Past exam of the computer science course of the University of Oxford / 2018 / Computational game theory / 1 / d / Solution

Under the intended positive rewards $0<h<d$, a hunter at the all-hare strategy profile receives $h$. A unilateral switch to deer leaves only one participant. Since the integer threshold satisfies $k>n/2$ with $n\ge 3$, we have $k\ge 2$, so that deer hunt fails and pays zero. Thus no player can gain by switching, and the all-hare profile is a Nash equilibrium. At $h=0$ it remains an equilibrium through indifference; negative $h$ would invalidate the claim.