Discuss the below:
Q: There exist two agents with the cost functions ci(yi) = yi2/(2ri), i = 1, 2. The principal's income func- tion represents the sum of agents' actions. Individual rewards of the agents satisfy the independent con- straints d1 ≤ σ1 ≤ D1 and d2 ≤ σ2 ≤ D2 (i.e., there are "wage brackets"). In addition, the global constraint σ2 ≥ β σ1 takes place (agent 2 possesses a higher skill level than agent 1: r2 ≤ r1; hence, the former gains a greater reward than the latter for performing the same actions: β ≥ 1). Find an optimal solution to the incen-tive problem.