Nash implementing social choice rules with restricted ranges
Sanver, Remzi (2017), Nash implementing social choice rules with restricted ranges, Review of Economic Design, 21, 1, p. 65-72. 10.1007/s10058-016-0195-z
TypeArticle accepté pour publication ou publié
Journal nameReview of Economic Design
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Abstract (EN)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.
Subjects / KeywordsNash implementation; Maskin monotonicity; Range restrictions; Walrasian solution; Solomon’s Dilemma
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Positively responsive collective choice rules and majority rule: A generalization of May’s theorem to many alternatives, Horan, Sean; Osborne, Martin; Sanver, Remzi (2019) Article accepté pour publication ou publié