Question

Can anyone help me solve this saw it in a YT video for our class and cant seem to figure out where he got 1/6

∑u (-3) + (1 - ∑u) (1) = ∑u (2) + (1- ∑u) (0)


∑u is equal to the probability that player 1 goes with option 1 or "up" like he described in the video.

you can find the video on YT it is called :  Game Theory 101 MOOC (#8): The Mixed Strategy Algorithm



I know its inverse operations

Answer 1

To simplify the notation I will use "p" to denote probability player 1 goes up.

From equation you have, you set left utility equal to right utility, then solve for p.

-3p + (1-p) = 2p + 0

-4p + 1 = 2p

1 = 6p

p = 1/6

So 1/6 is the probability of player1 choosing up to create Nash equilibrium.