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Proportional scheduling, split-proofness, and merge-proofness

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  • Moulin, Hervé

Abstract

If shortest (respectively longest) jobs are served first, splitting a job into smaller jobs (respectively merging several jobs) can reduce the actual wait. Any deterministic protocol is vulnerable to strategic splitting and/or merging. This is not true if scheduling is random, and users care only about expected wait. The Proportional rule draws the job served last with probabilities proportional to size, then repeats among the remaining jobs. It is immune to splitting and merging. Among split-proof protocols constructed in this recursive way, it is characterized by either one of three properties: job sizes and delays are co-monotonic; total delay is at most twice optimal delay; the worst (expected) delay of any job is at most twice the smallest feasible worst delay. A similar result holds within the family of separable rules,

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  • Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    • Handle: RePEc:eee:gamebe:v:63:y:2008:i:2:p:567-587
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    References listed on IDEAS

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    3. William Thomson, 2014. "New variable-population paradoxes for resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 255-277, February.
    4. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "Compensation and sacrifice in the probabilistic rationing of indivisible units," European Journal of Operational Research, Elsevier, vol. 302(2), pages 740-751.
    5. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "Reassignment-proof rules for land rental problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 173-193, March.
    6. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2015. "Non-manipulable rules for land rental problems," MPRA Paper 67334, University Library of Munich, Germany.
    7. Bloch, Francis, 2017. "Second-best mechanisms in queuing problems without transfers:The role of random priorities," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 73-79.
    8. Liu, Siwen & Borm, Peter & Norde, Henk, 2023. "Induced Rules for Minimum Cost Spanning Tree Problems : towards Merge-proofness and Coalitional Stability," Discussion Paper 2023-021, Tilburg University, Center for Economic Research.
    9. Liu, Siwen & Borm, Peter & Norde, Henk, 2023. "Induced Rules for Minimum Cost Spanning Tree Problems : towards Merge-proofness and Coalitional Stability," Other publications TiSEM bf366633-5301-4aad-81c8-a, Tilburg University, School of Economics and Management.
    10. Conan Mukherjee, 2013. "Weak group strategy-proof and queue-efficient mechanisms for the queueing problem with multiple machines," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 131-163, February.
    11. Andreas Darmann & Christian Klamler, 2014. "Knapsack cost sharing," Review of Economic Design, Springer;Society for Economic Design, vol. 18(3), pages 219-241, September.
    12. María Gómez-Rúa & Juan Vidal-Puga, 2017. "A monotonic and merge-proof rule in minimum cost spanning tree situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 813-826, March.
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