Problem $2(20$ points$).$ Consider the atomic

selfish routing instance depicted on the right.

Suppose there are two players who want to

send $($unsplittable$)$ flow from $s$ to $t.$ Let the

demands of player $1$ and player $2$ be $r_1=1$

and $r_2=2,$ respectively.

Prove that no Nash flow exists for this in$-$

stance.