Consider a problem in which the cost of building an irrigation canal has to be divided among a set of people. Each person has different needs. When the needs of two or more people overlap, there is congestion. In problems without congestion, a unique canal serves all the people and it is enough...

We consider school choice problems (Abdulkadiroglu and Sönmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the...

This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of...

We consider school choice problems. We are interested in solutions that satisfy consistency. Consider a problem and a recommendation made by the solution for the problem. Suppose some students are removed with their positions in schools. Consider the “reduced” problem consisting of the...