Some things couples always wanted to know about stable matchings (but were afraid to ask)

In this note we study the National Resident Matching Program (NRMP) algorithm in the US market for physicians. We report on two problems that concern the presence of couples, a feature explicitly incorporated in the new NRMP algorithm (cf. Roth and Peranson in Am Econ Rev 89:748–780, 1999). First, we show that the new NRMP algorithm may not find an existing stable matching, even when couples’ preferences are ‘responsive’, i.e., when Gale and Shapley’s (Am Math Monthly 69:9–15, 1962) deferred acceptance algorithm (on which the old NRMP algorithm is based) is applicable. Second, we demonstrate that the new NRMP algorithm may also be anipulated by couples acting as singles.      

The relative value of growth

Most executives would say that adding a point of growth and gaining a point of operating-profit margin contribute about equally to shareholder value. Margin improvements hit the bottom line immediately, while growth compounds value over time. But the reality is that the two are rarely equivalent. Growth often is far more valuable than managers think. For some companies, convincing the market that they can grow by just one additional percentage point can be worth six, seven, or even ten points of margin improvement. This article presents a new strategic metric, called the relative value of growth (RVG), which gives managers a clear picture of how growth projects and margin improvement initiatives affect shareholder value. Using basic balance sheet and income sheet data, managers can determine their companies' RVGs, as well as those of their competitors. Calculating RVGs gives managers insights into which corporate strategies are working to deliver value and whether their companies are pulling the most powerful value-creation levers. The author examines a number of well-known companies and explains what their RVG numbers say about their strategies. He reviews the unspoken assumption that growth and profits are incompatible over the long term and shows that a fair number of companies are effective at delivering both. Finally, he explains how managers can use the RVG framework to help them define strategies that balance growth and profitability at both the corporate and business unit levels.     

Desegregation in Pietersburg after the repeal of the Group Areas Act

Since the Group Areas Act was repealed in 1991, black people have for the first time become legal home‐owners in previously whites‐only areas of South African cities. This survey is concerned with residential changes in Pietersburg between June 1991 and May 1993. The residential location of black people was monitored and mapped, and the first new black home‐owners were interviewed to determine their reasons for moving to Pietersburg. The survey shows that only blacks in the middle‐ and high‐income groups made the move, and that property values were not a deciding factor in the purchase of a home.     

On the invariance of the set of Core matchings with respect to preference profiles

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal.