Question 3 Consider an Augmented Hawk Dove Bourgeois game, where Doves (and Bourgeois when acting like Doves) pay a small cost of & for negotiating, when they agree to share the prize with another Dove. Moreover, 11 = c, 8 = v, and 1 = k. The payoff matrix for this Augmented Hawk Dove Bourgeois game is given below: Hawk Dove Bourgeois Hawk (v-c)/2, (v-c)/2 v, 0 v/2 + (v-c)/4, (v-c)/4 Dove 0, v (v-k)/2, (v-k)/2 (v-k)/4, V/2 + (v-k)/4 Bourgeois (v-c)/4, v/2 + (v-k)/4, v/2 + (v-c)/4 (v-k)/4 (v-k)/2, (v-k)/2 a) Find the Nash equilibrium(s). b) Is Bourgeois Evolutionary Stable Strategy (ESS)? If so, explain why. If not, why? Show mathematically. c) Suppose a yacht with a few Hawk types washed up on the shores of an Island whose (large) population was entirely Bourgeois. Can Hawk types invade the mixed population of the Island? (15 marks)