Reference functions and balanced concessions in bargaining

In bargaining, agents expect their concessions to be reciprocated. Using the 'reference function' concept of Thomson (1981), this paper constructs a class of solutions the outcomes of which lead to balanced concessions by agents as prescribed by the reference function adopted. The Kalai/Smorodinsky solution arises as a special case. Another solution in this class, which depends on the entire feasible set, is generated by using the centre of gravity as the reference function.