The interaction between a lender and a borrower is an example of a sequential-move game. The game tree, along with the payoffs, is shown below. A represents the applicant, and B represents the bank.
It is a sequential move game because the applicant gets the chance to invest in the project of her choice only after the bank has released the money.
Based on the payoff, it is easy to find that the bank gets a good deal only when the applicant invests in a safe project. If the bank doubts the applicant’s intention, it will reject the application straight away. In such a case, the applicant has only two choices: 1) convince the bank that she would invest in a safe project, 2) give collateral to guarantee the bank.
