A project costing $100 yields a gross return of $110. A lender (player 1) is approached by a debtor (player 2) requesting a standard loan contract to complete the project. If the lender chooses not to offer a loan, then both parties earn nothing. If the lender chooses to offer a loan of $100, the debtor can realize the projects gains, and is obliged by contract to repay $105. For simplicity, assume that money is continuous, and that the debtor can choose to return any amount of money 110. Also, ignore the time value of money. Assume first that no legal system is in place that can cause the lender to repay, so that default on the loan (less than full repayment) carries no repercussions for the debtor.

a) Model this as an extensive form game tree as best as you can and find a subgame perfect equilibrium of this game. Is it unique?

b) Now assume that there is a legal system in place that allows the lender to voluntarily choose whether to sue or not to sue when the debtor defaults and repays an amount 105. Furthermore, assume that it is costless to use the legal system (it is supplied by the state), and if the lender sues a debtor that defaulted, the lender will get the $105 repaid in full. After paying the lender, the borrower will pay a fine of $5 to the court above and beyond the repayment. Model this as an extensive form game tree as best as you can and find a subgame perfect equilibrium of this game. Is it unique?

c) Are there Nash equilibria in the game described in (b) above that are not subgame perfect equilibria?

d) Now assume that using the legal system is costly: if the lender sues, he pays the lawyer a legal fee of $105 (this is the lawyer's price which is unrelated to the contract above). The rest proceeds the same as before (if the lender sues a debtor that defaulted, the lender will get repaid in full; after paying the lender, the borrower will pay a fine of $5 above and beyond the repayment.) Model this as an extensive form game tree as best as you can and find a subgame perfect equilibrium of this game. Is it unique?