Strategic Effects and Incentives in Multi-issue Bargaining Games

and the equilibrium payoffs are as follows:

1 - δ2

-----——2 ^[(1 — ^δ1^δ2)(¹ + ^α2^λ2)^λι ⁺ (^δ1 — ^δ2)(^α1 — ^α2^λ1^λ2)]

δ1δ )²

¹---_χ .''_i2∖ ^{[(1 — δ}1^δ2)(^λ1 ^{+ α}1) + (^δ1 ^{— δ}2)(^α1 ^{— α}2^λ1^λ2)]

— δ1δ2)²λ1

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

(1 — δ2)[l — δ1δ2 + α2λ2(l — δ1)(1 + δ2)]
^{(1 — δ}ι^δ2)

and the equilibrium payoffs are as follows:

(1 — δ2)[λ1(l — δ1δ2 + α2λ2(l — δι)(1 + δ2)) + α1δ1]

1 — δ1δ2

δ2[1 — δ1δ2 + α2λ2(1 — δ1)]

1 — δ1δ2

Proof. The indifference conditions between accepting and rejecting an offer are the

following

^{1 — χ}1 ^{+ α}2^λ2_l-δ^δδ2 = ^δ2 (^y2 + ^α2^λ2(1-δ1δ^δ2)
^{(1 — y}2)^λ1 ^{+ α}11--^δδ2 = ^δ1 (^x1^λ1 ^{+ α}1 (1-δ2δ21 ´

The solution of the system (13) are the demands x1 and y2 defined in (6) and (7)

above. It can be shown that x₁ > 0 if and only if α₁ <aand x₁ < 1 if and only if

α1 >b. Similarly, y2 > 0 if and only if α1 >f and y2 < 1 if and only if α1 <g. It is

straightforward to see that f ≤ b and g ≤ a. Then, there is an intersection between
the interval [b, a] and [f, g] if and only if g > b, that is λ₂ ≤ λ₂. Under this condition we
can distinguish three sections on the α1 axis. First, when 0 ≤ α1 ≤ b, the equilibrium

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