I cant tell where you went wrong because you jumped from the expression for qi and qj to the final profit. Here's the solution.
Okay kind of a basic one here, just going through the Gibbons book question 1.5,
I'm trying to calculate the both payoffs in the monopoly game
I have my profit function
And my quantities in monopoly are qm - after maximising profits
since in monopoly
my profits are (a-c)^2 / 4
which is wrong and should be divided by 8 - not sure where I have gone wrong...