Stability in matching models with capacity constraint with agents’ responsive preferences, the set of qE-stable-G

Resumo

In this paper, a variant to the many-to-one matching model is presented, in which two types of complementary agents and an institution intervene. The latter wants to assign agents to perform certain tasks, each of which can be done by one agent from one set with many agents from the other. The institution has preferences over the possible matchings and a quota q, which is the maximum number of agents it can hire. In this model, considering responsive references for the agents, two concepts of stability are extended in a natural way and the concepts of q-stability-R and q-stability-G are defined. It is shown, under the institution’s responsive preference costraint, that there are sets of the matchings q-stable-G, and their complete characterization is obtained.