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The Price of Anarchy in Two-Stage Scheduling Games

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10628))

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Abstract

We consider a scheduling game, in which both the machines and the jobs are players. A job attempts to minimize its completion time by switching machines, while each machine would like to maximize its workload by choosing a scheduling policy from the given set of policies. We consider a two-stage game. In the first stage every machine simultaneously chooses a policy from some given set of policies, and in the second stage, every job simultaneously chooses a machine. In this work, we use the price of anarchy to measure the efficiency of such equilibria where each machine is allowed to use at most two policies. We provide nearly tight bounds for every combination of two deterministic scheduling policies with respect to two social objectives: minimizing the maximum job completion, and maximizing the minimum machine completion time.

Research was supported in part by NSFC (11671355, 11271325).

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References

  1. Ashlagi, I., Tennenholtz, M., Zohar, A.: Competing schedulers. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI), pp. 691–696 (2010)

    Google Scholar 

  2. Azar, Y., Jain, K., Mirrokni, V.: (Almost) optimal coordination mechanisms for unrelated machine scheduling. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 323–332 (2008)

    Google Scholar 

  3. Caragiannis, I.: Efficient coordination mechanisms for unrelated machine scheduling. In: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 815–824 (2009)

    Google Scholar 

  4. Chen, X., Epstein, L., Kleiman, E., van Stee, R.: Maximizing the minimum load: the cost of selfishness. Theoret. Comput. Sci. 482, 9–19 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, X., Hu, X., Ma, W., Wang, C.: Efficiency of dual equilibria in selfish task allocation to selfish machines. In: Proceedings of the 6th International Conference on Combinatorial Optimization and Applications (COCOA), pp. 312–323 (2012)

    Google Scholar 

  6. Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination mechanisms. In: Proceedings of the 31st International Colloquium on Automata, Languages, and Programming (ICALP), pp. 45–56 (2004)

    Google Scholar 

  7. Cole, R., Correa, J.R., Gkatzelis, V., Mirrokni, V., Olver, N.: Inner product spaces for minsum coordination mechanisms. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (STOC), pp. 539–548 (2011)

    Google Scholar 

  8. Deuermeyer, B.L., Friesen, D.K., Langston, M.A.: Scheduling to maximize the minimum processor finish time in a multiprocessor system. SIAM J. Algebraic Discrete Meth. 3(2), 190–196 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dobson, G.: Scheduling independent tasks on uniform processors. SIAM J. Comput. 13, 705–716 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dubey, P.: Inefficiency of Nash equilibria. Math. Oper. Res. 11(1), 1–8 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  11. Epstein, L., Kleiman, E., Stee, R.: Maximizing the minimum load: the cost of selfishness. In: Proceedings of the 5th International Workshop on Internet and Network Economics (WINE), pp. 232–243 (2009)

    Google Scholar 

  12. Epstein, L., Kleiman, E., Stee, R.: The cost of selfishness for maximizing the minimum load on uniformly related machines. J. Comb. Optim. 27(4), 767–777 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  13. Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a network creation game. In: ACM Symposium on Principles of Distributed Computing (PODC), pp. 347–351 (2003)

    Google Scholar 

  14. Feldman, M., Immorlica, N., Lucier, B., Roughgarden, T., Syrgkanis, V.: The price of anarchy in large games. In: Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC), pp. 963–976 (2016)

    Google Scholar 

  15. Finn, G., Horowitz, E.: A linear time approximation algorithm for multiprocessor scheduling. BIT Numer. Math. 19(3), 312–320 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  16. Friesen, D.K.: Tighter bounds for LPT scheduling on uniform processors. SIAM J. Comput. 16, 554–560 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  17. Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)

    Article  MATH  Google Scholar 

  18. Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 263–269 (1969)

    MATH  MathSciNet  Google Scholar 

  19. Heydenreich, B., Müller, R., Uetz, M.: Games and mechanism design in machine scheduling-an introduction. Prod. Oper. Manag. 16(4), 437–454 (2007)

    Article  Google Scholar 

  20. Hoeksma, R., Uetz, M.: The price of anarchy for minsum related machine scheduling. In: Proceedings of the 9th International conference on Approximation and Online Algorithms (WAOA), pp. 261–273 (2011)

    Google Scholar 

  21. Immorlica, N., Li, L.E., Mirrokni, V.S., Schulz, A.S.: Coordination mechanisms for selfish scheduling. Theoret. Comput. Sci. 410, 1589–1598 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  22. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-49116-3_38

    Chapter  Google Scholar 

  23. Lin, L., Tan, Z.: Inefficiency of Nash equilibrium for scheduling games with constrained jobs: a parametric analysis. Theoret. Comput. Sci. 521, 123–134 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  24. Lucier, B., Borodin, A.: Price of anarchy for greedy auctions. In: Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 537–553 (2010)

    Google Scholar 

  25. Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  26. Roughgarden, T., Tardos, E.: Bounding the inefficiency of equilibria in nonatomic congestion games. Games Econ. Behav. 47(2), 389–403 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  28. Tan, Z., Wan, L., Zhang, Q., Ren, W.: Inefficiency of equilibria for the machine covering game on uniform machines. Acta Informatica 49(6), 361–379 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  29. Vetta, A.R.: Nash equilibria in competitive societies with applications to facility location, traffic routing and auctions. In: Symposium on the Foundations of Computer Science (FOCS), pp. 416–425 (2002)

    Google Scholar 

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Acknowledgment

The authors thank anonymous referees for helpful comments and suggestions to improve the presentation of this paper.

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Authors and Affiliations

  1. College of Computer Science, Zhejiang University, Hangzhou, 310027, China

    Deshi Ye & Guochuan Zhang

  2. Department of Computer Science, University of Houston, Houston, TX, USA

    Lin Chen

Authors
  1. Deshi Ye
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  2. Lin Chen
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  3. Guochuan Zhang
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Corresponding author

Correspondence to Deshi Ye .

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Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Ye, D., Chen, L., Zhang, G. (2017). The Price of Anarchy in Two-Stage Scheduling Games. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-71147-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71146-1

  • Online ISBN: 978-3-319-71147-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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