SCIENTIFIC PROGRAMS AND ACTIVITIES

October 17, 2018

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

July-December 2014
Thematic Program on
Variational Problems in Physics, Economics and Geometry

September 11-12
Preconference Minischool
on Optimization, Transportation and Equilibrium in Economics


Organizing
Committee
Pierre-Andre Chiappori (Columbia)
Alfred Galichon (Sciences Po)
Robert McCann (Toronto)
Xianwen Shi (Toronto)


MINISCHOOL PROGRAMME

THURSDAY September 11
8:45-9:00
Welcoming Remarks

9:00-10:15

Robert McCann
Mathematical transportation and applications to economic theory
1

10:00-10:30

Coffee break

10:45-12:00

Robert McCann
Mathematical transportation and applications to economic theory 2

12:00-1:50

Lunch break

2:00-3:00

Xianwen Shi (Slides)
Introduction to Mechanism Design 1

3:00-3:15

Tea break
3:15-4:45
Xianwen Shi
Introduction to Mechanism Design
2
FRIDAY September 12

9:00-10:15

P-A Chiappori (Slides)
Economic applications of matching models, 1

10:00-10:30

Coffee break

10:45-12:00

P-A Chiappori
Economic applications of matching models, 2

12:00-1:50

Lunch break

2:00-3:00

Rakesh Vohra (Slides)
Applications of Linear Programming to Economic Theory 1

3:00-3:10

Tea break
3:10-3:50

Meet the Mentors
A very brief introduction to selected faculty mentors participating in the
theme semester on Variational Problems in Physics, Economics and Geometry,
and their research interests:

1) Walter Craig (Fields Director)
2) Wilfrid Gangbo (Georgia Institute of Technology)
3) Young-Heon Kim (University of British Columbia)
4) Almut Burchard (University of Toronto)
5) Robert Jerrard (University of Toronto)
6) Jochen Denzler (University of Tennessee at Knoxville)
7) Slim Ibrahim (University of Victoria)
8) Nader Masmoudi (New York University)
9) Kostantin Khanin (University of Toronto)
10) Dmitry Panchenko (University of Toronto)
11) Jeremy Quastel (University of Toronto)
11) Matheus Grasselli (Fields Deputy Director)

4:00-5:30
Rakesh Vohra
Applications of Linear Programming to Economic Theory 1

 

SPEAKERS, TITLE AND ABSTRACT INFO FOR MINISCHOOL

Pierre-Andre Chiappori (Columbia University)
Economic applications of matching models

Robert McCann (University of Toronto)
Mathematical transportation and applications to economic theory

Optimal transportation has enjoyed a mathematical renaissance over the last twenty-five years, weaving together threads from analysis, geometry, partial differential equations and dynamical systems. Its connection to economic applications such as transferable utility matching has been recognized since Shapley and Shubik (1972). These mathematical developments have also led to new progress on economic applications including problems of asymmetric information (such as monopolist nonlinear pricing or multidimensional screening), and the existence of equilibria for multi-stage decision problems in steady-state, multidimensional settings. We give an overview of this mathematical topic and related developments in economic theory.

References:
1) R.J. McCann and N. Guillen: Five lectures on optimal transportation: geometry, regularity and applications. In Analysis and Geometry of Metric Measure Spaces: Lecture Notes of the Seminaire de Mathematiques Superieure (SMS) Montreal 2011. G. Dafni et al, eds. Providence: Amer. Math. Soc. (2013) 145-180.
2) R.J McCann. Academic wages, singularities, phase transitions and pyramid schemes , Proceedings of the 2014 International Congress of Mathematics at Seoul (submitted).

Xianwen Shi (University of Toronto)
Introduction to Mechanism Design

This mini-course will provide a brief introduction to the theory of mechanism design, which has found applications in almost every area of economics, and which also plays an important role in parts of political science. We will primarily focus on the classical static setting where agents' types are one-dimensional, statistically independent, and agents' valuations on allocations depend only on their own types (i.e., private values). Both dominant strategy implementation and Bayesian implementation will be discussed. We will also very briefly mention how these results might be extended to dynamic settings, why multi-dimensional types or interdependent values will complicate the analysis, and why the theory of convex analysis and optimal transport may be helpful in advancing the theory of mechanism design.

Rakesh Vohra (University of Pennsylvania) Slides
Applications of Linear Programming to Economic Theory'

Linear programming plays an important role in economic theory. Its duality theorem can be used to prove existence of a value for zero-sum games, existence of walrasian equilibria in assignment markets and the existence of risk neutral probabilities in the absence of arbitrage. In this `nano' course I will discuss the use of linear programming techniques in mechanism design and a related `inverse' problem of rationalizing choices.

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