Due Wed 29 Aug Assignment 1.
Due Wed 5 Sep Assignment 2.
Due Wed 19 Sep Assignment 3
As I mentioned in class, it is possible to give a proof of the existence of optimal mixed strategies using analysis. The advantage of this proof is that it is relatively self-contained. The disadvantage is that the proof doesn't supply a method to find the optimal mixed strategies; it only shows that they must exist.
Click here for the proof.
Due Wed 26 Sep Assignment 4
The
FAQ page of the
Optimization Technology Center contains a wealth of information on linear optimization. In particular, it contains a link to a nice
Java applet that implements the simplex method to solve linear programming problems. If you don't already have a favorite LP solver, I recommend you use this
Java applet to numerically solve small (7 variables or less) problems.
Due Wed 3 Oct Assignment 5
It has come to my attention that the
Java LP solver is hard to interpret.
Here are some hints:
- You don't need to explicitly enter the constraint that you want a
solution where are the variables are positive. The LP solver already
knows this.
- After you enter your objective function and the constraints, you get a
new window with lots of colored boxes. Just click the "Do A Full
Iterate" button at the bottom of the screen until the message
You've Done It!
You've Solved It!
appears in the message panel at the bottom of the screen. If you get the
message
The problem is unbounded.
it probably means that either you forgot the preliminary step of adding a
constant to the entries of the payoff matrix to get a new payoff matrix
where all the payoffs are positive, or you forgot to set the LP solver to "Maximize" or "Minimize" the objective function as appropriate; this option is available as a pulldown menu on the panel where you enter your linear program.
- The "Current Objective Value" will appear just above the message
panel. This is the maximum value of the objective function, and is the
number we called "w" in lecture.
- The values of some of the variables will appear in the purple box on
the lefthand side of the screen. The values of all other variables are
zero.
- The program will generate extra "slack" variables; for example, if you
had four variables, x1,x2,x3,and x4, then the program will generate four
slack variables x5,x6,x7,x8. The values of those slack variables might
appear in the purple box. Just ignore them. They are important for doing
the simplex method, but they aren't part of the final solution.
Midterm Info
The math 486 midterm will be in-class on Fri Oct 12. It will focus on
basic concepts and computations, covering the lectures through 2 player
zero-sum games, and the homeworks through the one due Wed 3 Oct. It will
be a pencil-and-paper test with no recourse to the book, notes,
calculators, computers, etc.
Due Fri Oct 12 Assignment 6.
Midterm Solution
Here is the midterm solution.
The Game of Hex
Here is a blank Hex board.
Due Fri Oct 19 Assignment 7.
Change in Assignment 8
Problem #3 on Assignment 8 has been moved to Assignment 9. Only do Problems #1 and #2 on Assignment 8.
Due Fri Oct 26 Assignment 8.
The relevant sections of Binmore for this assignment are 2.1 and 2.2 for lotteries, 3.1 for preferences, 3.2 for utility functions, and 3.4 for risk aversion, neutrality, etc. Binmore is on 2 hour reserve in the math library on the ground floor of McAllister.
Due date changed.
Due Wed Nov 7 Assignment 9.
The final exam will be in-class on Mon Dec 3
Due Wed Nov 14 Assignment 10.
Due Wed Nov 21 Assignment 11.
Lecture notes of Fri Nov 16 through Wed Nov 21.
Due Mon Dec 3 Assignment 12.