A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that the students apply for programmes and they are ranked according to their scores. Students who apply for a programme with the same score are in a tie. Ties are broken by lottery in Ireland, by...

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative...

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 C̱ 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...

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...

Scarf's algorithm [18] provides fractional core elements for NTU-games. Biró and Fleiner [3] showed that Scarf's algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different...

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

One of the aims of the new electoral law of Hungary has been to define a fairer apportionment into voting districts. This is ensured by a set of rules slightly more premissive than those laid out in the Code of Good Practice in Electoral Matters of the Venice Commission. These rules fix the...

The aim of this paper is to propose a new solution for the roommate problem with strict references. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable matchings (Tan [30] [32]). We find that almost stable matchings...