This paper studies welfare tradeoffs in two-sided, one-to-one matching markets. We begin by providing theoretical upper bounds on a utilitarian price of stability, and show that these bounds vary with the composition of participants’ ordinal preference lists. We then turn to simulation experiments to describe how changes in basic characteristics of agents’ preferences can increase or decrease the average price of stability as measured by both utilitarian and Rawlsian welfare criteria. Our results indicate that markets featuring moderate degrees of correlation (...) and positive intercorrelation in the preferences of participants exhibit the steepest tradeoffs between stability and utilitarian welfare and between stability and Rawlsian welfare. (shrink)

Two forms of continuity are defined for Pareto representations of preferences. They are designated “continuity” and “coordinate continuity.” Characterizations are given of those Pareto representable preferences that are continuously representable and, in dimension two, of those that are coordinate-continuously representable.

The topological structures imposed on the collection of binary relations on a given set by the symmetric difference metric and the Hausdorff metric provide opportunities for learning about how collections of binary relations with various properties fit into the collection of all binary relations. For example, there is some agreement and some disagreement between conclusions drawn about the rarity of certain properties of binary relations using first the symmetric difference metric and then the Hausdorff metric.

Two scenarios illustrate uses of von Neumann–Morgenstern stable sets in the construction of choice functions. A comparison is made to the construction of choice functions by the selection of maximal elements. A characterization is given of choice functions that are von Neumann–Morgenstern stable set rationalizable by acyclic, asymmetric binary relations. Two examples illustrate the use of the characterization.

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. The concept was introduced informally by Knoblauch (2005). We give a clear, complete definition below. We prove that a characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. We also prove a simple but useful nonexistence theorem and (...) apply it to three examples. (shrink)