For each assignment market, an associated bargaining problem is defined and some bargaining solutions to this problem are analyzed. For a particular choice of the disagreement point, the Nash solution and the Kalai-Smorodinsky solution coincide and give the midpoint between the buyers-optimal core allocation and the sellers-optimal core allocation, and thus they belong to the core. Moreover, under the assumption that all agents in the market are active, the subset of core allocations that can be obtained as a Kalai- Smorodinsky solution, from some suitable disagreement point, is characterized as the set of stable allocations where each agent is paid at least half of his maximum core payoff. All allocations in this last set can also be obtained by a negotiation procedure µa la Nash.
