Advanced Economic Theory (A1, 2016)

OYAMA Daisuke
oyama@e.u-tokyo.ac.jp

In this course, we study algorithmic/computational approaches in economic theory. The first half disucsses methods to compute Nash equilibria or fixed points in general. Topics in the second half are to be decided according to the participants' interests. Candiates include repeated games, population game dynamics, stable matching problems, or topics from Quantitative Economics such as dynamic programming techniques and their applications to macroeconomics.

Some opportunities are given (mainly via homework assignments) to practice programming. We will use Python and/or Julia. To set up your Python/Julia environments, refer to

• Setting up Your Python Environment
• Setting up Your Julia Environment

Grading based on participation, presentation, and final project.

Course repository

Notice

Lecture by Prof. John Stachurski on computational economics on 10/4 at Keio University:

• Modern Tools for Computational Economics by Prof John Stachurski

Readings

Computation of Nash equilibria/fixed points

• *von Stengel, B. (2007). ``Equilibrium Computation for Two-Player Games in Strategic and Extensive Form,'' Chapter 3, Algorithmic Game Theory.
• von Stengel, B. (2002). ``Computing Equilibria for Two-Person Games,'' Chapter 45, Handbook of Game Theory. [Longer earlier version (1996)]
• *McLennan, A. and R. Tourky (2006). ``From Imitation Games to Kakutani.''
• McLennan, A. and R. Tourky (2010). ``Imitation Games and Computation,'' Games and Economic Behavior 70, 4-11.
• Lemke, C. E. and J. T. Howson, Jr. (1964). ``Equilibrium Points of Bimatrix Games,'' J. SIAM 12, 413-423.
• Lemke. C. E. (1965). ``Bimatrix Equilibrium Points and Mathematical Programming,'' Management Science 11, 681-689.
• Shapley, L. S. (1974). ``A Note on the Lemke-Howson Algorithm.''
• Murty, K. G. (1988). Linear Complementarity, Linear and Nonlinear Programming.
• Vorob'ev, N. N. (1958). ``Equilibrium Points in Bimatrix Games,'' Theory of Probability and Its Applications 3, 297-309.
• Kuhn, H. W. (1961). ``An Algorithm for Equilibrium Points in Bimatrix Games,'' Proceedings of the National Academy of Sciences of the United States of America 47, 1657-1662.
• Mangasarian, O. L. (1964). ``Equilibrium Points in Bimatrix Games,'' J. SIAM 12, 778-780.
• Avis, D., G. Rosenberg, R. Savani, and B. von Stengel (2010). ``Enumeration of Nash Equilibria for Two-Player Games,'' Economic Theory 42, 9-37.
• Special Issue of Economic Theory on Computation of Nash Equilibria in Finite Games.
• Rosenberg, G. D. (2005). ``Enumeration of All Extreme Equilibria of Bimatrix Games with Integer Pivoting and Improved Degeneracy Check,'' CDAM Research Report LSE-CDAM-2004-18.

Slides

• Introduction (9/27)
• Equilibrium Computation for Two-Player Games in Strategic Form: Part I (9/27), Part II (9/30), Part III (10/4)
• From Imitation Games to Kakutani (10/21)

Office hours

Class schedule