PROBLEM 3 Mike wants to eat some cereal but there's no cereal left, and he is too lazy to go the store himself. He's thinking of sending E of his kids to the store. He can choose to send Agatha, Bustier, or Celine. Whichever kid is sent will be allowed to pick one ofthe three cereal brands available at the store: Cheerios, Froot Loops, or Honey Bits. Cereal boxes at this store are large enough so that everyone in the family will be able to eat from it once it's heme. The enjoyment level each member of the family gets from the three different brands is given in the following table. Whoeverends up going to the store will actually have to walk there, and this will reduce his/her enjoyment level by 2. Family Enjoyment of Enjoyment of Enjoyment of member (I'liein'ios5 Front Loops Honey Uhs In what follows, assume that Mike's strategies and payoffs are listed rst, Agatha's are listed second, Bastiat's third, and Celine's fourth. Part 1 {5 marks]: Construct an extensive form to represent this game. Part 2 {29 marks}: Consider the strategy combination [BastinL Front L, Front L, Front L]. a} Is it a Nash Equilibrium? If so, explain why. If not, state who'd benefit by switching unilaterally to a different strategy. b) Is it a Subgan'ie Perfect Equilibrium? Explain your answer. cl which of the Front Loops strategies inside it isfare non-credible threats? d) Now consider [Agnthn,Froot L, Front L.Froot L}. Is this strategy combination a i-iash Equilibrium? If so, explain why. If not, state who'd benefit by switching unilaterally to a different strategy. Part 3 {15 marks}: Find all the Subgame Perfect Equilibria for this game