Optimal agendas for multi-issue negotiation

Abstract

There are two ways of handling bilateral multi-issue negotiations - one is to negotiate all the issues together, and the other is to negotiate them one by one. The order in which issues are negotiated in issue-by-issue negotiation is specified by the agenda, which can be defined in two ways. One way is to decide it exogenously, i.e., before negotiation begins. The other way is to let the players decide which issue they will negotiate next, during the process of negotiation, i.e., the agenda is determined endogenously. Against this background, the paper studies the effect of combining the exogenous and endogenous agendas on the players' utilities. More specifically, we determine whether, decomposing a set of N issues into k stages (for 1<k<N), determining the issues to be negotiated at each stage exogenously, and negotiating each stage sequentially using an endogenous agenda can improve an agent’s utility relative to the utility it gets if the agenda for all the N issues is defined endogenously. For each agent, we find the expected utility for each value of k between 1 and N. The value of k that gives an agent maximum utility is its optimal number of stages. Our study shows that, in some negotiation scenarios, the optimal value of k is identical for the two players, and is greater than one. In other words, in some negotiation scenarios, both the agents can improve their utilities by using the k-stage negotiation relative to the single stage negotiation. However, since the players have incomplete information about the negotiation parameters, they cannot identify such scenarios. We therefore present an extended alternating offers protocol, that allows the agents to identify such scenarios through a mediator, thereby resulting in improved utility to both the agents.

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