Lecture 1: Introduction to Optimization Problem
Characteristics of Microeconomic Theory:
I.
Optimization
1. Static vs. dynamic
2. Certainty vs. uncertainty
3. Single decision-maker vs. multiple decision-makers
II. Equilibrium Analysis
1. Statics vs. comp
12 September 2009 Eric Rasmusen, Erasmuse@indiana.edu. Http:/www.rasmusen.org
3 Mixed and Continuous Strategies
A pure strategy maps each of a players possible
information sets to one action. si : i ai.
A mixed strategy maps each of a players possible inf
3 September 2009 Eric Rasmusen, Erasmuse@indiana.edu.
http:/www.rasmusen.org/.
Table 1: Ranked Coordination
Jones
Large
Small
Large 2,2 1, 1
Smith
Small 1, 1 1,1
Payos to: (Smith, Jones). Arrows show how a
player can increase his payo.
1
The strategic for
Optimization with Mathematica
1. Unconstrained Optimization
(1) Functions of a Single Variable
Example : Plot the following function: f ( x) =x 4 - 2 x 2 +1 , which is defined
on the interval S=[-2,2].
Clear[f,x];
f[x_]:=x^4-2*x^2+1;
Plot[f[x],cfw_x,-2,2,
Calculus and Quadratic Form
Calculus
Calculus is a way of tying linear algebra and analysis together by
approximating certain functions by linear functions.
One Variable Calculus
Derivative at a point:
Given a function f: R R , let ( x 0 , f ( x 0 ) be a
19 September 2009 Eric Rasmusen, Erasmuse@indiana.edu. Http:/www.rasmusen.org
Follow the Leader I, which has three pure strategy
Nash equilibria of which only one is reasonable.
Equilibrium
Strategies
Outcome
E1
cfw_Large, (Large, Large) Both pick Large.
Introduction to Mathematica
You normally interact with Mathematica through documents called
notebooks. This tutorial is an example of a notebook. Notebooks can
have many forms. But typically they consist of cells that can contain text,
calculations, or gr
5 Reputation and Repeated Games with
Symmetric Information
5 October 2009 Eric Rasmusen, Erasmuse@indiana.edu.
Http:/www.rasmusen.org.
The Chainstore Paradox
Suppose that we repeat Entry Deterrence I 20 times in
the context of a chainstore that is trying