a professor at the University of Maryland asked this
awesomely evil test question you have the opportunity to earn extra points for
this exam
select whether you want two points or six points
but there's a small catch if more than 10 percent in the class pick six points
then no one will get any points only I will see your selection it will be
anonymous to the rest of the class
do you pick two points or six points? when this question was
posted to Twitter it went viral with a lot of people discussing the question
it looks like there's a dilemma here and a lot of people thought that
look if we at least pick two points everyone can cooperate then at least we
can get two
but that's not the game theory way to think about this question
so let's try and to analyze what the correct strategic decision
should be given the incentives of this question
you want to think about your choice
relative to what the other people in the class are doing
and the relevant characteristic is how many people
are picking 6 it could be that more than 10 percent in the class is picking 6
it could be the case that fewer than 10 percent in the class is picking six
or there's a small probability that may be exactly 10 percent of the other
people are picking 6
we'll construct a matrix based on what the other people are doing
to see what your payoff will be if more than 10 percent in the class
is picking 6 then it doesn't matter whether you pick two or six
everyone is going to get zero points
now, if fewer than 10 percent to the other people are picking six
say everyone else is picking two then you are going to get the number points
that you pick
if you pick two points you get two, if you pick six points you get six
and now you can see something very interesting you are
always better off at least as good of picking 6
as if you are picking two so picking six here
is a logical choice whether the class is more than 10 percent picking 6
or less than 10 percent
picking 6 you are always going to score more points if you pick 6
versus 2 now there's one
third case to consider that may be exactly 10 percent pick 6
in this case you would get two if you picked two
but you would ruin it for everyone and get zero
if you pick 6 you would, you know, increase the threshold beyond 10 percent
so in this one small scenario
you're actually better off picking two points but is kinda
rare and there's no way you can know that exactly 10 percent in the class
is picking 6 so in a class of ten that would be
exactly one person picking 6 and everyone else
picking two this is a very unlikely scenario
so you can kinda disregard this third possibility and you could say picking 6
is the logical thing to do
but there's another reason to think about why picking six is logical
exams are not usually based on the absolute number of points you get
it's not usually a point threshold that ninety percent is in a eighty percent is a B
that's usually true in grade school or high school but once you get to college
everything is usually graded on a curve your grade
is based on how much better you do relative to everyone else
so you don't want to think about the absolute number of points you're getting
you want to think about how many more points you're getting than other people
so when you think in this relativistic method
if you get 2 and everyone else gets 2 your getting zero extra points
whereas if you get six and other people get 2
then you have a chance to get four extra points so we want to reduce the payouts
when points are awarded by two
so if the class is getting more than 10 percent's picking 6 no one's getting
points anyway
if you fewer than 10 percent are picking 6
then when you pick two if everyone gets two,
you're not getting any more points than anyone else who's picking 2
but if you get six and other people are getting two you get four extra points
and then look at the third scenario where exactly 10 percent is picking six
so say one in 10
out of your ten percent class is picking six and
one person's picking six and every one else is picking two
then you're not going to do any better than the people who are picking two
and if you pick six and spoil it for everyone then you
get zero so when you look at the payouts now
picking six is always at least as good as picking two
so in this case picking 6 is the logical choice
and it's what's known as a weakly dominant strategy so when you have a
weakly dominant strategy you're gonna wanna play it
now the unfortunate outcome even though everyone individually is thinking about
picking six and they all pick six
you end in a situation that everyone ends up with zero points
but this is not because any individual person is thinking wrong
this game is sorta rigged so that the group outcome sorta says oh you pick 6
you're selfish
but that's not really the case I think it should be your decision to pick six
and that's the logical thing to do thanks for watching this video
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you can also catch me on social media at Presh Talwalker
and if you like this video please check out my books I've written a book about
game theory an introduction to strategic thinking
which will help you understand this example and many more ways to use
math to
outsmart your opponents