Strategic Effects and Incentives in Multi-issue Bargaining Games

below:

(1 — δι)[1 — δ₁δ2 + αιλι(1 + δι)(1 — δ₂)]
⁽¹^-^δι^δ2)

(24)

Then the equilibrium payoffs are as follows:

1 — δ₁δ₂ + α₁δ₁λ₁(1 — δ₁δ₂)

1 — δ1δ2

α2(1 — δι)

1 — δ1δ2

(25)

(26)

2) If o ≤ α₁ ≤ q, the equilibrium demands are defined in (27) and (28) below

(1 — δ₂)[(1 — διδ₂)λι + (1 — δ1)(α2λ1λ2(1 + δ₂) — δ₂αι(1 + δι))]
^λ1(¹^—^δ1^δ2)2

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

(27)

(28)

and the equilibrium payoffs are as follows:

1 — δ2
λ2(1 — δ₁δ2)²

[(λ₂ + α₂)(1 — δ₁δ₂) + (α₂ — α₁λ₁λ₂)(δ₂

— δ1)]

δ2(¹^—^δ1)
⁽¹^—^δ1^δ2)²

[λ2(1 + α1λ1)(1 — δ1δ2) + (α2 — α1λ1λ2)(δ2

— δ1)]

(29)

(30)

3) If q ≤ α₁ ≤ 1, the equilibrium demands are y₂ =1 and x₁ = xe₁ ∈ (0, 1), where

(1 — δ2)[(1 — δ₁δ2)λ2 + α₂(1 — δ₁)(1 + δ₂)]
(1 — δ1δ2)λ2

(31)

and the equilibrium payoffs are as follows:

(1 — δ2)[λ2(1 — δ1δ2) + α₂(1 + δ₂)(1 — δ1) + α1δ1λ1λ2]
λ2(1 — δ1δ2)

δ2[λ2(1 — δ1δ2) + α2δ2(1 — δ₁)]

1 — δ1δ2