Essays on Market/Mechanism Design

<div>We extend the preference domain of the assignment problem to accommodate ordinal, cardinal and mixed</div><div>preferences and thereby allow the mechanism designer to elicit different levels of information about individuals’</div><div>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</div><div>multi-utility representation. Although it is possible to construct a mechanism in the extended domain where</div><div>the agents with ordinal preferences don’t have an incentive to deviate from truth telling, agents with cardinal</div><div>preferences may deviate even if the deviations are restricted to ordinal preference reports.</div>