Strategic Effects and Incentives in Multi-issue Bargaining Games

an agenda where the issue that is valued relatively more strongly by his opponent is
postponed (see, e.g., case 5 in proof of Proposition 3). Indeed, an important feature of
the bargaining game that affects parties’ preferences over agendas is that concessions
can be made only at the negotiations on the first issue (before the second has been
settled) and these concessions can be large or small depending on the difference in
the relative importance of an issue, not simply on the value of the importance of an
issue.

In some cases, more than one incentive work in the same direction. For instance,
if players have opposite preferences over issues (e.g., λ_i = λ with i =1, 2), then
the incentive to put the most important issue first and the incentive to postpone
the rival’s most important issue coincide. However, when players have the same
preferences over issues (e.g., λ1 > 1 and λ2 < 1), the incentive to put the most
important issue first is in contrast with the incentive to postpone the rival’s most
important issue. Proposition 3 shows that both incentives can be dominant (and
under which conditions).

In conclusion, the key elements in defining players’ preferences over agendas are
not only the value of the importance of an issues (is λi larger or smaller than 1?),
but also their difference (is λ1λ2 larger or smaller than 1?), players’ between-cake
discount factors and in general their rates of time preferences.

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