= Solution
\b[Yes to both questions, for both players.] Site one is <strictly dominated> by site two. Against opposing site $y$, the <payoff> difference is
$$
u(2,y)-u(1,y)=\begin{cases}k-2,&y=1\text{ or }2,\\1,&3\leq y\leq k.\end{cases}
$$
Every difference is positive for $k\geq4$. By reflection, site $k$ is <strictly dominated> by site $k-1$. These endpoint actions are therefore also <weakly dominated strategies>, since <strict dominance> is stronger than the requirement of being no worse everywhere and better somewhere.
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