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The geometry of implementation: a necessary and sufficient condition for straightforward games (*)

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  • G. Chichilnisky

    (Program on Information and Resources, Columbia University, 405 Law Memorial Library, New York, NY 10027, USA)

  • G. M. Heal

    (Program on Information and Resources, Columbia University, 405 Law Memorial Library, New York, NY 10027, USA)

Abstract

We characterize games which induce truthful revelation of the players' preferences, either as dominant strategies (straightforward games) or in Nash equilibria. Strategies are statements of individual preferences on Rn. Outcomes are social preferences. Preferences over outcomes are defined by a distance from a bliss point. We prove that g is straightforward if and only if g is locally constant or dictatorial (LCD), i.e., coordinate-wise either a constant or a projection map locally for almost all strategy profiles. We also establish that: (i) If a game is straightforward and respects unanimity, then the map g must be continuous, (ii) Straightforwardness is a nowhere dense property, (iii) There exist differentiable straightforward games which are non-dictatorial. (iv) If a social choice rule is Nash implementable, then it is straightforward and locally constant or dictatorial.

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 14 (1997)
Issue (Month): 2 ()
Pages: 259-294

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Handle: RePEc:spr:sochwe:v:14:y:1997:i:2:p:259-294

Note: Received: 30 December 1994/Accepted: 22 April 1996
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Cited by:
  1. Ernesto Savaglio & Stefano Vannucci, 2012. "Strategy-proofness and unimodality in bounded distributive lattices," Department of Economics University of Siena 642, Department of Economics, University of Siena.
  2. Svensson, Lars-Gunnar & Torstensson, Pär, 2005. "Strategy-Proof Allocation of Multiple Public Goods," Working Papers 2005:3, Lund University, Department of Economics, revised 02 Feb 2007.
  3. Reffgen, Alexander & Svensson, Lars-Gunnar, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, vol. 7(3), September.
  4. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
  5. Schummer, James, 2000. "Manipulation through Bribes," Journal of Economic Theory, Elsevier, vol. 91(2), pages 180-198, April.

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