Michelle wants to eat some cereal but there's no cereal left, and she is too lazy to go the store herself. She is thinking of sending one of her kids to the store. She can choose to send Aggie, Brian, or Selena. Whichever kid is sent will be allowed to pick one of the three cereal brands available at the store: Corn Flakes, Capin Crunch, or French Toast Crunch. Cereal boxes at this store are large enough so that everyone in the family will be able to eat from it once it's home. The enjoyment level each member of the family gets from the three different brands is given in the following table. Whoever ends up going to the store will actually have to enjoyment level by 2. Family member Michelle Aggie Brian Selena Enjoyment of Corn flakes 5 3 1 3 Enjoyment of Capin crunch 0 2 3 3 Enjoyment of French toast crunch 0 1 2 2 In what follows, assume that Michelle's strategies and payoffs are listed first, Aggie's are listed second, Brian's third, and Selena's fourth. Part 1 : Construct an extensive form to represent this game. Part 2 : Consider the strategy combination {Brian, Capin C, Capin C, Capin C}. a) Is it a Nash Equilibrium? If so, explain why. If not, state who would benefit by switching unilaterally to a different strategy. b) Is it a Subgame Perfect Equilibrium? Explain your answer. c) Which of the Capin Crunch strategies inside it is/are non-credible threats? d) Now consider {Aggie, Capin C, Capin C, Capin C}. Is this strategy combination a Nash Equilibrium? If so, explain why. If not, state who would benefit by switching unilaterally to a different strategy. Part 3: Find all the Subgame Perfect Equilibria for this game.