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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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    1. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 381-413.
    2. Hain, Roland & Mitra, Manipushpak, 2004. "Simple sequencing problems with interdependent costs," Games and Economic Behavior, Elsevier, vol. 48(2), pages 271-291, August.
    3. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
    4. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, vol. 125(1), pages 1-35, November.
    5. Jeroen Suijs, 1996. "On incentive compatibility and budget balancedness in public decision making," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 193-209, December.
    6. Moulin, Herve & Stong, Richard, 2003. "Filling a multicolor urn: an axiomatic analysis," Games and Economic Behavior, Elsevier, vol. 45(1), pages 242-269, October.
    7. Thomas Kittsteiner & Benny Moldovanu, 2005. "Priority Auctions and Queue Disciplines That Depend on Processing Time," Management Science, INFORMS, vol. 51(2), pages 236-248, February.
    8. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    9. Youngsub Chun, 2000. "Agreement, separability, and other axioms for quasi-linear social choice problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 507-521.
    10. Moulin, Herve, 2004. "On Scheduling Fees to Prevent Merging, Splitting and Transferring of Jobs," Working Papers 2004-04, Rice University, Department of Economics.
    11. Biung-Ghi Ju, 2003. "Manipulation via merging and splitting in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 205-215, October.
    12. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer;Society for Economic Design, vol. 4(3), pages 255-272.
    13. Fishburn, Peter C., 1992. "Induced binary probabilities and the linear ordering polytope: a status report," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 67-80, February.
    14. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
    15. Manipushpak Mitra, 2002. "Achieving the first best in sequencing problems," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 75-91.
    16. Robert J. Dolan, 1978. "Incentive Mechanisms for Priority Queuing Problems," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 421-436, Autumn.
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    5. 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.
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    7. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2015. "Non-manipulable rules for land rental problems," MPRA Paper 67334, University Library of Munich, Germany.
    8. 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.
    9. Elena Panova, 2023. "Sharing cost of network among users with differentiated willingness to pay," Post-Print hal-04556220, HAL.
    10. 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.
    11. Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2024. "Merge-proofness and cost solidarity in shortest path games," MPRA Paper 120606, University Library of Munich, Germany.
    12. 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.
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