Solve the below problem:
Q: A principal organizes planning of the volume of works in a department according to the following planning mechanism: si Î[0; 1], xi > 0, g1 (s ) = s1 + a(s2 + s3 ),
gi (s ) = bs1 + si , α > 0, β 1/4. Note that agent 1 is the head of the department, while agents i = 2, 3 are the subordinates. The parameters α and β describe the impact of increased requests on the planned work of the principal and vice versa.
Establish conditions that ensure the existence of an equivalent direct mechanism for the planning mecha- nism considered.