A task-allocation problem

We consider a task-allocation problem in which agents differ in terms of their seniority and their experience with tasks. We introduce two mechanism classes: the feasibility augmented serial dictatorship (FSD) and the minimally reluctant efficient priority (MREP). The first class is efficient, senior-optimal, and strategy-proof. However, a disadvantage of this class is that a greater number of agents can be assigned to tasks that they unwillingly perform – we call such tasks “unwillingly acceptable” – than what is actually achievable. We say that a mechanism is minimally reluctant if it always minimizes the number of agents who are matched with their unwillingly acceptable tasks. The second mechanism class is minimally reluctant, efficient, and constrained senior-optimal — senior-optimal in the class of minimally reluctant mechanisms. No minimally reluctant mechanism is strategy-proof, which implies that no MREP mechanism is strategy-proof. Each MREP mechanism has a unique equilibrium outcome that is equivalent to the truthtelling outcome of a particular FSD mechanism. Hence, in equilibrium, each MREP mechanism is efficient, senior-optimal, but not minimally reluctant. Nevertheless, no mechanism is minimally reluctant in equilibrium either.