Constrainedly fair job assignments under minimum wages

A number of jobs are to be assigned to a greater number of workers. While having to abide by the law of minimum wages, firms must determine who should be assigned which job and at what salary. In such situations fair (envy-free) allocations usually fail to exist. To cope with this situation, this paper proposes a new concept of fairness, called constrained fairness. Among the set of constrainedly fair allocations, the so-called constrainedly fair and minimal allocations are of particular interest. The reason for this is that the salaries are not only compatible with the minimum wages; they are also optimal from the standpoint of cost-minimizing firms and the assignment of jobs is efficient from the viewpoint of workers. A convergent dynamic procedure that identifies constrainedly fair and minimal allocations is proposed. Furthermore, strategic properties of the mechanism are derived, and two notions of efficiency are evaluated.