Draw the game tree for the sequential game between Sarah and her parents that was described on page 327. The first move is Sarah's; she decides whether to work during the summer or not work. At the end of the summer her parents decide whether or not to pay for Sarah's tuition. Using backward induction, what is the equilibrium for this game? Now add a new first stage in which Sarah's parents announce that they will only pay for the tuition if Sarah works. Is this announcement credible? Use this example to explain what is meant by time inconsistency.