Strategic Effects and Incentives in Multi-issue Bargaining Games

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 (r_i = r, λ_i = 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)

λ(1 + δ)(1 - aδ) + (1 - aδλ²)(1 - aδ²)
λ(1 + δ)(1 - a²δ²)

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