= Solution
Both players can guarantee $k$ by part (d), so at any <Nash equilibrium> each must receive at least $k$. Their <payoffs> sum to $2k$, forcing both equilibrium <payoffs> to equal $k$.
Moreover, an equilibrium action must itself have the maxmin guarantee $k$. If a player's chosen action allowed an opposing response that reduced its <payoff> below $k$, that response would give the opponent more than $k$, a profitable <unilateral deviation>. Thus both equilibrium sites belong to the central <set> identified in part (d).
Conversely, if both choose from that central <set>, each chosen action guarantees $k$. Neither can improve above $k$, because the other player's fixed central action still guarantees the other player $k$. Consequently, \b[all pure <Nash equilibria> are]
$$
\boxed{\begin{cases}((k+1)/2,(k+1)/2),&k\text{ odd},\\(x,y)\in\{k/2,k/2+1\}^2,&k\text{ even}.\end{cases}}
$$
For even $k$, this includes both co-located central profiles and both orders of the two distinct central sites.
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