Multi-agent Task Allocation Under Unrestricted Environments

Suppose that a construction manager is assigning agents (construction robots) to the set of tasks M. Each task has a weak/linear preference over the coalitions of robots. However, the manager only knows the preferences of N. M; perhaps because estimating the preferences of M\N takes an unreasonable amount of time/cost. The present paper explores whether the manager can find a Pareto optimal (PO) allocation of the robots for the entire M. Two approaches are axiomatically studied. One approach is to find an entire allocation that is PO under any realization of the preferences of M\N. The other is to first allocate within the tasks in N and then assign the remaining robots withinM\N (after their preferences are obtained), so that the entire allocation is PO. The contribution of this paper is twofold. We first prove that the first (second) approach is possible if and only if there exists an allocation for N that is PO and non-idling (NI) (weakly non-idling [WNI]); where NI is an axiom demanding that no allocation weakly dominates the allocation with some agents unassigned. The second result is from an algorithmic perspective; we prove that serial dictatorship must find a PO and WNI allocation (if it exists) under a linear preference domain.