The Anarchy of Scheduling Without Money

  • Yiannis Giannakopoulos
  • Elias Koutsoupias
  • Maria Kyropoulou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9928)

Abstract

We consider the scheduling problem on n strategic unrelated machines when no payments are allowed, under the objective of minimizing the makespan. We adopt the model introduced in [Koutsoupias 2014] where a machine is bound by her declarations in the sense that if she is assigned a particular job then she will have to execute it for an amount of time at least equal to the one she reported, even if her private, true processing capabilities are actually faster. We provide a (non-truthful) randomized algorithm whose pure Price of Anarchy is arbitrarily close to 1 for the case of a single task and close to n if it is applied independently to schedule many tasks. Previous work considers the constraint of truthfulness and proves a tight approximation ratio of \((n+1)/2\) for one task which generalizes to \(n(n+1)/2\) for many tasks. Furthermore, we revisit the truthfulness case and reduce the latter approximation ratio for many tasks down to n, asymptotically matching the best known lower bound. This is done via a detour to the relaxed, fractional version of the problem, for which we are also able to provide an optimal approximation ratio of 1. Finally, we mention that all our algorithms achieve optimal ratios of 1 for the social welfare objective.

References

  1. 1.
    Angel, E., Bampis, E., Pascual, F., Tchetgnia, A.-A.: On truthfulness and approximation for scheduling selfish tasks. J. Sched. 12(5), 437–445 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Ashlagi, I., Dobzinski, S., Lavi, R.: Optimal lower bounds for anonymous scheduling mechanisms. Math. Oper. Res. 37(2), 244–258 (2012)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    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
  4. 4.
    Christodoulou, G., Gourvès, L., Pascual, F.: Scheduling selfish tasks: about the performance of truthful algorithms. In: Lin, G. (ed.) COCOON 2007. LNCS, vol. 4598, pp. 187–197. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Christodoulou, G., Koutsoupias, E., Kovács, A.: Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms 6(2), 38: 1–38: 18 (2010)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Dughmi, S., Ghosh, A.: Truthful assignment without money. In: EC, pp. 325–334 (2010)Google Scholar
  7. 7.
    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
  8. 8.
    Giannakopoulos, Y., Koutsoupias, E., Kyropoulou, M.: The anarchy of scheduling without money. CoRR, abs/1607.03688 (2016). http://arxiv.org/abs/1607.03688
  9. 9.
    Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41(4), 587–601 (1973)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Guo, M., Conitzer, V.: Strategy-proof allocation of multiple items between two agents without payments or priors. In: AAMAS, pp. 881–888 (2010)Google Scholar
  11. 11.
    Koutsoupias, E.: Scheduling without payments. Theory Comput. Syst. 54(3), 375–387 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65–69 (2009)MATHCrossRefGoogle Scholar
  13. 13.
    Koutsoupias, E., Vidali, A.: A lower bound of 1+\(\varphi \) for truthful scheduling mechanisms. Algorithmica 66(1), 211–223 (2013)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Levin, H., Schapira, M., Zohar, A.: Interdomain routing and games. In: STOC, pp. 57–66 (2008)Google Scholar
  15. 15.
    Mu’alem, A., Schapira, M.: Setting lower bounds on truthfulness: extended abstract. In: SODA, pp. 1143–1152 (2007)Google Scholar
  16. 16.
    Nisan, N., Ronen, A.: Algorithmic mechanism design. Games Econ. Behav. 35(1/2), 166–196 (2001)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, New York (2007)MATHCrossRefGoogle Scholar
  18. 18.
    Nissim, K., Smorodinsky, R., Tennenholtz, M.: Approximately optimal mechanism design via differential privacy. In: ITCS, pp. 203–213 (2012)Google Scholar
  19. 19.
    Penna, P., Ventre, C.: Optimal collusion-resistant mechanisms with verification. Games Econ. Behav. 86, 491–509 (2014)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: EC, pp. 177–186 (2009)Google Scholar
  21. 21.
    Satterthwaite, M.A.: Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theory 10(2), 187–217 (1975)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yiannis Giannakopoulos
    • 1
  • Elias Koutsoupias
    • 2
  • Maria Kyropoulou
    • 2
  1. 1.University of LiverpoolLiverpoolUK
  2. 2.University of OxfordOxfordUK

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