Nash implementing social choice rules with restricted ranges

Remzi Sanver

Review of Economic Design, 2017, vol. 21, issue 1, No 4, 65-72

Abstract: Abstract We consider Nash implementation of social choice rules with restricted ranges, i.e., where some of the available alternatives are chosen at no preference profile. We show that the appropriate adaptation of Maskin monotonicity to this context depends on the range of the mechanisms: the wider is this range, the weaker is the monotonicity condition to be used. As a result, mechanisms employing outcome functions which allow for out-of-range alternatives at off-equilibrium messages can Nash implement social choice rules which fail to be Nash implementable by mechanisms whose ranges are restricted to the range of the social choice rule to be implemented. The Walrasian social choice correspondence is a particular instance of this. Moreover, social choice rules which are not Maskin monotonic can be “monotonized” by the addition of artificial out-of-range alternatives—a point we illustrate through Solomon’s Dilemma.

Keywords: Maskin monotonicity; Nash implementation; Range restrictions; Walrasian solution; Solomon’s Dilemma (search for similar items in EconPapers)
JEL-codes: D79 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10058-016-0195-z

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