Two-sided market situations with existing contracts

The main aim of this paper is to study two-sided market situations where there are existing contracts which are exogenously given. These existing contracts could come from a previous competitive period or from any other circumstances. In any case, all these existing contracts provide an initial feasible solution for the two-sided market situation, perhaps non optimal in the sense the agents do not obtain jointly the maximum profit that they could get by cooperation. Therefore, the agents could be interested in improving their results through cooperation but taking into account the existing bilateral contracts. Thus, taking as starting point what each agent has got with the existing contracts, they have to distribute among themselves the extra amount that they could get by cooperation. For this kind of cooperative situation we propose different models and prove some results about the nonemptiness of the core and its relationship with the Owen set.