Skip to main content
SpringerLink
Log in

An efficient solution of the resource allotment problem with the Groves–Ledyard mechanism under transferable utility

  • Large Scale Systems Control
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This paper designs an allotment mechanism for a limited amount of an infinitely divisible good (resource) among a finite number of agents under transferable utility. The mechanism is efficient in the sense of total agents’ utility maximization. As a solution, we introduce an adaptation of the Groves–Ledyard “quadratic government” that was initially suggested for the problem of public good.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Boss, V., Lektsii po matematike: differentsial’nye uravneniya (Lectures on Mathematics: Differential Equations), Moscow: Editorial URSS, 2004.

    Google Scholar 

  2. Burkov, V.N., Danev, B., Enaleev, A.K., et al., Bol’shie sistemy: modelirovanie organizatsionnykh mekhanizmov (Large Systems: Modeling of Organizational Mechanisms), Moscow: Nauka, 1989.

    Google Scholar 

  3. Burkov, V.N., Dzhavakhadze, G.S., Dinova, N.I., and Shchepkin, D.A., Primenenie igrovogo imitatzionnogo modelirovaniya dlya otsenki effektivnosti ekonomicheskikh mekhanizmov (Application of Game Simulation Modeling for Estimating the Efficiency of Economic Mechanisms), Moscow: Inst. Probl. Upravlen., 2003.

    Google Scholar 

  4. Goubko, M.V. and Novikov, D.A., Teoriya igr v upravlenii organizatsionnymi sistemami (Game Theory and Organizational Systems Control), Moscow: Sinteg, 2002.

    Google Scholar 

  5. Goubko, M.V. and Spryskov, D.S., Consideration of Cooperative Interactions in Planning Mechanisms, Upravlen. Bol’sh. Sist., 2000, no. 2, pp. 28–38.

    Google Scholar 

  6. Iskakov, M.B., Equilibrium in Safety Strategies and Equilibriums in Objections and Counter-objections in Noncooperative Games, Autom. Remote Control, 2008, vol. 69, no. 2, pp. 278–298.

    Article  MathSciNet  MATH  Google Scholar 

  7. Korgin, N.A., Representing a Sequential Resource Allotment Rule in the Form of a Strategy-proof Mechanism of Multicriteria Active Expertise, Autom. Remote Control, 2014, vol. 75, no. 5, pp. 983–995.

    Article  MATH  Google Scholar 

  8. Korgin, N.A. and Khristyuk, A.A., The Effective Mechanism of Active Examination with the Payment for Participation as the Tool of Acceptance of the Coordinated Decisions, Vestn. Voronezh. Gos. Tekh. Univ., 2011, vol. 7, no. 6, pp. 117–121.

    Google Scholar 

  9. Korepanov, V.O. and Novikov, D.A., The Reflexive Partitions Method in Models of Collective Behavior and Control, Autom. Remote Control, 2012, vol. 73, no. 8, pp. 1424–1441.

    Article  MathSciNet  MATH  Google Scholar 

  10. Mazalov, V.V., Mencher, A.E., and Tokareva, Yu.S., Peregovory. Matematicheskaya teoriya (Negotiations. Mathermatical Theory), St. Petersburg: Lan’, 2012.

    Google Scholar 

  11. Novikov, D.A., Theory of Control in Organizations, New York: Nova Science, 2013.

    Google Scholar 

  12. Arifovic, J. and Ledyard, J.O., A Behavioral Model for Mechanism Design: Individual Evolutionary Learning, J. Econom. Behav. Organiz., 2011, no. 78, pp. 375–395.

    Google Scholar 

  13. Barberá, S., Jackson, M., and Neme, A., Strategy-Proof Allotment Rules, Games Econom. Behav., 1997, vol. 18, no. 1, pp. 1–21.

    Article  MathSciNet  MATH  Google Scholar 

  14. Basar, T. and Maheswaren, R., Social Welfare of Selfish Agents: Motivating Efficiency for Divisible Resources, Proc. Control Decision Conf. (CDC), 2004, pp. 2004–361.

    Google Scholar 

  15. Boyd, S., Parikh, N., and Chu, E., Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Foundat. Trends Machine Learn., 2011, vol. 3, no. 1, pp. 1–122.

    Article  MATH  Google Scholar 

  16. Fischbacher, U., z-Tree—Zurich Toolbox for Ready-made Economic Experiments, Experim. Econom., 2007, vol. 10, no. 2, pp. 171–178.

    Google Scholar 

  17. Fudenberg, D. and Levine, D., Theory of Learning in Games, Cambridge: MIT Press, 1999.

    MATH  Google Scholar 

  18. Goetz, R., Martinez, Y., and Jofre, R., Water Allocation by Social Choice Rules: The Case of Sequential Rules, Ecol. Econom., 2008, vol. 65, no. 2, pp. 304–314.

    Article  Google Scholar 

  19. Groves, T. and Ledyard, J.O., The Existence of Efficient and Incentive Compatible Equilibria with Public Goods, Econometrica, 1980, no. 6, pp. 1487–1506.

    Article  MathSciNet  MATH  Google Scholar 

  20. Healy, P. and Mathevet, L., Designing Stable Mechanisms for Economic Environments, Theoret. Econom., 2012, vol. 7, no. 3, pp. 609–661.

    Article  MathSciNet  Google Scholar 

  21. Hurwicz, L., Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points, Rev. Econom. Stud., 1979, no. 46, pp. 217–225.

    Article  MathSciNet  MATH  Google Scholar 

  22. Jain, R. and Walrand, J., An Efficient Nash-Implementation Mechanism for Divisible Resource Allocation, Automatica, 2010, vol. 46, no. 8, pp. 1276–1283.

    Article  MathSciNet  MATH  Google Scholar 

  23. Johari, R. and Tsitsiklis, J.N., Efficiency of Scalar-ParameterizedMechanisms, Oper. Res., 2009, no. 57, pp. 823–839.

    Article  MathSciNet  MATH  Google Scholar 

  24. Kakhbod, A. and Teneketzis, D., An Efficient Game Form for Unicast Service Provisioning, IEEE Trans. Autom. Control, 2012, vol. 57, no. 2, pp. 392–404.

    Article  MathSciNet  Google Scholar 

  25. Kruskal, W.H. and Wallis, W.A., Use of Ranks in One-Criterion Variance Analysis, J. Am. Statist. Ass., 1952. vol. 47, pp. 583–621.

    Article  MATH  Google Scholar 

  26. Lefebvre, M., Sharing Rules for Common-Pool Resources When Self-insurance Is Available: An Experiment, Working Papers 11–22, LAMETA, Univ. of Montpellier, 2012.

    Google Scholar 

  27. Maskin, E., The Theory of Nash Equilibrium: A Survey, in Social Goals and Social Organization, Hurwicz, L., Schmeidler, D., and Sonnenschein, H., Eds., Cambridge: Cambridge Univ. Press, 1985, pp. 1985–173.

    Google Scholar 

  28. Mathevet, L., Supermodular Mechanism Design, Theoret. Econom., Econometr. Soc., 2010, vol. 5(3), pp. 403–443.

    MathSciNet  MATH  Google Scholar 

  29. Moulin, H., An Efficient and Almost Budget Balanced Cost Sharing Method, Games Econom. Behav., 2010, vol. 70, no. 1, pp. 107–131.

    Article  MathSciNet  MATH  Google Scholar 

  30. Sprumont, Y., The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Rule, Econometrica, 1991, vol. 59, pp. 509–519.

    Article  MathSciNet  MATH  Google Scholar 

  31. van Essen, M., A Note on the Stability of Chen’s Lindahl Mechanism, Soc. Choice Welfare, 2012, vol. 38(2), pp. 365–370.

    Article  MathSciNet  MATH  Google Scholar 

  32. Walker, M., A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations, Econometrica, 1981, no. 49, pp. 65–71.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    N. A. Korgin & V. O. Korepanov

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    N. A. Korgin

  3. Skoltech Center for Energy Systems, Skolkovo Institute of Science and Technology, Moscow, Russia

    N. A. Korgin

Authors
  1. N. A. Korgin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. O. Korepanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. A. Korgin.

Additional information

Original Russian Text © N.A. Korgin, V.O. Korepanov, 2013, published in Upravlenie Bol’shimi Sistemami, 2013, No. 46, pp. 216–265.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Korgin, N.A., Korepanov, V.O. An efficient solution of the resource allotment problem with the Groves–Ledyard mechanism under transferable utility. Autom Remote Control 77, 914–942 (2016). https://doi.org/10.1134/S0005117916050131

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117916050131

Keywords

Search

Navigation