2005 Bullerwell Lecturer

Lecturer: Lecturer Name Date: Date

The goal of this document is to provide a computationally practical guide to game-theoretic problems. We discuss the current intractibility of finding Nash Equilibria exactly, and of even specifying a game in normal form for a large number of players. But hope is not lost. Efficiently computable solution concepts are presented as alternatives to Nash Equilibria, with a corresponding notion of P...

Lecture 2 Introduction to Some Convergence theorems Friday 14 , 2005 Lecturer : Nati Linial

r∈Z f̂(r)e In the last lecture, we proved Fejér’s theorem f ∗ kn → f where the ∗ denotes convolution and kn (Fejér kernels) are trignometric polynomials that satisfy 1. kn ≥ 0 2. ∫ T kn = 1 3. kn(s) → 0 uniformly as n→∞ outside [−δ, δ] for any δ > 0. If X is a finite abelian group, then the space of all functions f : X → C forms an algebra with the operations (+, ∗) where + is the usual pointwis...

Lecture 1 Introduction to Fourier Analysis Jan 7 , 2005 Lecturer : Nati Linial

Consider a vector space V (which can be of finite dimension). From linear algebra we know that at least in the finite-dimension case V has a basis. Moreover, there are more than one basis and in general different bases are the same. However, in some cases when the vector space has some additional structure, some basis might be preferable over others. To give a more concrete example consider the...

on the Border of Economics and Computation November 6 , 2005 Lecture 2 Lecturer

Lecturer : Constantinos

We start with a review of some elements from last lecture. Let us consider a marketplace where the excess demand on goods is a well-defined vector-valued function f(p) of the prices p. This happens, e.g., when traders’ utility functions are strictly concave, so that they have unique utility-optimizing bundles. In this case, the excess demand function is the difference of the total demand and th...