Dominant Strategies and Direct Mechanisms

  • Luis C. Corchón


In this chapter we will study the implementation of social choice functions by means of dominant strategies. Our first result is the so-called Revelation Principle which says that a necessary condition for implementation in dominant strategies is that there exist a direct mechanism — that is, a mechanism where each agent announces her characteristic — for which to reveal the true characteristic is a dominant strategy, in other words, truth-telling is an equilibrium (Proposition 1). We will also see how, if truth-telling is a dominant strategy, it is a Nash equilibrium and vice versa (Proposition 2). In section 3.3 we will study the incentives to tell the truth in economic environments. We will prove that under reasonable conditions there is no truth-telling mechanism, either in private good economies or in public good economies (Propositions 3 and 4). In section 3.4 we will see how if the preferences are quasi-linear and the full Pareto efficiency of the allocation as well as the individual rationality of the outcomes are not required, there is a mechanism in which the truth is a dominant strategy and the decision regarding the public good is optimal (Proposition 5). Under some additional conditions this mechanism is unique (Proposition 6). However, if individual rationality is assumed, any mechanism which induces truth-telling will almost always produce inefficient results (Proposition 7). Finally, section 3.5 is devoted to studying the incentives to reveal the true initial endowments also with similar negative results (Proposition 8).


Utility Function Nash Equilibrium Public Good Dominant Strategy Private Good 
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  1. The impossibility theorems for economies with private goods, with public goods and in social choice environments can be found respectively in L. Hurwicz (1972), ‘On Informationally Decentralized Systems’ in R. Radner and C.B. McGuire (eds), Decision and Organization: A Volume in Honor of Jacob Marshak (Amsterdam: North-Holland) pp. 297–336.Google Scholar
  2. J. Ledyard and J. Roberts (1974) ‘On the Incentive Problem with Public Goods’, Discussion Paper 116, Center for Mathematical Studies in Economics and Management Science, Northwestern University.Google Scholar
  3. M. Satterthwaite (1975), ‘Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions’, Journal of Economic Theory, vol. 10, pp. 187–217.CrossRefGoogle Scholar
  4. A. Gibbard (1973), ‘Manipulation of Voting Schemes: A General Result’, Econometrica, vol. 41, pp. 587–602.CrossRefGoogle Scholar
  5. This last article also established the revelation principle for the first time. Other papers dealing with the Gibbard—Satterthwaite theorem are: S. Barbera and B. Peleg (1990), ‘Strategy-Proof Voting Schemes with Continuous Preferences’, Social Choice and Welfare, 7, pp. 31–8CrossRefGoogle Scholar
  6. L. Zhou (1991), ‘Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods’, Review of Economic Studies, 58, pp. 107–9.CrossRefGoogle Scholar
  7. The following paper characterizes strategy-proof mechanisms in pure exchange economies: S. Barbera and M. Jackson ‘Strategy-Proof Exchange’, Econometrica, (forthcoming).Google Scholar
  8. The original papers on the Clarke—Groves mechanism are E. Clarke (1971), ‘Multipart Pricing of Public Goods’, Public Choice, pp. 19–33Google Scholar
  9. T. Groves (1973), ‘Incentives in Teams’, Econometrica, 41, pp. 617–631.CrossRefGoogle Scholar
  10. A good exposition of the Clarke—Groves mechanisms, where the space of public projects is {0, 1}, can be found in the book by Laffont (1988), Fundamentals of Public Economics (MIT Press).Google Scholar
  11. The following book concentrates on the study of such mechanisms. J. Green and J.J. Laffont (1979), Incentives in Public Decision Making (Amsterdam: North-Holland).Google Scholar
  12. Proposition 5 outlined in this chapter was first proved in T. Groves and M. Loeb (1975), ‘Incentives and Public Inputs’, Journal of Public Economics, 4, pp. 311–326.CrossRefGoogle Scholar
  13. The proof of proposition 6 was taken from J.J. Laffont and E. Maskin (1980), ‘A Differential Approach to Dominant Strategy Mechanisms’, Econometrica, 48, pp. 1507–20.CrossRefGoogle Scholar
  14. Proposition 7 is a simpler version of a theorem established by M. Walker (1980), ‘On the Nonexistence of a Dominant-Strategy Mechanism for Making Optimal Public Decisions’, Econometrica, vol. 48 pp. 1521–40CrossRefGoogle Scholar
  15. L. Hurwicz and M. Walker (1990), ‘On the Generic Nonoptimality of Dominant-Strategy Mechanisms: A General Theorem that Includes Pure Exchange Economies’, Econometrica, vol. 58 no. 3. pp. 683–704.CrossRefGoogle Scholar
  16. The version offered in the text is taken from C. Bevia and Corchôn, L. (1995), ‘On the Generic Impossibility of Truthful Behavior’, Economic Theory, 6, pp. 365–71.CrossRefGoogle Scholar
  17. The original article on the manipulation of initial endowments is A. Postlewaite (1979), ‘Manipulation Via Endowments’, Review of Economic Studies, vol. 46, pp. 245–262.CrossRefGoogle Scholar
  18. See also W. Thomson (1979), ‘Comment’ in Laffont (ed.), Aggregation and Revelation of Preferences (Amsterdam: North-Holland) pp. 428–30.Google Scholar

Copyright information

© Luis C. Corchón 1996

Authors and Affiliations

  • Luis C. Corchón
    • 1
  1. 1.Universidad de AlicanteAlicanteSpain

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