In a faraway prairie live three types of critters: Altis, Bukis, and Cotos. At any point in time, one of these creatures can randomly bump into another. The benefit each critter obtains in one of these random encounters depends on their types. If two Altis meet: each gets a benefit of 1 If an Altis and a Bukis meet: each gets a benefit of 3 If an Altis and a Cotos meet: the Altis gets a benefit of 2, the Cotos gets a benefit of 1 If two Bukis meet: each gets a benefit of 1 If a Bukis and a Cotos meet: each gets a benefit of 2 If two Cotos meet: each gets a benefit 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 Cotos in this prairie, respectively. 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. a) Is (a = b = c = 0) an equilibrium of this system? b) Is (a = 0,b=2,c=) an equilibrium of this system? Part 3 (15 marks). Find an equilibrium of this system in which a > 0, b>0, and c> 0. In a faraway prairie live three types of critters: Altis, Bukis, and Cotos. At any point in time, one of these creatures can randomly bump into another. The benefit each critter obtains in one of these random encounters depends on their types. If two Altis meet: each gets a benefit of 1 If an Altis and a Bukis meet: each gets a benefit of 3 If an Altis and a Cotos meet: the Altis gets a benefit of 2, the Cotos gets a benefit of 1 If two Bukis meet: each gets a benefit of 1 If a Bukis and a Cotos meet: each gets a benefit of 2 If two Cotos meet: each gets a benefit 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 Cotos in this prairie, respectively. 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. a) Is (a = b = c = 0) an equilibrium of this system? b) Is (a = 0,b=2,c=) an equilibrium of this system? Part 3 (15 marks). Find an equilibrium of this system in which a > 0, b>0, and c> 0