Consider a variant of the Stag Hunt game. There are 10 hunters. Each hunter has two

strategies: Stag or Hare. The value of a stag is V and the value of a hare is 1. If a player chooses Hare

then the player always captures a hare and receives payoff 1 no matter what the other players do. On

the other hand, a stag can be caught if and only if at least 7 players choose Stag. The captured stag

is equally shared by the players who chose Stag.

Assume each hunter prefers 1/8 share of the stag to a hare, but prefers a hare to 1/9 (or smaller)

share of the stag. In other words, V/8 > 1 > V/9 > V/10.

Determine if each of the following profiles of strategies is a Nash equilibrium. Explain why.

(a) (2pts) All players choose Stag.

(b) (2pts) All players choose Hare.

(c) (2pts) (8S, 2H) (meaning 8 stag-hunters and 2 hare-hunters. The same notations below.)

(d) (2pts) (9S, 1H)

(e) (2pts) (7S, 3H)

(f) (2pts) (6S, 4H)