Problem of the Week Day 1: Week of 8/20/12 - 8/24/12

Today marks the start of 2012's final problem of the week. Back in July, I gave hints for each problem. This month, it's all you now. I will just give the problem and you will find the answer. Remember to save your answer so you can plug it into the next day's problem.

Rather than kicking it off with triangles or puzzles, I decided to start with some game theory. We have gone over everything you will need to know in the past three weeks, so you will be all set. If you didn't read the posts of the past three weeks, it shouldn't take too long, and it is very useful, practical stuff.

Easy: Take the following game matrix:

	a	b
x	0, 6	2, 4
y	5, -6	3, 2

Determine player one's best strategy for this game. First, look for a dominant strategy. Otherwise, find the mixed strategy equilibrium. Round to the nearest tenth of a percent.

x = ____%
y = ____%

Hard: Take the following game matrix:

	a	b
x	5, 3	-1, 10
y	7, -4	0, 0
z	2, -1	3, -2

Determine both player's best strategies for this game. First, look for dominated strategies. Then, look for a mixed strategy equilibrium. Round to the nearest tenth of a percent.

a = ____%
b = ____%
x = ____%
y = ____%
z = ____%

You will need all five answers tomorrow, so make sure to save them all.