I am having difficulty solving this question and would be glad if someone can suggest an approach to this problem.
Consider 2 players playing a simultaneous game where each player chooses $x_i>0,i= 1,2$. Each player receives a payoff of $\pi_i(x_1,x_2)=2x_i +2x_1x_2-x_i^2$.
What are the pure strategy Nash equilibria? If the set of strategies is limited to [0,N], $N >0$, what are the pure strategy Nash equilibria now?
I tried to differentiate $\pi_i$ wrt. $x_i$ and $x_2$ and solve the 2 equations simultaneously but I obtained $x_2=x_2+2$