Assignment:
Henry seeks a loan to form a new company, and submits a request for a loan to Rockefeller. Rockefeller knows that p percent of people asking him for loans are conscientious, who feel guilty if they default on their loans, and 1 − p percent of people asking him for loans have no compunction about defaulting on their loans, but he does not know whether or not Henry is a conscientious borrower. Rockefeller is free to grant Henry a loan, or to refuse to give him a loan. If Henry receives the loan, he can decide to repay the loan, or to default. If Rockefeller refuses to loan money to Henry, both sides receive 10 units. If Rockefeller loans Henry the money he needs to form a company, and Henry repays the loan, Rockefeller receives 40 units, while Henry receives 60 units. If Rockefeller loans Henry the money he needs to form a company, but Henry defaults on the loan, Rockefeller loses x units, and Henry’s payoff depends on his type: if he is a conscientious borrower, he receives 0, but if he has no compunction about defaulting, he gains 150 units. Answer the following questions:
(a) Describe this situation as an extensive-form game, where the root of the game tree is a chance move that determines Henry’s type.
(b) Find all the Nash equilibria, and the sequential equilibria, of this game, in the following three cases:
- p = 1/3, and x = 100
- p = 0.1 and x = 50
- p =0, and x = 75
Provide complete and step by step solution for the question and show calculations and use formulas.