International Journal of Game Theory

, Volume 48, Issue 1, pp 337–361 | Cite as

Full implementation of social choice functions in dominant strategies

  • Sven O. Krumke
  • Clemens ThielenEmail author
  • Philipp Weinschenk
  • Stephan Westphal
Original Paper


We consider the classical mechanism design problem of fully implementing social choice functions in dominant strategies in settings where monetary payments are allowed and the utility functions are quasi-linear. We consider both the general question of full implementation by indirect mechanisms and the special case of full implementation by incentive compatible direct revelation mechanisms. For the general case of full implementation by indirect mechanisms, we prove that one can restrict attention to incentive compatible augmented revelation mechanisms, in which the type space of each agent is a subset of the set of her possible bids and truthful reporting is a dominant strategy equilibrium. When the type spaces of the agents are finite, we give a complete characterization of the set of social choice functions that can be fully implemented in dominant strategies. For the case that one restricts to incentive compatible direct revelation mechanisms, we show that an adaption of the well-known negative cycle criterion for partial implementability also characterizes the social choice functions that are fully implementable.


Full implementation Dominant strategies Augmented revelation mechanism 


  1. Bergemann D, Morris S (2005) Robust mechanism design. Econometrica 73(6):1771–1813CrossRefGoogle Scholar
  2. Cormen TH, Stein C, Leiserson CE, Rivest RL (2009) Introduction to algorithms, 3rd edn. MIT Press, CambridgeGoogle Scholar
  3. Demski J, Sappington D (1984) Optimal incentive contracts with multiple agents. J Econ Theory 33(1):152–171CrossRefGoogle Scholar
  4. Gui H, Müller R, Vohra RV, (2005) Dominant strategy mechanisms with multidimensional types. In: Lehmann D, Müller R, Sandholm T (eds) Computing and markets. No. 05011 in Dagstuhl seminar proceedingsGoogle Scholar
  5. Jackson MO (1991) Bayesian implementation. Econometrica 59(2):461–477CrossRefGoogle Scholar
  6. Ma C, Moore J, Turnbull S (1988) Stopping agents from cheating. J Econ Theory 46(2):355–372CrossRefGoogle Scholar
  7. Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic theory. Oxford University Press, OxfordGoogle Scholar
  8. Mizukami H, Wakayama T (2007) Dominant strategy implementation in economic environments. Games Econ Behav 60(2):307–325CrossRefGoogle Scholar
  9. Mookherjee D, Reichelstein S (1990) Implementation via augmented revelation mechanisms. Rev Econ Stud 57(3):453–475CrossRefGoogle Scholar
  10. Palfrey TR (1992) Implementation in Bayesian equilibrium: the multiple equilibrium problem in mechanism design. In: Laffont J-J (ed) Advances in economic theory: sixth World Congress, vol 1, Chap 6. Cambridge University Press, Cambridge, pp 283–323Google Scholar
  11. Palfrey TR, Srivastava S (1987) On Bayesian implementable allocations. Rev Econ Stud 54(2):193–208CrossRefGoogle Scholar
  12. Palfrey TR, Srivastava S (1989) Implementation with incomplete information in exchange economies. Econometrica 57(1):115–134CrossRefGoogle Scholar
  13. Postlewaite A, Schmeidler D (1986) Implementation in differential information economies. J Econ Theory 39(1):14–33CrossRefGoogle Scholar
  14. Rochet J-C (1987) A necessary and sufficient condition for rationalizability in a quasilinear context. J Math Econ 16:191–200CrossRefGoogle Scholar
  15. Saijo T, Sjöström T, Yamato T (2007) Secure implementation. Theor Econ 2(3):203–229Google Scholar
  16. Van Huyck JB, Battalio RC, Beil RO (1990) Tacit coordination games, strategic uncertainty, and coordination failure. Am Econ Rev 80(1):234–248Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Department of EconomicsUniversity of KaiserslauternKaiserslauternGermany
  3. 3.Institute for Applied Stochastics and Operations ResearchClausthal University of TechnologyClausthal-ZellerfeldGermany

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