In a two-sided matching market when agents on both sides have preferences the stability of the solution is typically the most important requirement. However, we may also face some distributional constraints with regard to the minimum number of assignees or the distribution of the assignees...

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network in which vertices express their preferences over their...

An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player...

The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case of uncoordinated processes in stable allocation...

Potent immunosuppressant drugs suppress the body's ability to reject a transplanted organ up to the point that a transplant across blood- or tissue-type incompatibility becomes possible. In contrast to the standard kidney exchange problem, our setting also involves the decision about which...

The chosen tournament format has a fundamental impact on the popularity and success of a sport. Efficiency of a format describes how well it can reproduce the real but hidden power ranking of the participants. We compare the efficiency of the formats of two individual sports that share similar...

The phenomenon of infrequent price changes has troubled economists for decades. Intuitively one feels that for most price-setters there exists a range of inaction, i.e. a substantial measure of the states of the world, within which they do not wish to modify prevailing prices. However, basic...

Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In...

A matching game is a cooperative game (N; v) defined on a graph G = (N;E) with an edge weighting w : E ! R+. The player set is N and the value of a coalition S N is defined as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n2 log n) algorithm that tests...

The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it...