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 first for efficiency. The server can monitor the length of a job, but not the identity of its user, thus merging, splitting or partially transferring jobs offer cooperative strategic opportunities. 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 pair-wise 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.