Strategic Effects and Incentives in Multi-issue Bargaining Games

4 Urgent/difficult issue

In this section we assume that one issue is difficult in the sense that a rejection of
a proposal regarding this issue may lead to the negotiations breaking down. For in-
stance, in a peace process there can be an issue characterised by this feature, similarly,
in the bargaining between a buyer and a seller there can be a difficult item. In these
cases, what are the driving forces in the bargaining games and as a consequence, how
should the agenda be set?

To investigate this case we modify the model described in section 2 in two ways.
First, we assume that there is no time lapse between bargaining stages (τ =0), this is
a simplifying assumption (the result below can be re-established when τ is positive).
Second, the parameter α now represents the probability of game continuation after a
rejection of a proposal regarding the difficult issue, say cake 1. In other words, after
a rejection of a proposal regarding the division of cake 1, not only does the discount
factor δi apply but also the probability of game continuation α, while after a rejection
regarding the proposal of cake 2, only the discount factor δ_i applies. This does not
imply that cake 1 also represents the most important issue. The importance of an
issue still depends on the parameters λi with i =1, 2 as in the model described in
section 2. When there is a rejection in the bargaining stage related to the division of
cake 1, it is as if players are characterised by a smaller discount factor, δiα (rather
than δi). In other words, cake 1 represents an urgent issue in the sense that the

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