Strategic Effects and Incentives in Multi-issue Bargaining Games

Proof. The proof follows the same reasoning as in Proposition 1.

The interplay of the forces in this game is similar to the ones defined for Agenda
1, with the only difference that now the first issue is represented by cake 2 rather
than 1. To show which incentives are the dominant ones we look at the case in which
parties can form preferences over agendas.

3.1 The Best Agenda

Whenever the differences in player i’s payoffs v_i - u_i (with v_i and u_i defined in Propo-
sition 1 and 2) for i =1, 2, have the same sign, players prefer the same agenda. In the
following proposition we show that the best agenda exists both in the case in which
there is consensus over the importance of the issues, and in the case in which parties
have different preferences over issues.

Proposition 3 In sequential bargaining procedures, there is consensus over agendas.
When players demand interior solutions in both agendas, then the best agenda consists
in setting the most important issue first, assuming that a player is characterised
by a sufficiently small α_i . When at least one player demands an extreme share in
equilibrium, then consensus over agenda can arise also when parties have different
preferences over issues.

Proof. The proof consists in analysing the sign of the differences vi - ui for any i.
Since each equilibrium payoff v_i and u_i can assume at most three values, according

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