Mathematical Economics (S2, 2023)

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

Monday, Friday 10:25-12:10
First session June 5
Class room 7

Syllabus/Introduction

In this course, we study mathematical tools useful for advanced level economics, including important topics from convex analysis, as well as advanced topics from discrete mathematics such as lattices, supermodularity, and matroids.

Textbook

R. V. Vohra, Advanced Mathematical Economics, Routledge, 2004. [Amazon]

References

L. D. Berkovitz, Convexity and Optimization in Rn, Wiley, 2003. [Amazon]
S. Fujishige, Submodular Functions and Optimization, Second Edition, Elsevier, 2005. [Amazon]
A. Schrijver, Theory of Linear and Integer Programming, Wiley, 1998. [Amazon]
J. Dow and S. Werlang, ``Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio,'' Econometrica 60, 197-204, 1992.
P. Milgrom and J. Roberts, ``Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities,'' Econometrica 58, 1255-1277, 1990.
L. S. Shapley, ``Cores of Convex Games,'' International Journal of Game Theory 1, 11-26, 1971.

Topics

  1. Farkas' Lemma [Slides (6/12)]
  2. Separating Hyperplane Theorems [Slides (6/19)]
  3. Structure of Polyhedra [Slides (6/26)]
  4. Lattices and Supermodularity [Slides (7/3)]
  5. Cores of Convex Games [Slides (7/7)]
  6. Matroids and Polymatroids [Slides (7/13)]
  7. Choquet Integral [Slides (7/21)] New

Homeworks

Homework 1 (due on June 12)
Homework 2 (due on June 19)
Homework 3 (due on June 26)
Homework 4 (due on July 3)
Homework 5 (due on July 10)

Submit your homework through ITC-LMS

Office hours

Friday 14:00-15:30
Economics Research Building 10th floor, 1012