A competitive firm faces two types of potential employees: low (L) and high (H) productivity employees. A potential employee's type is private information known to the potential employee only. The marginal revenue product and hence wage of an employee known to be L is 16, and the marginal revenue product and hence wage of an employee known to be H is 160.

The utility functions of the two types of employees are given by

: (,) = 9²

: (,) = ²

where w is the wage the employee gets and e is the amount of education chosen by an employee.

Construct the signaling game tree of the problem.