Skip to main content
SpringerLink
Log in

Cost-Sharing Games in Real-Time Scheduling Systems

  • Conference paper
  • First Online:
Web and Internet Economics (WINE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11316))

Included in the following conference series:

Abstract

We apply non-cooperative game theory to analyze the server’s activation cost in real-time scheduling systems. An instance of the game consists of a single server and a set of unit-length jobs. Every job needs to be processed along a specified time interval, defined by its release-time and due-date. Jobs may also have variable weights, which specify the amount of resource they require. We assume that jobs are controlled by selfish agents who act to minimize their own cost, rather than to optimize any global objective.

The jobs processed in a specific time-slot cover the server’s activation cost in this slot, with the cost being shared proportionally to the jobs’ weights. Known result on cost-sharing games do not exploit the special interval-structure of the strategy space in our game, and are therefore not tight. We present a complete analysis of equilibrium existence, computation, and inefficiency in real-time scheduling cost-sharing games. Our tight analysis covers various classes of instances, and distinguishes between unilateral and coordinated deviations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Throughout this paper, we consider pure strategies, as is the case for the vast literature on cost-sharing games. Unlike mixed strategies, pure strategies may not be random, or drawn from a distribution.

References

  1. Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. J. ACM 55(6), 25:1–25:22 (2008)

    Article  MathSciNet  Google Scholar 

  2. Adany, R., Tamir, T.: Algorithms for battery utilization in electric vehicles. Appl. Artif. Intell. 28(3), 272–291 (2014)

    Article  Google Scholar 

  3. Albers, S.: On the value of coordination in network design. SIAM J. Comput. 38(6), 2273–2302 (2009)

    Article  MathSciNet  Google Scholar 

  4. Albers, S.: Energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)

    Article  Google Scholar 

  5. Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. Games Econ. Behav. 65(2), 289–317 (2009)

    Article  MathSciNet  Google Scholar 

  6. Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)

    Article  MathSciNet  Google Scholar 

  7. Aumann, R.: Acceptable points in general cooperative n-person games. In: Contributions to the Theory of Games IV, vol. 4 (1959)

    Google Scholar 

  8. Avni, G., Kupferman, O., Tamir, T.: Network-formation games with regular objectives. J. Inf. Comput. 251, 165–178 (2016)

    Article  MathSciNet  Google Scholar 

  9. Avni, G., Tamir, T.: Cost-sharing scheduling games on restricted unrelated machines. Theor. Comput. Sci. 646, 26–39 (2016)

    Article  MathSciNet  Google Scholar 

  10. Baptiste, P.: Batching identical jobs. Math. Methods Oper. Res. 52(3), 355–367 (2000)

    Article  MathSciNet  Google Scholar 

  11. Bar-Noy, A., Guha, S., Naor, J., Schieber, B.: Approximating the throughput of multiple machines in real-time scheduling. SIAM J. Comput. 31(2), 331–352 (2001)

    Article  MathSciNet  Google Scholar 

  12. Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606–637 (2011)

    Article  MathSciNet  Google Scholar 

  13. Chang, J., Erlebach, T., Gailis, R., Khuller, S.: Broadcast scheduling: algorithms and complexity. ACM Trans. Algorithms 7(4), 47:1–47:14 (2011). https://doi.org/10.1145/2000807.2000815. Article No. 47

    Article  MathSciNet  MATH  Google Scholar 

  14. Chang, J., Gabow, H.N., Khuller, S.: A model for minimizing active processor time. Algorithmica 70(3), 368–405 (2014)

    Article  MathSciNet  Google Scholar 

  15. Chekuri, C., Chuzhoy, J., Lewin-Eytan, L., Naor, J., Orda, A.: Non-cooperative multicast and facility location games. IEEE J. Sel. Areas Commun. 25(6), 1193–1206 (2007)

    Article  Google Scholar 

  16. Chen, H., Roughgarden, T.: Network design with weighted players. Theory Comput. Syst. 45(2), 302–324 (2009)

    Article  MathSciNet  Google Scholar 

  17. de Jong, J., Klimm, M., Uetz, M.: Efficiency of equilibria in uniform matroid congestion games. In: Gairing, M., Savani, R. (eds.) SAGT 2016. LNCS, vol. 9928, pp. 105–116. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53354-3_9

    Chapter  Google Scholar 

  18. von Falkenhausen, P., Harks, T.: Optimal cost sharing for resource selection games. Math. Oper. Res. 38(1), 184–208 (2013)

    Article  MathSciNet  Google Scholar 

  19. Flammini, M., Monaco, G., Moscardelli, L., Shachnai, H., Shalom, M., Tamir, T., Zaks, S.: Minimizing total busy time in parallel scheduling with application to optical networks. Theor. Comput. Sci. 411(40–42), 3553–3562 (2010)

    Article  MathSciNet  Google Scholar 

  20. Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish unsplittable flows. Theor. Comput. Sci. 348(2–3), 226–239 (2005)

    Article  MathSciNet  Google Scholar 

  21. Gairing, M., Schoppmann, F.: Total latency in singleton congestion games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 381–387. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77105-0_42

    Chapter  Google Scholar 

  22. Gkatzelis, V., Kollias, K., Roughgarden, T.: Optimal cost-sharing in general resource selection games. J. Oper. Res. 64(6), 1230–1238 (2016)

    Article  MathSciNet  Google Scholar 

  23. Harks, T., Klimm, M.: On the existence of pure nash equilibria in weighted congestion games. Math. Oper. Res. 37(3), 419–436 (2012)

    Article  MathSciNet  Google Scholar 

  24. Harks, T., Miller, K.: The worst-case efficiency of cost sharing methods in resource allocation games. Oper. Res. 59(6), 1491–1503 (2011)

    Article  MathSciNet  Google Scholar 

  25. Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: a simple class of congestion games. In: Proceedings of the 20th AAAI, pp. 489–494 (2005)

    Google Scholar 

  26. Irani, S., Pruhs, K.R.: Algorithmic problems in power management. SIGACT News 36(2), 63–76 (2005)

    Article  Google Scholar 

  27. Jensen, J.L.W.V.: Sur les fonctions convexes et les ingalits entre les valeurs moyennes. Acta Math. 30, 175–193 (1906)

    Article  MathSciNet  Google Scholar 

  28. Khandekar, R., Schieber, B., Shachnai, H., Tamir, T.: Real-time scheduling to minimize machine busy time. J. Sched. 18(6), 561–573 (2015)

    Article  MathSciNet  Google Scholar 

  29. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65–69 (2009)

    Article  Google Scholar 

  30. Leung, J., Kelly, L., Anderson, J.H.: Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press Inc., Boca Raton (2004)

    Google Scholar 

  31. Milchtaich, I.: Congestion games with player-specific payoff functions. Games Econ. Behav. 13(1), 111–124 (1996)

    Article  MathSciNet  Google Scholar 

  32. Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. Int. J. Game Theory 2, 65–67 (1973)

    Article  MathSciNet  Google Scholar 

  33. Syrgkanis, V.: The complexity of equilibria in cost sharing games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 366–377. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17572-5_30

    Chapter  Google Scholar 

  34. Vöcking, B.: Selfish load balancing. In: Algorithmic Game Theory. Cambridge University Press (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, The Interdisciplinary Center (IDC), Herzliya, Israel

    Tami Tamir

Authors
  1. Tami Tamir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tami Tamir .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    George Christodoulou

  2. Universität Augsburg, Augsburg, Germany

    Tobias Harks

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tamir, T. (2018). Cost-Sharing Games in Real-Time Scheduling Systems. In: Christodoulou, G., Harks, T. (eds) Web and Internet Economics. WINE 2018. Lecture Notes in Computer Science(), vol 11316. Springer, Cham. https://doi.org/10.1007/978-3-030-04612-5_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04612-5_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04611-8

  • Online ISBN: 978-3-030-04612-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation