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Game Theory 2017

Exam

The exam is planned for January 22nd-25th. Some administrative information:

  • preparation is closed book (no notes, books, electronic equipment etc.)
  • if you are not there when your name is called, you unfortunately fail
  • no electronic equipment (mobile phones, tablets, smart watches etc.) is allowed during preparation or examination; secure storage possibilities for such items are not provided.

For the exam you should expect the following:

  • you randomly draw a question
  • you have 15-20 minutes preparation time
  • you are examined for 15 minutes and receive the grade afterwards; you can present what you prepared and you should expect some follow up questions, i.e. the examination is not necessarily restricted to the questions you drew.

Exam questions usually have 2-4 subquestions. One subquestion is often about explaining concepts and results covered in the lecture. One subquestion is often an exercise similar to those done in class. Sometimes you are asked to link concepts. Sometimes you are asked to give an example for something. You do not have to know all the proofs we did by heart but you should know the main idea; in particular, you should be able to explain why a result holds. You are responsible for the time management, i.e. for covering all subquestions within the 15 minutes. In the interest of time, it can be better to tell us immediately if you did not understand a subquestion. Sometimes we can then resolve the misunderstanding.

Organization

Lectures: Thursday 10:00-13:00 in 35-3-12 (apart from first lecture which is in 26.2.21)

If you have not taken Micro C (or forgotten most of it…), you should (re-)read chapters 1.1-1.3.A, 2.1 and 3.1, 3.2 in Robert Gibbons’ Game Theory book before the course starts.

You are expected to read the math handout before the course and to read the handout on notation before the second lecture.

Midterm

The midterm is a take home exam. You have to pass the midterm in order to be admitted to the final exam. The midterm should be done in groups of up to three people. You have the weeks 41 and 42 (mid October) to work on the midterm. Deadline for handing in is October 23, 18:00. The midterm exercises are here: Midterm

A solution to the midterm is now available.

Here is a list with students that are admitted to the final exam. Please, check whether you are on it and contact me if you are not (though you think you should).

Final Exam

The final is an oral exam (with 20 minutes closed book preparation time).

Lecture Plan

Uncertainty and risk

Lecture 1: Intro expected utility theorem

  • Introduction
  • What is GT?
  • expected utility theorem
  • reading: MSZ 2.1-2.5 or MWG 6.A-6.B, (supplementary reading: Gilboa et al. (2014))

Solution concepts

Lecture 2: NE

  • Fixed point theorems
  • Nash existence theorem
  • reading: MSZ 5.3, (supplementary reading: OR 2.4; a proof of Brouwer’s fixed point theorem can be found in MSZ 23.1 but reading this proof is by no means necessary)

Lecture 3: Rationalizability and dominance

  • Rationalizability and iterated elimination of dominated strategies
  • reading: OR 4 or MSZ 4.5, 4.7, 4.11,

Lecture 4: Correlated equilibrium

  • Correlated equilibrium
  • reading: OR 3.3 or MSZ 8

Lecture 5: Risk preferences

  • risk preferences
  • impact of risk attitudes on the equilibrium set
  • reading: MWG 6.C or MSZ 2.7-2.8, Weinstein (2016)

Lecture 6: Supermodular games: when solution concepts coincide

  • Amir (2005), (supplementary reading: Milgrom and Roberts (1990))

Knowledge

Lecture 7: Knowledge I

  • Hat game
  • Aumann model
  • reading: OR 5.1-5.2 (or MSZ 9.1)

Lecture 8: Knowledge II

  • No agree to disagree
  • (Common) knowledge and solution concepts
  • Electronic mail game
  • reading: OR 5.3-5.5 (or MSZ 9.2)

Lecture 9: Global Games I

  • stag hunt
  • reading: Carlson and van Damme (p. 989-993)

Lecture 10: Global Games II

  • private and public signal
  • reading: Morris and Shin (2001)

Matching

Lecture 11: Deferred acceptance algorithm

  • reading: Gale and Shapley (1962)

Lecture 12: School Choice

  • top trading cycles algorithm
  • reading: Abdulkadiroglu and Sönmez (2003)

Material

Handouts

Lecture slides

The “extra” material is for your pleasure and entertainment and not relevant for the exam. The code you find in there is written in Python (there are literally hundreds of Python guides on the web if you are interested, e.g. https://lectures.quantecon.org/py/).

Bibliography

OR: Osborne and Rubinstein 1994; A course in game theory; MIT Press (available as free ebook on the author’s website)

MSZ: Maschler, Salon and Zamir 2013; Game theory; Cambridge University Press (KU library link)

MWG: MasColell, Whinston and Green 1995; Microeconomic theory; Oxford University Press

FT: Fudenberg and Tirole 1991; Game theory; MIT Press

Abdulkadiroglu, Atila, and Tayfun Sönmez. “School choice: A mechanism design approach.” The American Economic Review 93.3 (2003): 729-747.

Amir, Rabah. “Supermodularity and complementarity in economics: an elementary survey”, Southern Economic Journal, Vol. 71, No. 3 (2005): 636-660. link

Aumann 1985: What is game theory trying to accomplish?; Frontiers of Economics; link

Carlson and van Damme “Global Games and Equilibrium Selection”, Econometrica, Vol. 61, No. 5 (Sep., 1993), pp. 989-1018; link

Gale, David, and Lloyd S. Shapley. “College admissions and the stability of marriage.” The American Mathematical Monthly 69.1 (1962): 9-15. link

Gilboa, Itzhak, et al. “Economic models as analogies.” The Economic Journal 124.578 (2014): pp.513-533. link

Jann, Ole, and Christoph Schottmüller. “Correlated equilibria in homogeneous good Bertrand competition.” Journal of Mathematical Economics 57 (2015): 31-37. link

Milgrom and Roberts “Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities”, Econometrica, Vol. 58, No. 6. (Nov., 1990), pp. 1255-1277; link

Morris and Shin “Global Games: Theory and Applications”, Econometric Society Monographs 35, 2003, 56-114 - Cambridge University Press; link

Morris, Stephen, and Hyun Song Shin. “Unique equilibrium in a model of self-fulfilling currency attacks.” American Economic Review, Vol. 88, No. 3 (1998): 587-597. link

Morris, S. and H. S. Shin (2001). Rethinking multiple equilibria in macroeconomicmodeling. In NBER Macroeconomics Annual 2000, Volume 15, pp. 139–182. MIT Press. link

Shapley, L. S. and M. Shubik (1971). The assignment game i: The core. International Journal of Game Theory 1 (1), 111–130.

Varian, Hal R. “Position auctions.” International Journal of industrial Organization 25.6 (2007): 1163-1178. link

Weinstein, Jonathan. “The Effect of Changes in Risk Attitude on Strategic Behavior.” Econometrica 84.5 (2016): 1881-1902. link