Skip to main content
SpringerLink
Log in

Decentralized Surplus Distribution Estimation with Weighted k-Majority Voting Games

  • Conference paper
  • First Online:
Highlights of Practical Applications of Cyber-Physical Multi-Agent Systems (PAAMS 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 722))

Abstract

Future energy grids and associated markets foster dynamic coalition formation in order to allow situational virtual power plant configurations. Collaboratively and distributed, such virtual power plants may take over responsibility on several emerging control tasks within the smart grid as a substitute for no longer available large plants. Temporary teamwork of individually owned and operated distributed energy resources demands for a proper and fair surplus distribution after product delivery. Distributing the surplus merely based on the absolute (load) contribution does not take into account that smaller units maybe provide the means for fine grained control as they are able to modify their load on a smaller scale. Bringing in flexibility, counts for several tasks. Shapley values provide a concept for the decision on how the generated total surplus of an agent coalition should be spread. In this paper, we propose a scheme for efficiently estimating computationally intractable Shapley values in a fully decentralized way. As a scheme to handle a set of different utility evaluation criteria we use weighted k-majority voting games. We demonstrate the applicability of the decentralized estimation by several simulation results in comparison with exact calculations.

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

References

  1. Awerbuch, S., Preston, A.M. (eds.): The Virtual Utility: Accounting, Technology & Competitive Aspects of the Emerging Industry Topics in Regulatory Economics and Policy. Topics in Regulatory Economics and Policy, vol. 26. Kluwer Academic Publishers, New York (1997)

    Google Scholar 

  2. Bachrach, Y., Markakis, E., Procaccia, A.D., Rosenschein, J.S., Saberi, A.: Approximating power indices. In: Padgham, L., Parkes, D.C., Müller, J.P., Parsons, S. (eds.) AAMAS, vol. 2, pp. 943–950. IFAAMAS (2008)

    Google Scholar 

  3. Beer, S.: Dynamic coalition formation in electricity markets. Ph.D. thesis (2017)

    Google Scholar 

  4. Bilbao, J., Fernndez, J., Jimnez, N., Lpez, J.: Voting power in the European union enlargement. Eur. J. Oper. Res. 143(1), 181–196 (2002)

    Article  MathSciNet  Google Scholar 

  5. Bremer, J., Lehnhoff, S.: Decentralized coalition formation in agent-based smart grid applications. In: Bajo, J., et al. (eds.) PAAMS 2016. CCIS, vol. 616, pp. 343–355. Springer, Cham (2016). doi:10.1007/978-3-319-39387-2_29

    Google Scholar 

  6. Bremer, J., Sonnenschein, M.: Constraint-handling for optimization with support vector surrogate models - a novel decoder approach. In: Filipe, J., Fred, A. (eds.) ICAART 2013 - Proceedings of the 5th International Conference on Agents and Artificial Intelligence, vol. 2, pp. 91–105. SciTePress, Barcelona (2013)

    Google Scholar 

  7. Bremer, J., Sonnenschein, M.: Estimating shapley values for fair profit distribution in power planning smart grid coalitions. In: Klusch, M., Thimm, M., Paprzycki, M. (eds.) MATES 2013. LNCS (LNAI), vol. 8076, pp. 208–221. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40776-5_19

    Chapter  Google Scholar 

  8. Chalkiadakis, G., Robu, V., Kota, R., Rogers, A., Jennings, N.: Cooperatives of distributed energy resources for efficient virtual power plants. In: The Tenth International Conference on Autonomous Agents and Multiagent Systems (AAMAS-2011), 2–6 May 2011, pp. 787–794. http://eprints.soton.ac.uk/271950/

  9. Champsaur, P.: How to share the cost of a public good? Int. J. Game Theory 4, 113–129 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  10. Deng, X., Papadimitriou, C.H.: On the complexity of cooperative solution concepts. Math. Oper. Res. 19(2), 257–266 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Elkind, E., Goldberg, L.A., Goldberg, P., Wooldridge, M.: On the dimensionality of voting games. In: In Proceedings of the Twenty Third AAAI Conference on Artificial Intelligence (AAAI-2008), pp. 13–17 (2008)

    Google Scholar 

  12. Fatima, S.S., Wooldridge, M., Jennings, N.R.: A linear approximation method for the shapley value. Artif. Intell. 172(14), 1673–1699 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fatima, S., Wooldridge, M., Jennings, N.R.: A heuristic approximation method for the banzhaf index for voting games. Multiagent Grid Syst. 8(3), 257–274 (2012). http://dx.doi.org/10.3233/MGS-2012-0194

    Article  Google Scholar 

  14. Friedman, E., Moulin, H.: Three methods to share joint costs or surplus. J. Econ. Theory 87(2), 275–312 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hinrichs, C.: Selbstorganisierte Einsatzplanung dezentraler Akteure im smart grid. Ph.D. thesis (2014). http://oops.uni-oldenburg.de/1960/

  16. Hinrichs, C., Bremer, J., Sonnenschein, M.: Distributed hybrid constraint handling in large scale virtual power plants. In: IEEE PES Conference on Innovative Smart Grid Technologies Europe (ISGT Europe 2013). IEEE Power & Energy Society (2013)

    Google Scholar 

  17. Hsu, M.C., Soo, V.W.: Fairness in Cooperating Multi-agent Systems – Using Profit Sharing as an Example. In: Lukose, D., Shi, Z. (eds.) PRIMA 2005. LNCS, vol. 4078, pp. 153–162. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03339-1_13

    Chapter  Google Scholar 

  18. Kahan, J., Rapoport, A.: Theories of coalition formation. Basic Studies in Human Behavior. L. Erlbaum Associates, London (1984)

    MATH  Google Scholar 

  19. Leech, D.: Computing power indices for large voting games. Manag. Sci. 49(6), 831–837 (2003). http://EconPapers.repec.org/RePEc:inm:ormnsc:v:49:y:2003:i:6:p:831–837

    Article  MATH  Google Scholar 

  20. Liben-Nowell, D., Sharp, A., Wexler, T., Woods, K.: Computing shapley value in supermodular coalitional games. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds.) COCOON 2012. LNCS, vol. 7434, pp. 568–579. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32241-9_48

    Chapter  Google Scholar 

  21. Lima, J., Pereira, M., Pereira, J.: An integrated framework for cost allocation in a multi-owned transmission-system. IEEE Trans. Power Syst. 10(2), 971–977 (1995)

    Article  Google Scholar 

  22. Lust, T., Teghem, J.: The multiobjective multidimensional knapsack problem: a survey and a new approach. CoRR abs/1007.4063 (2010)

    Google Scholar 

  23. Ma, R., Chiu, D., Lui, J., Misra, V., Rubenstein, D.: Internet economics: the use of shapley value for ISP settlement. In: Proceedings of the 2007 ACM CoNEXT Conference, CoNEXT 2007, pp. 6:1–6:12. ACM, New York (2007)

    Google Scholar 

  24. Mann, I., Shapley, L.: Values of large games, iv: evaluating the electoral college by montecarlo techniques. Technical report, Santa Monica, CA: RAND Corporation (1960). http://www.rand.org/pubs/research_memoranda/RM2651

  25. Mas-Colell, A.: Remarks on the game-theoretic analysis of a simple distribution of surplus problem. Int. J. Game Theory 9, 125–140 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  26. Matsui, Y., Matsui, T.: NP-completeness for calculating power indices of weighted majority games. Theor. Comput. Sci. 263(1–2), 306–310 (2001)

    MathSciNet  MATH  Google Scholar 

  27. McArthur, S., Davidson, E., Catterson, V., Dimeas, A., Hatziargyriou, N., Ponci, F., Funabashi, T.: Multi-agent systems for power engineering applications - Part I: concepts, approaches, and technical challenges. IEEE Trans. Power Syst. 22(4), 1743–1752 (2007)

    Article  Google Scholar 

  28. Nieße, A., Sonnenschein, M.: Using grid related cluster schedule resemblance for energy rescheduling - goals and concepts for rescheduling of clusters in decentralized energy systems. In: Donnellan, B., Martins, J.F., Helfert, M., Krempels, K.H. (eds.) SMARTGREENS. pp. 22–31. SciTePress (2013)

    Google Scholar 

  29. Nieße, A., Lehnhoff, S., Tröschel, M., Uslar, M., Wissing, C., Appelrath, H.J., Sonnenschein, M.: Market-based self-organized provision of active power and ancillary services: an agent-based approach for smart distribution grids. In: Complexity in Engineering (COMPENG), 2012. pp. 1–5 (June 2012)

    Google Scholar 

  30. Nieße, A., Beer, S., Bremer, J., Hinrichs, C., Lünsdorf, O., Sonnenschein, M.: Conjoint dynamic aggregation and scheduling for dynamic virtual power plants. In: Ganzha, M., Maciaszek, L.A., Paprzycki, M. (eds.) Federated Conference on Computer Science and Information Systems - FedCSIS 2014, Warsaw, Poland (9 2014)

    Google Scholar 

  31. Nikonowicz, Ł.B., Milewski, J.: Virtual power plants - general review: structure, application and optimization. J. Power Technol. 92(3), 135 (2012)

    Google Scholar 

  32. Osborne, M.J., Rubinstein, A.: A Course in Game Theory, 1st edn. The MIT Press, Cambridge (1994)

    MATH  Google Scholar 

  33. Owen, G.: Multilinear extension of games. Manag. Sci. 18(5–Part–2), 64–79 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  34. Ramchurn, S.D., Vytelingum, P., Rogers, A., Jennings, N.R.: Putting the ‘smarts’ into the smart grid: a grand challenge for artificial intelligence. Commun. ACM 55(4), 86–97 (2012)

    Article  Google Scholar 

  35. Rapoport, A.: N-Person Game Theory: Concepts and Applications. Ann Arbor science library, University of Michigan Press, Michigan (1970)

    MATH  Google Scholar 

  36. Saad, W., Han, Z., Poor, H.V., Basar, T.: Game theoretic methods for the smart grid. CoRR abs/1202.0452 (2012)

    Google Scholar 

  37. Sen, A.K.: Labour allocation in a cooperative enterprise. Rev. Econ. Stud. 33(4), 361–371 (1966)

    Article  Google Scholar 

  38. Shapley, L.S.: A value for n-person games. Contrib. Theory Games 2, 307–317 (1953)

    MathSciNet  MATH  Google Scholar 

  39. Valiant, L.G.: The complexity of computing the permanent. Theor. Comput. Sci. 8, 189–201 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  40. Watts, D., Strogatz, S.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  41. Yen, J., Yan, Y.H., Wang, B.J., Sin, P.K.H., Wu, F.F.: Multi-agent coalition formation in power transmission planning. In: Hawaii International Conference on System Sciences, pp. 433–443 (1998)

    Google Scholar 

  42. Zlotkin, G., Rosenschein, J.S.: Coalition, cryptography, and stability: mechanisms for coalition formation in task oriented domains. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, pp. 32–437. AAAI Press (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Oldenburg, 26129, Oldenburg, Germany

    Jörg Bremer & Sebastian Lehnhoff

Authors
  1. Jörg Bremer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Lehnhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jörg Bremer .

Editor information

Editors and Affiliations

  1. Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Madrid, Spain

    Javier Bajo

  2. Polytechnic Institute of Porto, Porto, Portugal

    Zita Vale

  3. University of Southern Denmark, Odense, Denmark

    Kasper Hallenborg

  4. University of Porto, Porto, Portugal

    Ana Paula Rocha

  5. Lille University of Science and Technology, Lille, France

    Philippe Mathieu

  6. Poznan University of Technology, Poznan, Poland

    Pawel Pawlewski

  7. Polytechnic University of Valencia, Valencia, Spain

    Elena Del Val

  8. University of Minho, Braga, Portugal

    Paulo Novais

  9. National Laboratory of Energy and Geology, Lisbon, Portugal

    Fernando Lopes

  10. National University of Colombia, Manizales, Caldas, Colombia

    Nestor D. Duque Méndez

  11. Polytechnic University of Valencia, Valencia, Spain

    Vicente Julián

  12. Malmö University, Malmo, Sweden

    Johan Holmgren

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Bremer, J., Lehnhoff, S. (2017). Decentralized Surplus Distribution Estimation with Weighted k-Majority Voting Games. In: Bajo, J., et al. Highlights of Practical Applications of Cyber-Physical Multi-Agent Systems. PAAMS 2017. Communications in Computer and Information Science, vol 722. Springer, Cham. https://doi.org/10.1007/978-3-319-60285-1_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60285-1_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60284-4

  • Online ISBN: 978-3-319-60285-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation