Strategic Effects and Incentives in Multi-issue Bargaining Games

b<g<1). These are described in the following proposition. Some of these SPE do
not exist if some of the boundaries do not belong to the³ interval (0,1).

Proposition 1 Let λ₂ ≤ λ₂ with i =1, 2, then there is a unique SPE in which
the agreement 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 1 (2) is x₁ (y₂ , respectively), as defined in the following three cases.

1) If 0 ≤ α1 ≤ b, then the equilibrium demands at the first stage are x1 =1 and
y₂ = ye₂ ∈ (0, 1), defined below

(1 ^{- δ}1)[(1 ^{- δ}1^δ2)^λ1 ^{+ α}1(1 ^{+ δ}1)(1 ^{- δ}2)]
^λ1(1 ^{- δ}1^δ2)

Then the equilibrium payoffs are as follows:

= (1 — δ1δ2)λ1 + α1δ1 (1 — δ2)

1 — δ1δ2

1 — δ1

V2 = λ2α2------

1 — δ1 δ2

2) If b ≤ α1 ≤ g, the equilibrium demands are defined in (6) and (7) below

(1 — δ2)[(1 — δ1δ2)λ1 + (1 — δ1)(α2λ1λ2(1 + δ2) — δ2α1(1 + δ₁))]
^λ1(^{1 — δ}1^δ2)2

(1 — δ1)[(1 — δ1δ2)λ1 + (1 — δ2)(α1 (1 + δ1) — α2λ1λ2δ1(1 + δ2))]
λ1(1 — δ1δ2)²

³ For instance, if b<0, then the first equilibrium specified in the proposition below does not
exist.

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