Advanced Microeconomic Theory 805

 

Advanced Microeconomic Theory 805

Lones Smith

lones@ssc.wisc.edu              www.lonessmith.com

Monday/Wednesday 11AM-12:15PM in SS6112 Fall, 2010

Office hours: Thursday 2:30-4:30 or by appointment 

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.

The game theory topic selection presupposes that you will finish your education with Econ 806, taught by Antonio Penta. 

Prerequisites

I assume that your prior knowledge of economic theory x and your analytical ability y obey the inequality xy > c, where c > 0 is a constant that I cannot quantify. As always, it helps to be able to leap tall buildings in a single bound. The idea is that this is a sequel to Econ 703/711/713, but I will not enforce that rule, since your y may be high, or you may x may owe to other sources, like seeing “A Beautiful Mind” (I hope not). 

Grades

Three assignments count about 20% each (this may vary) and a take-home final exam 40%.

Books

There is no comprehensive text for information economics, and so we shall largely rely on articles (see below). I do recommend that serious theorists purchase Supermodularity and Complementarity, by Donald Topkis.

Game Theory by Fudenberg and Tirole is a pretty good advanced game theory text. But I have not required it to save you money, and since it is getting dated. It should (soon) be on reserve, along with the two wonderful texts by Myerson, Osborne and Rubinstein.

For those whole prefer intuition, or enjoy reading, try the purely prosaic book The Strategy of Conflict that won Schelling his Nobel Prize; he managed to anticipate many of the ideas in game theory in the 1980’s about two decades earlier. Here are some of my favorite snippets from his classic book when I read it several years ago:

• “strategy . . . is not concerned with the application of force but with the exploitation of potential force.”

• “Deterrence: influencing the choices another party will make by influencing his expectations of how we will behave.”

• “. . . most conflict situations are essentially bargaining situations.”

• “. . . madmen, like small children, can often not be controlled by threats.” 

 

Wisdom for Theorists

Economic theories should be judged by three criteria: generality, congruence with reality, and tractability. 

– George Stigler, Essays in the History of Economics (1965).

Make everything as simple as possible, but not simpler. – Albert Einstein

 

I. Information Economics (about seven lectures)

1.   Frictional Matching Models

• G.G. Lorentz (1953), "An Inequality for Rearrangements", American Mathematical Monthly, 60 (3), 176-179.
• Gary Becker (1973), A Theory of Marriage, Part I, The Journal of Political Economy, 81 (4), 813-846
• David Gale and Lloyd Shapley (1962), "College Admissions and the Stability of Marriage", The American Mathematical Monthly 69 (1), 9-15.
• Robert Shimer and Lones Smith. “Assortative Matching and Search”, Econometrica, 68(2): 343-370. 
• Lones Smith (2006), “The Marriage Model with Search Frictions,” Journal of Political Economy, 114(6): 1124-1144. 
• Ken Burdett and Melvyn Coles (1997), "Marriage and Class" Quarterly Journal of Economics, 112(1), 141-168.
•  Lones Smith (1998), ``A Model of Exchange Where Beauty is in the Eye of the Beholder,'' MIT Working paper. 
•  Axel Anderson and Lones Smith (2010), “Dynamic Matching and Evolving Reputations”, Review of Economic Studies, 77:3-29.2.  
  

 2. Comparative Statics under Certainty and Uncertainty

We explore modern lattice-theoretic methods of supermodularity and comparative statics. We then explore stochastic orders, and extend the monotone comparative statics to uncertainty. We explore total positivity, including log-supermodularity.

• S. L. Brumelle and R.G. Vickson (1975), “A Unified Approach to Stochastic Dominance”, in Stochastic Optimization Models in Finance, New York, Academic Press. 

• Paul Milgrom and Chris Shannon (1994), ”Monotone Comparative Statics”, Econometrica, 57: 157-180.
  
• Susan Athey (2000), "Characterizing Properties of Stochastic Objective Functions,'' MIT working paper. 
•  Michael Rothschild and Joseph Stiglitz (1970), ``Increasing Risk I: A Definition,'' Journal of Economic Theory, 2: 225-243. 
•  Erich Lehmann (1955), “Ordered Families of Distributions,” Annals of Mathematical Statistics, 26: 399-419.
•   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. 
•  Susan Athey (2002), “Monotone Comparative Statics Under Uncertainty”, Quarterly Journal of Economics, 117(1), 187-223. 
•  Peter Diamond and Joseph Stiglitz (1974), “Increases in Risk and in Risk Aversion”, Journal of Economic Theory, 8:337-60. 
•  Ken Burdett (1996), “Truncated Means and Variances”, Economics Letters, 52: 263-67. 
•  Donald Topkis, Supermodularity and Complementarity, Princeton University Press, 1998. 
•  Samuel Karlin, Total Positivity, vol. 1, Stanford University Press, 1968. 
•  Sudhakar Dharmadhikari and Kumar Joag-dev, Unimodality, Convexity, and Applications, Academic Press, 1988. 
•  Moshe Shaked and George Shanthikumar, Stochastic Orders and their Applications, Academic Press, 1994.

3.    Information
We contrast the foundations and recent work on value and demand for information, and how to rank informative signals.

• Samuel Karlin and Herman Rubin (1956), ``Distributions Possessing a Monotone Likelihood Ratio'', Journal of the American Statistical Association, 51: 637-643.
• Ward Whitt (1979), ``A Note on the Influence of the Sample on the Posterior Distribution,'' Journal of the American Statistical Association, 74 (366): 424-426.
• Paul Milgrom (1981), “Good News and Bad News: Representation Theorems and Applications,” Bell Journal of Economics, 12: 380-391.
• Laurence Glosten and Paul Milgrom (1985), “Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders”, Journal of Financial Economics, 13: 71-100.
• Lones Smith (2000), “Private Information and Trade Timing,'' American Economic Review, 90 (4): 1012-1017.
• David Blackwell (1953), “Equivalent Comparison of Experiments”, Annals of Mathematics and Statistics, 24: 265-272.
• Roy Radner and Joseph Stiglitz (1984), “A Nonconcavity in the Value of Information” in Bayesian Models in Economic Theory, Elsevier Science Publishers, New York, Marcel Boyer And Richard Kihlstrom, eds., pp. 33-52.
• Edward Schlee and Hector Chade (2001), “Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information,” Journal of Economic Theory, 107: 421-52.
• Erich Lehmann (1988), “Comparing Location Experiments”, Annals of Statistics, 16:521-33.
• Giuseppe Moscarini and Lones Smith (2002), “The Law of Large Demand for Information”, Econometrica, 70(6): 2351-2366.
• Jussi  Keppo, Giuseppe Moscarini, and Lones Smith (2008), Journal of Economic Theory, 138: 21-50.
• Jack Hirshleifer and John Riley, The Analytics of Uncertainty and Information, Cambridge University Press, 1992.
• Morris DeGroot, Optimal Statistical Decisions, 1970.

4. Social Learning

• Abhijit Banerjee (1992), "A Simple Model of Herd Behavior,'' Quarterly Journal of Economics, 107: 797-817.
• Sushil Bikhchandani, David Hirshleifer, and Ivo Welch (1992), “A Theory of Fads, Fashion, Custom and Cultural Change as Informational Cascades”, Journal of Political Economy, 100: 992—1026.
• Lones Smith and Peter Sorensen (2000), "Pathological Outcomes of Observational Learning,'' Econometrica, 68: 370-398.
• Lones Smith and Peter Sorensen (2001), “Informational Herding and Optimal Experimentation”, under revision for Review of Economic Studies.
• Giuseppe Moscarini, Marco Ottaviani, and Lones Smith (1997), “Social Learning in a Changing World”, Economic Theory, 11: 657-665.
• Margaret Bray and David Kreps (1987), “Rational Learning and Rational Expectations,” in Feiwel, G., ed., Kenneth Arrow and the Ascent of Economic Theory, 1987.

BONUS MATERIALS

Blackwell's excellent proof of his famous Theorem: PDF

Handout on the Dynkin martingale for Markov processes: PDF

II. Game Theory (about seven lectures)

1.    Static Games of Complete Information

• Nash equilibrium (1950), Zero-sum games and Minmax Theorem (von Neuman ‘28) 
• Applications: “Silent” Timing Games (Park-Smith ’08)

2.    Static Games of Incomplete Information

• Bayesian Nash Equilibrium (Harsanyi 1968); purified Nash Equilibrium (Harsanyi 1973)

3.    Dynamic Games of Complete and Almost Perfect Information

• Subgame perfection (Selten ’65), the backward induction paradox
• Perfect Information: Zermelo’s Theorem, present-biased preferences, blackmail, temporal monopoly bargaining (Rubinstein ’82)
• Action Tremble Refinements: trembling hand perfection (Selten ’75, Myerson ‘78)
• Timing games with observed actions: war of attrition, pre-emption games
• Repeated games with observed actions: dynamic programming, self-generation, stick-and-carrot punishments (Abreu, ’88), renegotiation-proofness
• Folk theorems for Repeated Games (Fudenberg-Maskin ’86, Abreu-Dutta-Smith ’04)
• Markov Perfect and Markovian Equilibrium, Aspirational bargaining (Smith-Stacchetti ’03)

4.    Dynamic Games of Incomplete or General Imperfect Information

• Extensive form games: sequential and perfect Bayesian equilibrium; imperfect recall and the absent minded driver (Kreps-Wilson ’82, Piccione-Rubinstein ‘97)
• Stability, Signaling games and Refinements (Kohlberg-Mertens ’86, Cho-Kreps ’87)
• Communication: cheap talk (Crawford-Sobel, ‘82), lying (Kartik-Ottaviani-Squintani ’07)
• Repeated Games with Imperfect Public Monitoring (Abreu-Pearce-Stacchetti  ’86 & ’90)
• Folk Theorem with Imperfect Monitoring (Fudenberg-Levine-Maskin ’94, Ely-Valimaki ’02)
• Repeated Games with Incomplete Info, Rendezvous Problem (Aumann-Maschler-Stearns, ‘68)
• Durable Monopoly, Bargaining (Gul-Sonnenschein-Wilson ’86)
• Continuous time games with Brownian Motion Noise
  • Imperfectly Observable Actions in Continuous Time (Sannikov ’07)
  • Information Monopoly (Back and Baruch ’04, Anderson-Smith ‘08)
  • Optimal Dynamic Contests (Moscarini-Smith ’07)