= Solution
Assume $0<h<d$ and the feasible threshold $2\leq k\leq n$. An unsuccessful deer hunter would gain by switching to hare, so an equilibrium with deer participants must have $s\geq k$. A deer hunter then earns $d/s$ and must not gain by changing to hare; this requires $d/s\geq h$. A hare hunter who joins would earn $d/(s+1)$, so staying with hare requires $h\geq d/(s+1)$. Hence the necessary and sufficient conditions for the stated range $0<s<n$ are
$$
\boxed{k\leq s<n,\qquad \frac d{s+1}\leq h\leq\frac ds.}
$$
These conditions check every possible unilateral change in this two-action <game>, so they also prove sufficiency. Equality is allowed because a <Nash equilibrium> rules out strict improvements, not indifferent deviations. The endpoint $s=n$ has no hare hunter to check; it is an equilibrium exactly when $d/n\geq h$.
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