How should you set up the game tree, and can you explain why you set it up the way you did?What is the rollback equilibrium? Note that your answer will depend on the value of p.

Context:

Finally, we consider a version of the nomination problem that considers both strategy and uncertainty. As in part (b), the leaders make their decision about whom to support first, and the activists second. Also, the leaders prefer A, the activists prefer B. Additionally, there is uncertainty about whether B is a star or a dud, and the probability that B is a star is p. The leaders make their support decision before B's true political ability is revealed; the activists make their decision afterward. If the party unites behind A, the pay-offs are the same as in (c): a pay-off of 5 for the leaders and 3 for the activists. Similarly, if the party unites behind B and B is a star, the leader's pay-off is 3 and the activist's is 6. If they unite behind B and she is a dud, however, both get a pay-off of 1. If the party fails to unite, both players get a pay-off of 0 with one exception. If B turns out to be a star, the activists will find her candidacy so exciting that they will get a pay-off of 4 from supporting her even if the leaders have supported A (the leader's pay-off in this case is still 0.)