Game Forms for Nash Implementation of General Social Choice Correspondences

Abstract

Several game forms are given for implementing general social choice correspondences (SCC's) which satisfy Haskin's conditions of monotonicity and No Veto Power. The game forms have smaller strategy spaces than those used in previously discovered mechanisms: the strategy for an individual consists of an alternative, two subsets (of alternatives), and a player number. For certain types of economic and political SCC's, including a-majority rule, the Walrasian, and Lindahl correspondence, the strategy space reduces to an alternative and a vector, where the number of components of the vector is at most twice the dimension of the alternative space.