Here is the strategic form game:
Player 2 Left Middle Right Top 2,2 0,0 1,3 Player 1 Middle 1,3 3,0 1,0 Bottom 3,1 2,3 2,2
First I performed an IDSDS and deleted Player 1's "Top" strategy since it is strictly dominated by the "Bottom" strategy. The resulting game is as follows:
Player 2 Left Middle Right Player 1 Middle 1,3 3,0 1,0 Bottom 3,1 2,3 2,2
Let p denote the probability that Player 1 will choose Middle.
Let r and s denote the probability that Player 2 will choose Left and Middle, respectively.
Now here's my first problem. When I try to equate the expected payoffs of Player 2 choosing Left, Middle, and Right, I can't derive any values:
3p + (1-p) = 3(1-p) = 2(1-p)\\
There is so such value for p here.
Moving on to expected payoffs of Player 1, I run into another problem:
$ r + 3s + (1-r-s) = 3r + 2s + 2(1-r-s)\\ s = 2r + (1-r-s)\\ r = 2s - 1 $
But now I am unsure of how to find the values of r and s.
Where am I going wrong?