Abstract
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 \(N \subseteq M\); perhaps because estimating the preferences of \(M\backslash N\) 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 \(M\backslash N\). The other is to first allocate within the tasks in \(N\) and then assign the remaining robots within \(M\backslash N\) (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.
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Notes
- 1.
As noted in this paragraph, the present paper mainly argues the context of assigning robots between tasks. Substituting tasks with people and robots with indivisible objects, one can translate our argument into the standard allocation models.
- 2.
Postponing the assignment for M\N (until their preferences become clear) is another possible approach (further discussion will be made after Definition 3). However, this might lead to the delay of the project due to the amount of uncertainties.
- 3.
With a little abuse of notation, we sometimes regard an N-allocation X as an |N|-tuple of subsets of K—satisfying (1) rather than the function from N to \({\mathcal{K}}\) literally.
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This work is supported by JST [Moonshot Research and Development], Grant Number [JPMJMS2032].
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Suzuki, T., Horita, M. (2022). Multi-agent Task Allocation Under Unrestricted Environments. In: Morais, D.C., Fang, L. (eds) Group Decision and Negotiation: Methodological and Practical Issues. GDN 2022. Lecture Notes in Business Information Processing, vol 454. Springer, Cham. https://doi.org/10.1007/978-3-031-07996-2_3
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