Scheduling without Payments

  • Elias Koutsoupias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6982)


We consider mechanisms without payments for the problem of scheduling unrelated machines. Specifically, we consider truthful in expectation randomized mechanisms under the assumption that a machine (player) is bound by its reports: when a machine lies and reports value \(\tilde{t}_{ij}\) for a task instead of the actual one t ij , it will execute for time \(\tilde{t}_{ij}\) if it gets the task—unless the declared value \(\tilde{t}_{ij}\) is less than the actual value t ij , in which case, it will execute for time t ij . Our main technical result is an optimal mechanism for one task and n players which has approximation ratio (n + 1)/2. We also provide a matching lower bound, showing that no other truthful mechanism can achieve a better approximation ratio. This immediately gives an approximation ratio of (n + 1)/2 and n(n + 1)/2 for social cost and makespan minimization, respectively, for any number of tasks.


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  1. 1.
    Alon, N., Feldman, M., Procaccia, A., Tennenholtz, M.: Strategyproof approximation of the minimax on networks. Mathematics of Operations Research 35(3), 513–526 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Auletta, V., De Prisco, R., Penna, P., Persiano, G.: The power of verification for one-parameter agents. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 171–182. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Christodoulou, G., Koutsoupias, E., Kovács, A.: Mechanism design for fractional scheduling on unrelated machines. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 40–52. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Dughmi, S., Ghosh, A.: Truthful assignment without money. In: Proceedings of the 11th ACM Conference on Electronic Commerce, pp. 325–334. ACM, New York (2010)Google Scholar
  5. 5.
    Fotakis, D., Tzamos, C.: Winner-imposing strategyproof mechanisms for multiple facility location games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 234–245. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica: Journal of the Econometric Society, 587–601 (1973)Google Scholar
  7. 7.
    Guo, M., Conitzer, V.: Strategy-proof allocation of multiple items between two agents without payments or priors. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 881–888. International Foundation for Autonomous Agents and Multiagent Systems (2010)Google Scholar
  8. 8.
    Koutsoupias, E., Vidali, A.: A lower bound of 1+ ϕ for truthful scheduling mechanisms. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 454–464. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Lu, P., Sun, X., Wang, Y., Zhu, Z.: Asymptotically optimal strategy-proof mechanisms for two-facility games. In: Proceedings of the 11th ACM Conference on Electronic Commerce, pp. 315–324. ACM, New York (2010)Google Scholar
  10. 10.
    Lu, P., Wang, Y., Zhou, Y.: Tighter bounds for facility games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 137–148. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Mu’alem, A., Schapira, M.: Setting lower bounds on truthfulness: extended abstract. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1143–1152. Society for Industrial and Applied Mathematics, Philadelphia (2007)Google Scholar
  12. 12.
    Nisan, N., Ronen, A.: Algorithmic mechanism design (extended abstract). In: Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, pp. 129–140. ACM, New York (1999)Google Scholar
  13. 13.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.: Algorithmic game theory. Cambridge Univ. Pr., Cambridge (2007)CrossRefzbMATHGoogle Scholar
  14. 14.
    Nissim, K., Smorodinsky, R., Tennenholtz, M.: Approximately optimal mechanism design via differential privacy. Arxiv preprint arXiv:1004.2888 (2010)Google Scholar
  15. 15.
    Procaccia, A., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the Tenth ACM Conference on Electronic Commerce, pp. 177–186. ACM, New York (2009)CrossRefGoogle Scholar
  16. 16.
    Roberts, K.: The characterization of implementable choice rules. Aggregation and Revelation of Preferences, 321–348 (1979)Google Scholar
  17. 17.
    Satterthwaite, M.: Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10(2), 187–217 (1975)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Elias Koutsoupias
    • 1
  1. 1.Department of InformaticsUniversity of AthensGreece

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