Symmetrically pairwise-bargained allocations in an assignment market

Consider an assignment game with transferable utility where the optimally assigned partners engage in bargaining of the sort modelled by Nash, using as their threats the maximum they could receive in an alternative match. A symmetrically pairwise-bargained (SPB) allocation is a core allocation such that all partners are in bargained equilibrium. It is shown that an SPB allocation always exists, that the set of SPB allocations coincides with the intersection of the kernel and the core, and that there is a rebargaining process which converges to an SPB allocation if it begins at a “distinguished point” in the core.