4. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff and the second entry is Animal B's payoff. Animal A Hawk Dove (rows)/Animal B (columns) Hawk (-10,-10) (20,0) Dove (0,20) (8,8) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. (a) Explain why there cannot be an equilibrium where all animals act as Doves. (1 mark) (b) Explore whether there are any Nash equilibria in pure strategies and explain which these are and why they are equilibria. (3 marks) (c) Derive the mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater that mixed strategy equilibrium proportion, which strategy does better, Hawks of Doves? Explain your answer. (4 marks) (d) Draw the best response functions and shown in the diagram all pure and mixed strategy equilibria. (4 marks)