Dominant and Nash Strategy Mechanisms for the Assignment Problem

Abstract

In this paper, I examine the problem of matching or assigning a fixed set of goods or services to a fixed set of agents. I characterize the social choice correspondences that can be implemented in dominant and Nash strategies when transfers are not allowed. This is an extension of the literature that was begun by Gibbard (1973) and Satterthwaite (1975), who independently proved that if a mechanism is nonmanipulable it is dictatorial. For the classes of mechanisms that are described in the paper, the results imply that the only mechanisms that are implementable in dominant and Nash strategies are choice mechanisms that rely only on ordinal rankings. I also describe a subclass of mechanisms that are Pareto optimal. In addition, the results explain the modeling conventions found in the literature - that when nontransfer mechanisms are studied individuals are endowed with ordinal preferences, and when transfer mechanisms are studied individuals are endowed with cardinal preferences.