This week, we will conclude the four game theory posts by learning how to determine your counter prudential strategy, which does exactly what it says: counters the prudential strategy.
First, you will have to figure out their prudential strategy though. Let's go back to the policecriminal game from last week.
Crime  Lay Low  

Patrol 
3, 5

0, 1

Donuts 
2, 3

2, 0

We had determined that the police's prudential strategy is 4/7 patrol and 3/7 donuts. So, what do the criminals do?
Well, this isn't their mixedstrategy equilibrium. Remember that the mixedstrategy equilibrium is a way to make the other player's payoffs equal so that they don't have an advantage by playing one way or another.
Since this is the prudential strategy, and therefore not the mixedstrategy equilibrium, the criminals do have an advantage by playing one way or another. So, let's determine the expected payoff of playing either strategy.
For committing crime, they will get 5 4/7 of the time and 3 3/7 of the time. So, we do:
5(4/7) +3(3/7) = 11/7
For laying low, we do the same thing:
1(4/7) + 0(3/7) = 4/7
Since 4/7 is greater than 11/7, the criminals should lay low every single time for their counter prudential strategy.
Though this type of thing isn't a proof or pattern like I normally post about, I find it really cool that you can analyze games just like you analyze math. If you have a lot more time, you can analyze games like chess, poker, black jack, and even sports.
Answer: Here is the answer to July's problem of the week. Make sure you do last week's as well!
Easy:
e = 24
h = 30
m = 12
n = 18
A = 81
Hard:
t = 45
z = 4.5
s = 50
a = 1
b = 1250
c = 390625
x = 625
P = 50π
For the rope problem from the hard problem of Monday, you must first set both ends of one rope on fire and set only one end of the other rope. Half an hour later, your first rope has burned completely leaving your second rope with 30 minutes left. Now, set the other end, and put your plant over the flame for its fifteen minute cooking.
Great post, i really like this post but do u knw how to teach kg 1st student in maths so pls tell me....
ReplyDeletethank you,

Abacus Franchise
wow.! this is very informative posting.. thanks for sharing this...
ReplyDeletecool math 4 kids