Hi, I would like to have some guidance to solve this problem related to dynamic game in game theory.

Consider the following model of international debt repayment: A bank (representing the coalition of creditors) faces two counties sequentially. At date t ? {1, 2}, country t decides whether to pay its debt, D^t , or to threaten default. If threatens default, the bank can either lend (or reschedule the debt) or not lend; the latter results in default. The game is illustrated in the next figure, where the first payoff is the bank's and the second is the country's. Assume 1 > ? > 0, ? > ? and k > 0. The bank can be "soft"(have payoff as in the figure) or be "tough"(never lend, because of pessimism about future repayment). Only the bank knows whether it is soft or tough. Assume that bank's discount factor is equal to 1 and that (1?p)(1??)D^t ?pk > 0 for t = 1, 2, where p is the prior probability that the bank is tough.

Solve for the equilibrium of this two period game. If the bank had the choice between facing the low-debt country or the high-debt country first, which one would it choose?

consider the attached imagen.