Advertisement

On the Efficiency of the Simplest Pricing Mechanisms in Two-Sided Markets

  • Volodymyr Kuleshov
  • Gordon Wilfong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We study the price of anarchy of a trading mechanism for divisible goods in markets containing both producers and consumers (i.e. in two-sided markets). Each producer is asked to submit a linear pricing function (or, equivalently, a linear supply function) that specifies a per-unit price p(d) as a function of the demand d that they face. Consumers then buy their preferred resource amounts at these prices.

We prove that having three producers for every resource guarantees the price of anarchy is bounded. In general, the price of anarchy depends heavily on the level of horizontal and vertical competition in the market, on the producers’ cost functions, and on the elasticity of consumer demand. We show how these characteristics affect economic efficiency and in particular, we find that the price of anarchy equals 2/3 in a perfectly competitive market, 3/4 in a monopsony, and 2ε(2 − ε)/(4 − ε) in a monopoly where consumer valuations have a fixed elasticity of ε. These results hold in markets with multiple goods, particularly in bandwidth markets over arbitrary graphs.

Pricing mechanisms are used in several real-world applications; our results suggest how to add formal efficiency guarantees to these mechanisms. On the theory side, we show that near-optimal efficiency can be achieved within two-sided markets by simple mechanisms in the spirit of Bertrand and Cournot. This result extends to the two-sided setting the analyses for fixed-supply and fixed-demand markets of Johari and Tsitsiklis (2005), Acemoglu and Ozdaglar (2007), and Correa et al. (2010).

Keywords

Nash Equilibrium Electricity Market Price Mechanism Price Function Arbitrary Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Acemoglu, D., Ozdaglar, A.: Competition and Efficiency in Congested Markets. Math. Oper. Res. 32, 1–31 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Baldick, R., Grant, R., Kahn, E.: Theory and Application of Linear Supply Function Equilibrium in Electricity Markets. Journal of Regulatory Economics 25(2), 143–167 (2004)CrossRefGoogle Scholar
  3. 3.
    Chawla, S., Roughgarden, T.: Bertrand Competition in Networks. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 70–82. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Correa, J.R., Lederman, R., Stier-Moses, N.E.: Pricing with markups under horizontal and vertical competition. In: Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions, pp. 92:1–92. ACM, New York (2010)CrossRefGoogle Scholar
  5. 5.
    Esquivel, H., Muthukrishnan, C., Niu, F., Chawla, S., Akella, A.: An Economic Framework for Flexible Routing. Technical report (2009)Google Scholar
  6. 6.
    Harks, T., Miller, K.: Efficiency and stability of Nash equilibria in resource allocation games. In: Proceedings of the First ICST International Conference on Game Theory for Networks, pp. 393–402. IEEE Press, Piscataway (2009)Google Scholar
  7. 7.
    Johari, R., Tsitsiklis, J.N.: Efficiency Loss in a Network Resource Allocation Game. Math. Oper. Res. 29, 407–435 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Johari, R., Tsitsiklis, J.N.: A scalable network resource allocation mechanism with bounded efficiency loss. IEEE Journal on Selected Areas in Communications 24(5), 992–999 (2005)CrossRefGoogle Scholar
  9. 9.
    Kelly, F.: Charging and rate control for elastic traffic. European Transactions on Telecommunications (1997)Google Scholar
  10. 10.
    Klemperer, P.D., Meyer, M.A.: Supply Function Equilibria in Oligopoly under Uncertainty. Econometrica 57(6), 1243–1277 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Kuleshov, V., Vetta, A.: On the Efficiency of Markets with Two-Sided Proportional Allocation Mechanisms. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 246–261. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Valancius, V., Feamster, N., Johari, R., Vazirani, V.: MINT: a Market for INternet Transit. In: Proceedings of the 2008 ACM CoNEXT Conference, pp. 70:1–70:6. ACM, New York (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Volodymyr Kuleshov
    • 1
  • Gordon Wilfong
    • 2
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Algorithms ResearchBell LaboratoriesMurray HillUSA

Personalised recommendations