When/where: Mondays and Wednesdays 4-5:30PM in 2260 USB 10/28/2009 - 12/14/2009
Section: Thursdays 6-7:30PM with Dmitry Lubensky (email@example.com)
Office hours: Tuesday 3-4:30 in Lorch 335A (firstname.lastname@example.org)
This is quarter 2 in the PhD microeconomics sequence. I assume that you are sophisticated and fully understand vNM expected utility from Econ 601. If not, please review it.
Grades. The midterm is worth 40% and is in-class on MONDAY, NOVEMBER, 23. The final exam 60%, and is annoyingly scheduled for WEDNESDAY, DECEMBER 23! I will rescale each exam by the class average. If your rescaled exam grade on the final is better, then it will count 100%.
Resources: The course text is MWG. Some specific articles might be cited too. I will post some links on the ctools cite. Read the funny ones to keep up your faith in life, and read the serious ones for their insights into economics and game theory.
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."
Problem Solving. The class will go fast. When you come to lecture, think of it as "the show". What I will say will be concise and maybe witty, but we have to learn an ocean of game theory in a blink of an eye. Before you know it, you will be eating some hapless Thanksgiving bird, and then leaving for the holidays.
So if you want to learn game theory, do lots of reading on your own and solve problems. Notice that while homework will have no formal weight, it ultimately will determine how you do on exams. Dmitry will supply solutions or solve questions in section.
Here’s how you get the most out of the homework: First try to solve each problem solo; if that fails after some passage of time, ask your friends; then ask for a hint from others; then read the solutions; then go ask Dmitry, or ask me. A doctor of philosophy ideally requires insight more than algorithm. Please expend the mental energy to learn the process of discovery. If you find the solution yourself, you will learn to think; even if you miss finding the solution yourself after hours of trial, you learn what lines of thinking lead to dead-ends. Everyone should master the basic principles of problem solving: It not only determines who passes the prelims, but who excels in research. You might wish to peruse Polya’s How to Solve It.
Like all courses in the theory sequence, if math is not your cup of tea, or coffee, then problem solving is even more important.
Getting help. Talk to Dmitry. Or, email me questions. My office hours are Tuesday 3-4:30PM. But the Econ 501 students often come too, so you can come a half hour earlier at 2:30 if you want.
I. Static Games of Complete Information (≈4 or 5 lectures)
* Normal Form Games
- MWG: Chapter 8. A
* Dominant Strategy Equilibrium
- MWG: Chapter 8. B, C
* Iterated Dominance and Rationalizability (eg. Guess 2/3 of the average)
* Nash equilibrium in Pure Strategies
- MWG Chapter 8.D (up to the top of page 250)
* Continuous and Discontinuous Payoffs
- examples: Hotelling and Bertrand competition
* General Nash equilibrium in Mixed Strategies (eg. public goods game, Caller #5)
- MWG: Chapter 8.D and Appendix A
* Constant-sum games, Minmax Theorem, and Uniqueness (sports applications)
* Large Population Games: Driving, Counterfeit Money, Disease Contagion
* Convergence to Equilibrium: Evolution, risk dominance, and Experimentation
* Supermodular Games and multiple equilibria
II. Static Games of Incomplete Information (≈1 or 2 lectures)
* Bayes Rule
* Bayesian Nash Equilibrium (eg. First and Second Price Auctions)
- MWG: Chapter 8.E
- Purified Nash Equilibrium (eg. Public Goods Game redux)
* Correlated Equilibrium
III. Dynamic Games of Complete Information
A. Perfect Information (≈2 lectures)
- MWG: Chapter 9. A and B, Chapter 12. D and E, Appendix A
* Strategic Decision Trees and Equivalent normal forms
* Credible Threats in Entry Deterrence
* Backwards Induction: Zermelo's Theorem (1912)
* the Ultimatum Game and Temporal Monopoly bargaining
* Timing games with alternating actions: war of attrition, pre-emption games
- Application: Time consistent choice over time and multiple selves
B. Almost Perfect Information (≈2 lectures)
* Extensive Form Games with subgames
* Subgame Perfect Equilibrium
- Applications: Stackelberg Equilibrium, Durable Monopoly
* Timing games redux, and Aspirational bargaining
* Folk theorem for repeated games
IV. General Extensive Form Games (≈4 lectures)
* Extensive form games without belief systems
* Kuhn’s Theorem: Mixed vs. Behavior Strategies
- Application: Imperfect recall and the absent minded driver
* Sequential equilibrium
- Applications: Bank runs, Cheap talk (time permitting)
- "Intuitive" Refinements and Forward induction (time permitting)
* Signaling Games (time permitting)
* Reputation (time permitting)
* Repeated Games with Imperfect Monitoring (time permitting)
* Bargaining with Incomplete Information (time permitting)
* Repeated Games with Incomplete Information (time permitting)