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Almost-dominant Strategy Implementation

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  • James Schummer

Abstract

Though some economic environments provide allocation rules that are implementable in dominant strategies (strategy-proof), a significant number of environments yield impossibility results. On the other hand, while there are quite general possibility results regarding implementation in Nash or Bayesian equilibrium, these equilibrium concepts make strong assumptions about the knowledge that players possess, or about the way they deal with uncertainty. As a compromise between these two notions, we propose a solution concept built on one premise: Players who do not have much to gain by manipulating an allocation rule will not bother to manipulate it. We search for efficient allocation rules for 2-agent exchange economies that never provide players with large gains from cheating. Though we show that such rules are very inequitable, we also show that some such rules are significantly more flexible than those that satisfy the stronger condition of strategy-proofness.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1278.

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Date of creation: Nov 1999
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Handle: RePEc:nwu:cmsems:1278

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Web page: http://www.kellogg.northwestern.edu/research/math/
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Related research

Keywords: Strategy-proof; almost dominant strategy;

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References

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  1. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  2. David A. Smith, 1999. "Manipulability measures of common social choice functions," Social Choice and Welfare, Springer, vol. 16(4), pages 639-661.
  3. Bevia, Carmen & Corchon, Luis, 1995. "On the Generic Impossibility of Truthful Behavior: A Simple Approach," Economic Theory, Springer, vol. 6(2), pages 365-71, July.
  4. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
  5. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  6. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
  7. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March.
  8. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-44, September.
  9. Jose M. Cordoba & Peter J. Hammond, 1998. "Asymptotically Strategy-Proof Walrasian Exchange," Working Papers 98005, Stanford University, Department of Economics.
  10. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation for Research in Economics, Yale University.
  11. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  12. Schummer, J. & Thomson, W., 1996. "Two Derivations of the Uniform Rule and an Application to Bankruptcy," RCER Working Papers 423, University of Rochester - Center for Economic Research (RCER).
  13. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  14. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer, vol. 4(3), pages 417-35, May.
  15. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  16. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer, vol. 5(2), pages 229-46, March.
  18. Barbera, S. & Peleg, B., 1988. "Strategy-Proof Voting Schemes With Continuous Preferences," UFAE and IAE Working Papers 91.88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  19. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer, vol. 14(1), pages 47-56.
  20. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  21. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-27, January.
  22. Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
  23. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  24. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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Citations

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Cited by:
  1. Ehlers,L. & Peters,Hans & Storcken,Ton, 2000. "Threshold Strategy-Proofness: On Manipulability in Large Voting Problems," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.

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