Outside Options in a Bargaining Model with Decay in the Size of the Cake (Now published in Economics Letters 40 (1992), pp.417-421.)
The paper analyses a simple Rubinstein-type bargaining model in which there is no discounting and the cake decays over time at a positive rate. As a consequence, outside options enter players' unique Perfect Equilibrium payoffs. It is then shown that these payoffs, when the interval between two subsequent calls shrinks to zero, take the 'split-the-difference' form. (These results generalise easily to the case of three-party bargaining). This can justify the common practice, in labour economics, of deriving wage-equation expressions from Nash-maximands in which the status-quo points are shifted to the outside option level.