the initial bargaining stage when r1 < r2λ1λ2 . The overall effects of an increase in τ
on player 2’s payoff is positive only if player 1 is sufficiently more patient than player
2(r1 < r2/(2 + λ1λ2)), in other words, the initial concessions are sufficiently large.
3 Changing the Order of the Issues
In this section, the focus is on agenda 2, in which the first issue is represented by
cake 2. We then show what incentives parties need to take into account in forming
their preferences over agendas. Let
= λ2(l — δ1δ2) + α2(l + δ2)(l — δι)) = (1 — δ2)α2 — λ2δ2(l — δ1δ2)]
λ1λ2δ2(l — δ2) , λιλ2δ2(1 + δι)(1 — δ2)
_ (1 — δ2)α2δι — λ2(l — δ1δ2)] = δ1(λ2(l — δ1δ2) + α2(l + δ2)(l — δι))
λ λ1λ2(l + δ1)(l — δ2) , λ1λ2(l — δ2)
As for the analysis of agenda 1, for α1 that varies between the boundaries p ≤ o ≤
q ≤ n, we can define different demands in SPE with immediate agreement. These are
at most three.
Proposition 2 Let λ2 ° λ2 with i = l, 2, then there is an SPE in which the agree-
ment is reached immediately over the partition of every single cake. At the second
stage, parties play as in the RBM. At the first stage, the equilibrium demand of player
l (2) is x1 (y2 , respectively), as defined in the following cases.
1) If 0 ≤ α1 ≤ o, the equilibrium demands are x1 =l and y2 = ye2 ∈ (0, l), defined
18
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