Strategic Effects and Incentives in Multi-issue Bargaining Games

To simplify let’s assume that λ<1. Then the demand x₁ belongs to (0,1) for r₃ <
α<r1, with

(1 ^{+ λ})(^{1 + δλ}) - \''^3       (1 ^{+ λ})(^{1 + δλ}) ^- √^δt1      ∕κ_θ∖

r³ =      2δ(λ + δλ + δ)2     , r¹ = -----------2-----------,      ⁽⁵²⁾

∆r1 = 1-4δ²λ+2λ(1-α)+λ²(1+δ²)+2λ³δ²(1+δ)+δ²λ⁴     (53)

∆_r3 =(1+δ²λ²)(1 + λ²) + 2λ(1 - λ² - λ(1 + δ²) + δ(1 + λ))       (54)

Moreover, r1 tends to 1 for δ → 1 while r3 can be larger than 1 for λ close to 1 and
δ<0.5.Whenα is smaller than r₃, then the SPE demand is a corner solution x₁ =1.
When α is larger than r1 (however, this case is not interesting for δ → 1), then we
have a corner solution of the system of indifference conditions and x1 =0. For λ<1,
the demand y₂ defined in (51) is always positive, however, it will be also larger than
1 unless λ is close to 1 and α is sufficiently large for δ large.

The conditions becomes more transparent forδ→1,then the demands (50) and
(51) becomes

λ² + 2λ - α
2λ(1 + α)

1 + 2λ - λ²α
2λ(1 + α)

the demand _lx₁ is in (0,1) for ʌ/! + α — 1 < λ < α + ʌ/a(l + α). Moreover, for
λ < 11 + α — 1, then _lx₁ < 0 while for λ > α + ʌ/a(! + α), then _lx₁ > 1. The

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