe Shaked and George Shanthikumar, Stochastic Orders and their Applications, Academic Press, 1994.
– Peter Diamond and Joseph Stiglitz (1974), “Increases in Risk and in Risk Aversion”, Journal of Economic Theory, 8:337-60.
– S. L. Brumelle and R.G. Vickson (1975), “A Unified Approach to Stochastic Dominance”, in Stochastic Optimization Models in Finance, New York, Academic Press.
– Susan Athey (2000), “Characterizing Properties of Stochastic Objective Functions,” mimeo
- Logsupermodularity and Monotone Comparative Statics under Certainty
– Karlin and Rinott (1980), “Classes of Orderings of Measures and Related Correlation Inequalities. I. Multivariate Totally Positive Distributions,” Journal of Multivariate Analysis, 10(4): 467-498.
– Erich Lehmann (1955), “Ordered Families of Distributions,” Annals of Mathematical Statistics, 26: 399-419.
– Susan Athey (2002), “Monotone Comparative Statics Under Uncertainty”, Quarterly Journal of Economics, 117(1), 187-223.
- Total Positivity and the Variation Diminishing Property
– Samuel Karlin, Total Positivity, vol. 1, Stanford University Press, 1968.
– Sudhakar Dharmadhikari and Kumar Joag-dev, Unimodality, Convexity, and Applications, Academic Press, 1988
Module 2: Ito Calculus, Optimization, and Optimal Stopping
Module 3: Information and Learning
- Blackwell’s Theorem and the Demand for Information
- Informational Herding
Module 4: Search and Experimentation
- Stigler’s fixed sample size search; simultaneous search; Pandora’s Box Problem
- Optimal Stopping and Search
- Bandits via Optimal Stopping
- Application: Frictional Matching Models
- The Optimal Level of Experimentation