3. {Sequential Game.) Parents have long used the rule \" One divides, the other chooses\" as a method of dividing desserts without a ght erupting. Suppose Bart and Lisa are brother and sister. Bart gets to cut a cake into 2 pieces. He can either cut a big and small piece? or he can cut two equal pieces. Lisa gets to choose which piece she would like. Suppose the pieces are put in front of Lisa and she picks either right or left. (a) Write out a game tree with Bart moving rst. Suppose a big piece is worth 90 utils and a small piece is worth 10. Equal pieces are worth 50 each. {b} Use backward induction method to nd out the subgame perfect Nash equilib rium. (c) If the utility over cake for any given size piece is twice as big for Bart, does his incentive to cut the cake change