On Scheduling Fees to Prevent Merging, Splitting, and Transferring of Jobs

A deterministic server is shared by users with identical linear waiting costs, requesting jobs of arbitrary lengths. Shortest jobs are served ...rst for e¢ciency. When the server can monitor the length of a job, but not the identity of its user, merging, splitting or partially transferring jobs may o¤er strategic opportunities to cooperative agents. Can we design cash transfers to neutralize such manipulations? We prove that merge-proofness and split-proofness are not compatible, and that it is similarly impossible to prevent all transfers of jobs involving three agents or more. On the other hand, robustness against pairwise transfers is feasible, and essentially characterize a one-dimensional set of scheduling methods. This line is borne by two outstanding methods, the merge-proof S+ and the split-proof S¡. Splitproofness, unlike Mergeproofness, is not compatible with several simple tests of equity. Thus the two properties are far from equally demanding.