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The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games

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Author Info

  • Heal, G.M.
  • Chichilnisky, G.

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

Paper provided by Columbia - Graduate School of Business in its series Papers with number 95-22.

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Length: 33 pages
Date of creation: 1995
Date of revision:
Handle: RePEc:fth:colubu:95-22

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Postal: U.S.A.; COLUMBIA UNIVERSITY, GRADUATE SCHOOL OF BUSINESS, PAINE WEBBER , New York, NY 10027 U.S.A
Phone: (212) 854-5553
Web page: http://www.columbia.edu/cu/business/
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Related research

Keywords: GAMES; GAME THEORY; POLITICS; VOTE; VOTING;

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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, 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, Lund University, Department of Economics 2005:3, Lund University, Department of Economics, revised 02 Feb 2007.
  3. James Schummer, 1997. "Manipulation Through Bribes," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1207, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.
  5. Reffgen, Alexander & Svensson, Lars-Gunnar, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, Econometric Society, vol. 7(3), September.
  6. 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.

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