Ms. Smith has three kids: Grace, Charlie, and Kim. One of them has broken a vase and Ms. Smith is trying to figure out who did it. Suppose that Ms. Smith asks each of her children to go into separate rooms without communicating with each other. Then, she asks each of them to write on a piece of paper either "Yes, I broke the vase" or "No, I did not break the vase." Ms. Smith tells her kids that if at least one of them says they broke the vase, then she will give $3 to each child who says they broke the vase and $6 to the each child who says they did not. She also tells her kids that if no one admits they broke the vase, then she will not give any money to anyone. For example, if Grace says they broke the vase and Charlie and Kim say they did not, then Grace would receive $3 and Kim and Charlie would receive $6 each. a) Find all pure strategy Nash equilibria of this game. Now suppose Ms. Smith gathers all her kids in the same room and asks her kids one by one to say whether or not they broke the vase. First Charlie will tell everyone whether or not he broke the vase. After seeing Charlie's response, then Grace will tell everyone whether or not they broke the vase. Finally after seeing Charlie's and Grace's responses, Kim will tell everyone whether or not she broke the vase. Similar to the scenario involving part a, Ms. Smith tells her kids that if at least one of them says they broke the vase, then she will give $3 to each child who says they broke the vase and $6 to the each child who says they did not. She also tells her kids that if no one admits they broke the vase, then Ms. Smith will not give money to anyone. b) Draw an extensive form game representing the game described in the previous paragraph. c) Use backward induction to determine how this game will be played.