bargaining round related to the division of cake 1 is longer than the bargaining round
in which players attempt to divide cake 2. Bearing in mind this double interpretation,
we derive the players’ preferences over agendas among the issue-by-issue procedures
in the presence of a difficult/urgent issue.
Moreover, to simplify the presentation, we focus on the case in which players are
symmetric and that some frictions tend to disappear (ri = r, λi = λ for i =1, 2
moreover, ∆ → 0).
Proposition 4 In agenda 1, for ∆ → 0, the SPE demands are as follows:
(2 + λ)(1 - α)
i X1 = ʌ-----⅞-----S i У2 = 1 (47)
2
fθr \/1 ' a - 1 < λ < √α(1+α)-α ;
λ2 +2λ - α 1+2λ - λ2α
lx1 = 2λ(1 + a) , ly2 = 2λ(1 + a) (48)
for √α(1+α) -α < λ < a + pa(1 + a) and
(1+ 2λ)(1 - α)
i xi = 1, 1У2 = ʌ------£------- (49)
2λ
for λ > a + √a(1 + a).
Proof. For ri = r, λi = λ for i =1, 2, The solution of the indifferent conditions are
as follows:
(λ2 - aδ)(1 - aδ2) + λ(1 + δ)(1 - aδ)
λ(1 + δ)(1 - a2δ2)
(50)
(51)
λ(1 + δ)(1 - aδ) + (1 - aδλ2)(1 - aδ2)
λ(1 + δ)(1 - a2δ2)
27
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