Home Dictatorial Mechanisms in Constrained Combinatorial Auctions
Article
Licensed
Unlicensed Requires Authentication

Dictatorial Mechanisms in Constrained Combinatorial Auctions

  • Anat Lerner EMAIL logo and Rica Gonen
Published/Copyright: June 21, 2013
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 13 Issue 1

Abstract

We study the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient combinatorial auctions in a model with two players and two nonidentical items (four outcomes). Our model has multidimensional types, private values, nonnegative prices, and quasilinear preferences for the players with one relaxation – the players are subject to publicly known budget constraints. We show that the space we study essentially includes one type of mechanisms: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient. The mechanisms in the autocratic families are identical except for two to three price parameters that differentiate them.

References

Arrow, K.J. 1950. “A Difficulty in the Concept of Social Welfare.” Journal of Political Economy 58 (4):328–46.10.1086/256963Search in Google Scholar

Ashlagi, I., M. Braverman, A. Hassidim, R. Lavi, and M. Tennenholtz. 2010. “Position Auctions with Budgets: Existence and Uniqueness.” The B.E. Journal of Theoretical Economics (Advances) 10 (1).10.2202/1935-1704.1648Search in Google Scholar

Bartal, Y., R. Gonen, and N. Nisan. 2003. Incentive Compatible Multi-unit Combinatorial Auctions.” In Proceedings of TARK, 72–87. Bloomington, Indiana: USA, June 20–22.Search in Google Scholar

Bhattacharya, S., V. Conitzer, K. Munagala, and L. Xiax. 2010. “Incentive Compatible Budget Elicitation in Multi-unit Auctions.” In Proceedings of SODA. Austin, Texas: USA, January 17–19.Search in Google Scholar

Budish, E., and E. Cantillon. 2010. “The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard.” In ECARES Working Paper.Search in Google Scholar

Clarke, E.H. 1971. “Multipart Pricing of Public Goods.” Public Choice 2:17–33.10.1007/BF01726210Search in Google Scholar

Dobzinski, S., R. Lavi, and N. Nisan. 2012. “Multi-unit Auctions with Budget Limits.” Games and Economic Behavior 74:486–503.10.1016/j.geb.2011.08.003Search in Google Scholar

Dobzinski, S., and N. Nisan. 2011. “Multi-unit Auctions: Beyond Roberts.” In Proceedings of EC’11, 233–42. San Jose, CA: USA, June 5–9.Search in Google Scholar

Fiat, A., S. Leonardi, J. Saia, and P. Sankowski. 2011. “Combinatorial Auctions with Budgets.” In Proceedings of EC’11.10.1145/1993574.1993609Search in Google Scholar

Gibbard, A. 1973. “Manipulation of Voting Schemes: A General Result.” Econometrica 41:587–601.10.2307/1914083Search in Google Scholar

Groves, T. 1973. “Incentives in Teams.” Econometrica 41:617–31.10.2307/1914085Search in Google Scholar

Hatfield, J.W. 2009. “Strategy-Proof, Efficient, and Non Bossy Quota Allocations.” Social Choice and Welfare 33:505–15.10.1007/s00355-009-0376-6Search in Google Scholar

Lavi, R., and M. May. 2012. “A Note on the Incompatibility of Strategy-proofness and Pareto-Optimality in Quasi-linear Settings with Public Budgets.” Economics Letters 115:100–03.10.1016/j.econlet.2011.11.043Search in Google Scholar

Lehmann, D., L.I. O’Callaghan, and Y. Shoham. 2002. “Truth Revelation in Approximately Efficient Combinatorial Auctions.” Journal of ACM 49 (5):577–602.10.1145/585265.585266Search in Google Scholar

Nisan, N., and A. Ronen. 2007. “Computationally Feasible VCG-Based Mechanisms.” Journal of Artificial Intelligence Research 29:19–47.10.1613/jair.2046Search in Google Scholar

Roberts, K. 1979. “The Characterization of Implementable Choice Rules.” In Aggregation and Revelation of Preferences, edited by J.-J. Laffont. North-Holland: North-Holland Publishing Company.Search in Google Scholar

Satterthwaite, M. 1975. “Strategy-Proofness and Arrow’s Condition: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions.” The Journal of Economic Theory 10:187–217.10.1016/0022-0531(75)90050-2Search in Google Scholar

Vickrey, W. 1961. “Counterspeculation, Auctions and Competitive Sealed Tenders.” Journal of Finance 16:8–37.10.1111/j.1540-6261.1961.tb02789.xSearch in Google Scholar

  1. 1

    We call the mechanisms autocratic and not dictatorial, as our domain of preferences is monetary and in that domain Groves has defined dictatorial mechanisms to allow for negative prices, which are not included in our model. A thorough discussion of the difference between Groves’s dictatorial mechanism and our autocratic mechanism is deferred to Section 2

  2. 2

    Dictatorship cannot be efficient.

  3. 3

    This article considers valuation spaces where not all valuations are included in the valuation space.

  4. 4

    y can be either a constant or a function . The function must satisfy .

  5. 5

    An example for a non-constant that satisfies the conditions when player 1 is the autocrat, , which is and, therefore, within the range of

  6. 6

    Note that the cases of equality in D2 and D3 can be randomly chosen. In such cases of equality, the players are indifferent to the alternative allocations of D2 and D3.

Published Online: 2013-6-21
Published in Print: 2013-1-1

©2013 by Walter de Gruyter Berlin / Boston

Articles in the same Issue

  1. Masthead
  2. Masthead
  3. Advances
  4. Dependence and Uniqueness in Bayesian Games
  5. Monopolistic Signal Provision†
  6. Multi-task Research and Research Joint Ventures
  7. Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information
  8. A Simple Bargaining Procedure for the Myerson Value
  9. On the Difference between Social and Private Goods
  10. Optimal Use of Rewards as Commitment Device When Bidding Is Costly
  11. Labor Market and Search through Personal Contacts
  12. Contributions
  13. Learning, Words and Actions: Experimental Evidence on Coordination-Improving Information
  14. Are Trust and Reciprocity Related within Individuals?
  15. Optimal Contracting Model in a Social Environment and Trust-Related Psychological Costs
  16. Contract Bargaining with a Risk-Averse Agent
  17. Academia or the Private Sector? Sorting of Agents into Institutions and an Outside Sector
  18. Topics
  19. Poverty Orderings with Asymmetric Attributes
  20. Dictatorial Mechanisms in Constrained Combinatorial Auctions
  21. When Should a Monopolist Improve Quality in a Network Industry?
  22. On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition
  23. Revenue Comparison in Asymmetric Auctions with Discrete Valuations
https://doi.org/10.1515/bejte-2013-0006

Articles in the same Issue

  1. Masthead
  2. Masthead
  3. Advances
  4. Dependence and Uniqueness in Bayesian Games
  5. Monopolistic Signal Provision†
  6. Multi-task Research and Research Joint Ventures
  7. Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information
  8. A Simple Bargaining Procedure for the Myerson Value
  9. On the Difference between Social and Private Goods
  10. Optimal Use of Rewards as Commitment Device When Bidding Is Costly
  11. Labor Market and Search through Personal Contacts
  12. Contributions
  13. Learning, Words and Actions: Experimental Evidence on Coordination-Improving Information
  14. Are Trust and Reciprocity Related within Individuals?
  15. Optimal Contracting Model in a Social Environment and Trust-Related Psychological Costs
  16. Contract Bargaining with a Risk-Averse Agent
  17. Academia or the Private Sector? Sorting of Agents into Institutions and an Outside Sector
  18. Topics
  19. Poverty Orderings with Asymmetric Attributes
  20. Dictatorial Mechanisms in Constrained Combinatorial Auctions
  21. When Should a Monopolist Improve Quality in a Network Industry?
  22. On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition
  23. Revenue Comparison in Asymmetric Auctions with Discrete Valuations
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 18.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/bejte-2013-0006/html
Scroll to top button