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

Author

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  • 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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Suggested Citation

  • Heal, G.M. & Chichilnisky, G., 1995. "The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games," Papers 95-22, Columbia - Graduate School of Business.
  • Handle: RePEc:fth:colubu:95-22
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    Cited by:

    1. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    2. Lars-Gunnar Svensson & Pär Torstensson, 2008. "Strategy-proof allocation of multiple public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 181-196, February.
    3. Schummer, James, 2000. "Manipulation through Bribes," Journal of Economic Theory, Elsevier, vol. 91(2), pages 180-198, April.
    4. repec:spr:joecth:v:64:y:2017:i:2:d:10.1007_s00199-016-0983-2 is not listed on IDEAS
    5. Parikshit De & Manipushpak Mitra, 2017. "Incentives and justice for sequencing problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 239-264, August.
    6. Reffgen, Alexander & Svensson, Lars-Gunnar, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, vol. 7(3), September.
    7. 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.
    8. 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.
    9. Ernesto Savaglio & Stefano Vannucci, 2014. "Strategy-proofness and single-peackedness in bounded distributive lattices," Papers 1406.5120, arXiv.org.

    More about this item

    Keywords

    GAMES; GAME THEORY; POLITICS; VOTE; VOTING;

    JEL classification:

    • 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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