The Game of Negotiations: Ordering Issues and Implementing Agreements
by
Lutz-Alexander Busch
University of Waterloo
Coauthors: Ignatius J. Horstmann (University of Western Ontario)

We study a bargaining situation involving two-issues. One of these has a surplus size which is public information, the other has a surplus size which is private information to one of the bargaining parties. We will call the former an ``easy'' issue, the latter a ``hard'' issue. Bargaining is by alternating offers under common time-discounting. The bargaining agenda is determined endogenously via the offers that players make. Players are free to offer on any number of outstanding issues. Offers must, however, be accepted or rejected in their entirety, that is, if an offer on both issues is received then either both prices or neither price must be accepted and it is not possible to accept only one of the prices. Once an offer has been accepted it is not renegotiable (and prices are bound to lie between zero and the value of the object.) We study this game under two alternative rules for implementing agreements. In the first, agreements are implemented as they are reached, in particular, if an offer on only one issue is made and accepted, then that issue is "consumed" immediately. In the alternative setting implementation is joint, so that even if an offer on one issue is accepted consumption of this surplus must nevertheless wait until the second issue is also settled. We show that the order in which issues are bargained in equilibrium is determined by three things: the implementation rule, the type of the informed player and the initial beliefs of the uninformed player. Specifically, an issue-by-issue bargaining agenda arises only when a low-valuation informed player faces an opponent who believes him to be likely a high-valuation type. In contrast to some writings in the negotiation practitioner literature, such initial agenda offers always involve concessions, that is, much smaller allocations to the informed player than in a bargain without agenda offers. We also show that it is the implementation rule which determines which issue leads in the agenda. When implementation takes place as agreements are reached, then the ``easy'' issue is negotiated first. If agreements are implemented only after all issues are settled, then, if order is relevant at all, it is size of surplus that matters, with large issues settled first. We also show that all parties prefer the former rules of implementation to the latter.

http://watserv1.uwaterloo.ca/~lbusch

Date received: April 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caez-57.