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

Graciela Chichilnisky and Geoffrey Heal

Social Choice and Welfare, 1997, vol. 14, issue 2, 259-294

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.

Date: 1997
Note: Received: 30 December 1994/Accepted: 22 April 1996
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Working Paper: The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games (1995)
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