Strategic Effects and Incentives in Multi-issue Bargaining Games

payoff player i obtains, v_i , is as follows, with i =1, 2.

v1 = δ^t₁(λ1x + δ₁ⁿα1(1 - y))

v₂ = δ^t₂ (1 - x + δ₂ⁿα₂λ₂y)                            (2)

Our technical assumption is as follows. Let λ₂ ≤ λ₂ ≤ λ₂ where

ʌ _ ^α2(^{1 - δ}1)(^{1 - δ}₂)         _    ^δ2(^{1 - δ}1^δ2)

^λ2 =    δ2(i - δ1δ2)    ^{an 2} = α2(i - δι)(i - δ2)

This assumption allows us to simplify the presentation. This is not a restrictive
assumption since in the most interesting case in which some frictions tend to disappear
(i.e., ∆ → 0), these bounds tends to include the entire positive real range (i.e., λ₂ → 0
and λ₂ → ∞).

2.1 Equilibrium

Let

_ λι(1 — δ1δ2 + α₂λ₂(i + δ2)(l — δι)) b _ λι[(1 — δ2)α₂λ₂ — δ2(l — δ1δ2)]

a =               δ2(i — δ2)              ^,   =        δ2(i + δι)(i — δ2)

P _ λι[(i — δ2)α₂λ₂δι — (i — δ1δ₂)]    _ λ1δ1(i — δ1δ₂ + α₂λ₂(i + δ₂)(i — δι))

^f =         (i+δι)(i — δ2)       ’ ^g =              (i—δ2)

For α₁ that varies between the boundaries² f ≤ b ≤ g ≤ a, we can define different

SPE demands. There are at most three SPE with immediate agreement (when 0 <

²The assumption λ₂ ≤ λ₂ implies that b ≤ g. When the frictions within the bargaining stage

tends to disappear, ∆ → 0,f= b and g = a.

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