Essays on Market/Mechanism Design

We extend the preference domain of the assignment problem to accommodate ordinal, cardinal and mixed

preferences and thereby allow the mechanism designer to elicit different levels of information about individuals’

preferences. Given a fixed preference relation over a finite set of alternatives, our domain contains preferences over lotteries that are monotonic, continuous and satisfy an independence axiom. Under a natural coarseness relation, the stochastic dominance relation is the coarsest element of the domain and represents fully ordinal preferences. Any von Neumann-Morgenstern expected utility preference is a finest element and represents fully cardinal preferences. The extended domain can be characterized by an expected

multi-utility representation. Although it is possible to construct a mechanism in the extended domain where

the agents with ordinal preferences don’t have an incentive to deviate from truth telling, agents with cardinal

preferences may deviate even if the deviations are restricted to ordinal preference reports.