PROBLEM 2 In a faraway prairie live three types of critters: Altis, Bukis, and Cotes. At any point in time, one of these creatures can randomly bump into another. The benet each critter obtains in one of these random encounters depends on their types. if two Aitis meet: each gets a benet of 1 If an Altis and a Bukis meet: each gets a benefit of 3 if an Altis and a Cotes meet: the Altis gets a benefit of 2, the Cotos gets a benefit of 1 if two Bukis meet: each gets a benet of 1 if a Bukis and a Cotos meet: each gets a benet of 2 if two Cotos meet: each gets a benet of 3 Part 1 (5 marks]. Build a payoff matrix to summarize the outcomes of any possible interaction Part 2 [10 marks). Let a, b, and c represent the proportions of Altis, Bukis, and Cotes in this prairie, respectiveiy. Answer the following questions by treating this problem as if it were a traditional Game instead of an Evolutionary Game. Then state and explain your answers using Evolutionary Game Theory terminology. ,c = 0) an equilibrium of this system? , c = i) an equilibrium of this system? Part3 [15 marks). Find an equilibrium of this system in which a > 0, b > 0, and c > 0