Overview
Consider variants of the n-hunter Stag Hunt in which only m hunters, with 2 ≤ m < n, need to pursue the stag in order to catch it. (Continue to assume that there is a single stag.) Assume that a captured stag is shared only by the hunters who catch it. Under each of the following assumptions on the hunters’ preferences, find the Nash equilibria of the strategic game that models the situation.
a. Each hunter prefers the fraction 1/n of the stag to a hare.
b. Each hunter prefers the fraction 1/k of the stag to a hare, but prefers a hare to any smaller fraction of the stag, where k is an integer with m ≤ k ≤ n.
c. Suppose there is a church of hunters that always receives 1/10 of the stag (and nothing from the hare) and returns nothing to the hunters. How does it affect the behavior of hunters in the equilibria of the game?