Bargaining with an Agenda

Abstract

We propose a new framework for bargaining in which the process follows an agenda. The agenda is represented by a family, parameterized by time, of increasing sets of joint utilities for possible agreements. This is in contrast to the single set used in the standard framework. The set at each time involves all possible agreements on the issues discussed up to that time. A \emph{bargaining solution} for an agenda specifies a path of agreements, one for each time. We characterize axiomatically a solution that is ordinal, meaning that it is covariant with order- preserving transformations of the utility representations. It can be viewed as the limit of a step-by-step bargaining process in which the agreement point of the last negotiation becomes the disagreement point for the next. The stepwise agreements may follow the Nash solution, the Kalai-Smorodinsky solution or many others, and the ordinal solution will still emerge as the steps tend to zero. Shapley showed that ordinal solutions exist for the standard framework for three players but not for two; the present framework generates an ordinal solution for any number of bargainers, in particular for two.bargaining, ordinal utility