The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games
AbstractWe 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 InfoPaper provided by Columbia - Graduate School of Business in its series Papers with number 95-22.
Length: 33 pages
Date of creation: 1995
Date of revision:
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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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GAMES; GAME THEORY; POLITICS; VOTE; VOTING;
Other versions of this item:
- G. Chichilnisky & G. M. Heal, 1997. "The geometry of implementation: a necessary and sufficient condition for straightforward games (*)," Social Choice and Welfare, Springer, Springer, vol. 14(2), pages 259-294.
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
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- 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.
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"Strategy-Proof Allocation of Multiple Public Goods,"
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Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science
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- Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.
- Reffgen, Alexander & Svensson, Lars-Gunnar, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, Econometric Society, vol. 7(3), September.
- 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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