The accountable function: a new approach to scheduling problems

Sreoshi Banerjee () and Christian Trudeau ()
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Sreoshi Banerjee: Climate Economics and Policy, Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
Christian Trudeau: Department of Economics, University of Windsor

No 2507, Working Papers from University of Windsor, Department of Economics

Abstract: We study cooperative cost-sharing in scheduling problems where agents differ in job lengths but share identical waiting costs. While the optimistic and pessimistic cost functions are natural approaches to compute the waiting cost of a coalition, their symmetry - well established for queueing problems - breaks down for scheduling. In particular, the pessimistic Shapley value violates equity by rewarding longer jobs. To address this, we propose an alternative formulation, termed ``accountable cost" of serving a coalition. Under this, the coalitional members are served first, but they internalize the externality imposed on the non-coalitional members. We show that the accountable cost game is concave and the Shapley value of this game coincides with the decreasing serial rule, thereby restoring the lost symmetry. We also provide axiomatic characterizations of both the optimistic and accountable Shapley values, explore extensions to multi-server environments, and discuss connections with general sequencing problems. These results position the accountable function as a principled counterpart to the optimistic approach, unifying efficiency and fairness in the cooperative analysis of scheduling problems.

Keywords: scheduling; cooperative game; cost sharing; Shapley value; serial (decreasing serial) rule. (search for similar items in EconPapers)
JEL-codes: C71 D63 D71 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2025-12
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