Skip to main content
SpringerLink
Log in

Efficiency and Budget Balance

  • Conference paper
  • First Online:
Web and Internet Economics (WINE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10123))

Included in the following conference series:

Abstract

We study efficiency and budget balance for designing mechanisms in general quasi-linear domains. Green and Laffont [13] proved that one cannot generically achieve both. We consider strategyproof budget-balanced mechanisms that are approximately efficient. For deterministic mechanisms, we show that a strategyproof and budget-balanced mechanism must have a sink agent whose valuation function is ignored in selecting an alternative, and she is compensated with the payments made by the other agents. We assume the valuations of the agents come from a bounded open interval. This result strengthens Green and Laffont’s impossibility result by showing that even in a restricted domain of valuations, there does not exist a mechanism that is strategyproof, budget balanced, and takes every agent’s valuation into consideration—a corollary of which is that it cannot be efficient. Using this result, we find a tight lower bound on the inefficiencies of strategyproof, budget-balanced mechanisms in this domain. The bound shows that the inefficiency asymptotically disappears when the number of agents is large—a result close in spirit to Green and Laffont [13, Theorem 9.4]. However, our results provide worst-case bounds and the best possible rate of convergence. Next, we consider minimizing any convex combination of inefficiency and budget imbalance. We show that if the valuations are unrestricted, no deterministic mechanism can do asymptotically better than minimizing inefficiency alone. Finally, we investigate randomized mechanisms and provide improved lower bounds on expected inefficiency. We give a tight lower bound for an interesting class of strategyproof, budget-balanced, randomized mechanisms. We also use an optimization-based approach—in the spirit of automated mechanism design—to provide a lower bound on the minimum achievable inefficiency of any randomized mechanism. Experiments with real data from two applications show that the inefficiency for a simple randomized mechanism is 5–100 times smaller than the worst case. This relative difference increases with the number of agents.

We are grateful to Ioannis Caragiannis, Vincent Conitzer, Debasis Mishra, Hervé Moulin, Ariel Procaccia, and Arunava Sen for useful discussions. Nath is funded by the Fulbright-Nehru postdoctoral fellowship. Sandholm is funded by the National Science Foundation under grants 1320620, 1546752, and 1617590, and by the ARO under award W911NF-16-1-0061.

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.

    Mechanisms using this idea have been presented with different names in the literature. The original paper by Green and Laffont [13] refers to this kind of agents as a sample of the population. Later Gary-Bobo and Jaaidane [11] formalized the randomized version of this mechanism which is known as polling mechanism. Faltings [9] refers to this as an excluded coalition (when there are multiple such agents) and Moulin [25] mentions this as residual claimants. However, we use the term ‘sink’ for brevity and convenience, and our paper considers a different setup and optimization objective.

  2. 2.

    For randomized mechanisms, results involving special domains are known, e.g., facility location [10, 29, 33], auctions [8], kidney exchange [2], and most of these mechanisms aim for specific objectives.

  3. 3.

    We have overloaded the notation of \(\pi \) following the convention in social choice literature (see, e.g., Myerson [27]). The notation \(\pi (v)\) denotes the valuation profile where the alternatives are permutated according to \(\pi \).

  4. 4.

    This definition is a generalization of auction revenue equivalence and is commonly used in the social choice literature (see, e.g., Heydenreich et al. [21]).

  5. 5.

    Green and Laffont’s impossibility result holds for efficient mechanisms, and all efficient mechanisms are neutral. However, there could be instances where multiple alternatives are efficient, i.e., there is a tie. The neutrality of an efficient rule is up to tie-breaking, and Green-Laffont applies no matter how the tie is broken. Similarly, our result also holds irrespective of how the tie is broken. Therefore, this theorem covers and generalizes that result since having at least one sink agent implies that the outcome cannot be efficient.

  6. 6.

    One can think of a more general class of sink mechanisms where multiple agents are treated as sink agents simultaneously. However, it is easy to see—by a similar argument to that in the context of deterministic mechanisms—that using multiple sinks cannot decrease inefficiency.

  7. 7.

    We overload the notation for the expected sample inefficiency \(r_n\) with \(r_{n,m}\) to make the number of alternatives explicit.

  8. 8.

    In both datasets there are missing values because a user has typically not rated all movies/jokes. Before our experiment, we filled the missing values with a random realization of ratings drawn from the empirical distribution for that alternative (movie or joke). The empirical distribution of an alternative is created from the histogram of the available ratings of the users. We cleaned the dataset by keeping only those alternatives that have at least 10 or more available ratings and filled the rest using their empirical distributions.

References

  1. Arrow, K.: The property rights doctrine and demand revelation under incomplete information. In: Economics and Human Welfare. New York Academic Press (1979)

    Google Scholar 

  2. Ashlagi, I., Fischer, F., Kash, I.A., Procaccia, A.D.: Mix and match: a strategyproof mechanism for multi-hospital kidney exchange. Games Econ. Behav. 91, 284–296 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bailey, M.J.: The demand revealing process: to distribute the surplus. Public Choice 91(2), 107–126 (1997)

    Article  Google Scholar 

  4. Cavallo, R.: Optimal decision-making with minimal waste: strategyproof redistribution of VCG payments. In: Proceedings of the Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 882–889 (2006)

    Google Scholar 

  5. Clarke, E.: Multipart pricing of public goods. Public Choice 8, 19–33 (1971)

    Google Scholar 

  6. Conitzer, V., Sandholm, T.: Complexity of mechanism design. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI), pp. 103–110. Morgan Kaufmann Publishers Inc. (2002)

    Google Scholar 

  7. d’Aspremont, C., Gérard-Varet, L.A.: Incentives and incomplete information. J. Public Econ. 11(1), 25–45 (1979)

    Article  Google Scholar 

  8. Dobzinski, S., Nisan, N., Schapira, M.: Truthful randomized mechanisms for combinatorial auctions. In: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 644–652. ACM (2006)

    Google Scholar 

  9. Faltings, B.: A budget-balanced, incentive-compatible scheme for social choice. In: Faratin, P., Rodríguez-Aguilar, J.A. (eds.) AMEC 2004. LNCS (LNAI), vol. 3435, pp. 30–43. Springer, Heidelberg (2006). doi:10.1007/11575726_3

    Chapter  Google Scholar 

  10. Feldman, M., Wilf, Y.: Randomized strategyproof mechanisms for facility location, the mini-sum-of-squares objective arXiv:1108.1762 (2011)

  11. Robert, R.J., Jaaidane, T.: Polling mechanisms and the demand revelation problem. J. Public Econ. 76(2), 203–238 (2000)

    Article  Google Scholar 

  12. Goldberg, K., Roeder, T., Gupta, D., Perkins, C.: Eigentaste: a constant time collaborative filtering algorithm. Inf. Retr. 4(2), 133–151 (2001)

    Article  MATH  Google Scholar 

  13. Green, J.R., Laffont, J.-J.: Incentives in Public Decision Making. North-Holland, Amsterdam (1979)

    MATH  Google Scholar 

  14. Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gujar, S.P., Narahari, Y.: Redistribution mechanisms for assignment of heterogeneous objects. J. Artif. Intell. Res. 41, 131–154 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Guo, M., Conitzer, V.: Optimal-in-expectation redistribution mechanisms. In: Proceedings of the Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 1047–1054 (2008)

    Google Scholar 

  17. Guo, M., Conitzer, V.: Worst-case optimal redistribution of VCG payments in multi-unit auctions. Games Econ. Behav. 67(1), 69–98 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Guo, M., Conitzer, V.: Better redistribution with inefficient allocation in multi-unit auctions. Artif. Intell. 216, 287–308 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gurobi. Gurobi optimizer reference manual (2015)

    Google Scholar 

  20. Harper, F.M., Konstan, J.A.: The movielens datasets: history and context. ACM Trans. Interact. Intell. Syst. (TiiS) 5(4), 19 (2016)

    Google Scholar 

  21. Heydenreich, B., Müller, R., Uetz, M., Vohra, R.V.: Characterization of revenue equivalence. Econometrica 77(1), 307–316 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Massó, J., Nicolò, A., Sen, A., Sharma, T., Ülkü, L.: On cost sharing in the provision of a binary and excludable public good. J. Econ. Theory 155, 30–49 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mishra, D., Sen, A.: Roberts’ theorem with neutrality: a social welfare ordering approach. Games Econ. Behav. 75(1), 283–298 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Mishra, D., Sharma, T.: On the optimality of the green-laffont mechanism. Preliminary Draft (2016)

    Google Scholar 

  25. Moulin, H.: Almost budget-balanced VCG mechanisms to assign multiple objects. J. Econ. Theory 144(1), 96–119 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Moulin, H., Shenker, S.: Strategyproof sharing of submodular costs: budget balance versus efficiency. Econ. Theor. 18(3), 511–533 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. Myerson, R.B.: Fundamentals of social choice theory. Q. J. Polit. Sci. 8(3), 305–337 (2013)

    Article  Google Scholar 

  28. Nath, S., Sandholm, T.: Efficiency and budget balance in general quasi-linear domains. arXiv:1610.01443 [cs.GT] (2016)

  29. Procaccia, A.D., Tennenholtz, M.: Approximate mechanism design without money. In: Proceedings of the 10th ACM Conference on Electronic Commerce (EC), pp. 177–186. ACM (2009)

    Google Scholar 

  30. Rothkopf, M.H.: Thirteen reasons why the Vickrey-Clarke-Groves process is not practical. Oper. Res. 55(2), 191–197 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  31. Roughgarden, T., Sundararajan, M.: Quantifying inefficiency in cost-sharing mechanisms. J. ACM (JACM) 56(4), 23 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  32. Sandholm, T.: Automated mechanism design: a new application area for search algorithms. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 19–36. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45193-8_2

    Chapter  Google Scholar 

  33. Thang, N.K.: On randomized strategy-proof mechanisms without payment for facility location games. In: Proceedings of the Web and Internet Economics (WINE), Stanford, USA, pp. 13–16 (2010)

    Google Scholar 

  34. Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Financ. 16(1), 8–37 (1961)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Swaprava Nath & Tuomas Sandholm

Authors
  1. Swaprava Nath
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tuomas Sandholm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Swaprava Nath .

Editor information

Editors and Affiliations

  1. School of Computer Science, McGill University, Montreal, Québec, Canada

    Yang Cai

  2. Department of Mathematics and Statistics, and School of Computer Science, McGill University, Montreal, Québec, Canada

    Adrian Vetta

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag GmbH Germany

About this paper

Cite this paper

Nath, S., Sandholm, T. (2016). Efficiency and Budget Balance. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-54110-4_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-54109-8

  • Online ISBN: 978-3-662-54110-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation