Computational Methods Assignment 3
1. A graduate student writes one research paper each year. With probability 0.5, the
student finds null results (-), with probability 0.25, he finds results that are statistically significant at the 10% level (*), with p
Note Set 8 Numerical Game Theory
8.1 Overview
In this note set, we will cover a number of techniques of computing numerical
solutions to games. We will consider both discrete strategy spaces and continuous
strategy spaces. Games with discrete strategy spa
Note Set 7 Nonlinear Equations
7.1 Overview
Often, we will be interested in solving a system of non-linear equations,
f ( x) = 0 . Non-linear equations are generally hard problems.
7.2 Newtons Method
Newtons method proceeds by using the approximation,
f (
Computational Methods Assignment 2
1.
Consider the following stylized model of the 2008 Republican Presidential
Primary. There are four candidates competing- Rudy Giuliani, John McCain, Mitt
Romney, and Fed Thompson. Each candidate can raise money in orde
Computational Methods Assignment 1
1.
Consider a game of electoral competition between two vote-maximizing
candidates, L and R , who take positions yL [0,1] and yR [0,1] . There is a continuum
of voters characterized by their ideal points v [0,1] and thei
Note Set 5 Constrained Optimization
5.1 Overview
In this note set, we consider constrained optimization.
5.2 Kuhn-Tucker Conditions
Suppose we have an optimization problem of the form,
max f ( x) such that ceq ( x) = 0 , cneq ( x) 0
x
This type of problem
Note Set 9 Dynamic Optimization Problems and
Dynamic Games
9.1 Overview
Often, we will be interested in solution dynamic optimization problems, where an
agent maximizing the discounted stream of utilities U ( x) = t u ( xt ) subject to some
t =0
constrain
Note Set 1 The Basics
1.1 Overview
In this note set, we will cover the very basic tools of numerical methods.
Numerical methods are useful for both formal theory and methods because they free us
from having to employ restrictive assumptions in order to ob
Note Set 2 Programming
2.1 Overview
In this note set, we will cover programming in c/c+ for numerical applications.
We will start by covering the basic of the language, with particular emphasis on the
difference in programming strategies between a mid-lev
Note Set 6 Simulation Methods
6.1 Overview
In Note Set 1, we discussed a number of methods for numerical integration. The
methods we used can be extended to multidimensional integrals. If we wanted to compute
a double integral using quadrature, we would a
Note Set 4 Unconstrained Optimization
4.1 Overview
In this note set, we will consider finding the (unconstrained) maximum of the function f ( x) . The methods we will use will depend on the smoothness of the function.
4.2 Newtons Method
The first set of a
Note Set 3 Numerical Linear Algebra
3.1 Overview
Numerical linear algebra includes a class of problems which involves multiplying
vectors and matrices, solving linear equations, computing the inverse of a matrix, and
computing various matrix decomposition