R
rhombus
Legend
Silver Level
+1Carry on sir, I'm ready to listen. Where have you been?
probably proper stuff like looking for a job!!
+1Carry on sir, I'm ready to listen. Where have you been?
Yea, I was actually looking for more of a summer internship (I'm still studying) but it turned out I could actually get a job after (or maybe even before) it ends :rock:
wasnt sure how it got to a=2b=2c (1/2, 1/4, 1/4)
thats what i was trying to say but probably didnt explain it wellwhat I'm basically saying is that B is not choosing anything. It's A actually in that example...
going back to the a = 2b = 2c
from
<B, rock > = c - b
<B, paper > = a - 2c
<B, scissors > = 2b - a
not sure how we get a=2b=2c
As I said, you want to make B indifferent so you search for (a, b, c) that make B's EVs equal.
EV(rock) = EV(paper) = EV(scissors)
c - b = a - 2c = 2b - a
Three equations, three variables:
1) c - b = a - 2c => a = 3c - b
2) a - 2c = 2b - a => b = a - c
3) c - b = 2b - a => c = 3b - a
Now you can pick for example first equation and
* substitute for c (from 3)): a = 3(3b - a) - b => a = 2b
* substitute for b (from 2)): a = 3c - a + c => a = 2c
You get that a = 2b AND a = 2c which can be also written as: a = 2b = 2c
It's an arrow I use it to indicate that something is related to or came from something. Viewing it as "therefore" probably works too. I will use "->" in the future because you are right that "=>" can be confused with "greater or equal".what does the => mean, does it eman therefore as in excel it means Equal or greater than.
I'm not sure I understand what you mean... You picked some number for, let's say: b, and the other ones (a and c) come out "wrong"?Also is the 2nd equation right, when i substituted the letter for numbers i got the 1st and 3rd to work out but not the 2nd
It's an arrow I use it to indicate that something is related to or came from something. Viewing it as "therefore" probably works too. I will use "->" in the future because you are right that "=>" can be confused with "greater or equal".
I'm not sure I understand what you mean... You picked some number for, let's say: b, and the other ones (a and c) come out "wrong"?
But in Equation 2
2) a - 2c = 2b - a => b = a - c
a = 12 b = 15 c = 3
so 12 - 6 = 30 - 12
1st part is 6 and 2nd part is 18
Because b = 9 not 15 (a - c = 12 - 3 = 9). I'm still not sure what you're trying to do tbh...because if you randomly pick two numbers (eg: a and b) and then calculate the third one (c)...both sides of the equation will always be equal because...that's the point of solving the equation after all... Am I missing something?
Ok the simpler the betterThat's actually really impressive that you are willing to go over/solve those examples on your own (I was too lazy to do it, I just "accepted" the solutions/results that were already written in the book ).
There is one more thing I would like to discuss, that is not mentioned in the book (or maybe it is, I don't know I haven't seen it yet), but it might come in handy in the near future Epsilon-equilibrium. It's really cool because it allows us to estimate how close a particular solution/guess is to Nash equlibrium without even knowing the equlibrium itself (which is often the case). I will get back to it tomorrow/Friday.
In the meantime, does anyone want to try to solve a simple game?
Ok the simpler the better
working backwards from 4 as player 2 cant finish, Player 1 should try to go to 8 12 16 20.
so whatever player 2 does player 1 will go down in 4s so 1st move is 20 maybe
0 1 2 3 4 5 6 7 8 9 10 ... 19 20 21 ... (number of chips)
P N N N P N N N P N N ... N P N ... (position)