**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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