Consider the following game. Avery and Carolina can choose either left (/) or right (r). The table provided below gives the payoffs to Avery and Carolina given any set of choices, where Avery's payoff is the first number and Carolina's payoff is the second number. Carolina Left (1) Right (r) Left (1) 4,4 1,6 Avery Right (r) 6,1 -3,-3 a) Solve for the pure strategy Nash Equilibrium. b) Suppose Avery chooses / with probability p and Carolina chooses / with probability q. Determine Avery's best response to any choice of q by Carolina, and Carolina's best response to any choice of p by Avery. Find the mixed strategy Nash equilibrium. c) Show these best Response functions and all the possible equilibria on a graph. d) Now suppose that Carolina moves first, and Avery moves second. Show the game information in extensive form. What is the Nash equilibrium in this case? e) Would Avery prefer the mixed strategy equilibrium in b) or the sequential move equilibrium in d)? Explain fully.