Strategic Effects and Incentives in Multi-issue Bargaining Games

that player 1 is indifferent between accepting and rejecting this offer so as to demand
for the entire surplus:

e l' (1 — αδ²)(1 + λ) — δ(1 — α)   λ(1 — α)

a^{g2 y}2 = ∆→o         1 + αδ          = 1 + α

On the other hand, if λ > 1, player 2 demands y₂ = 1 while player 1 demands a share
equal to _ag2 xe1 where _ag2 xe1 is such that player 2 is indifferent between accepting and
rejecting this offer so as to demand for the entire surplus:

₁e, = lim^{(1 - αδ}2)(^{1 + λ})^{- δλ}(^{1 - α})

^ag2     ∆→0          (1 + αδ)λ

We can now show that when there is a difficult/urgent issue, parties prefer to
postpone it and to agree over the easy issue first, even if this is not very important.

Proposition 6 When there is a difficult/urgent issue, parties can only agree in post-
poning such an issue regardless of its importance.

Proof. Let’s assume α> 1/3, given the SPE demands in Agenda 1, we distinguish
5 cases:

A) Let 0 < λ < λGR, where λG_r = V^α(^1+α) ^-α, in this case in agenda 1 Player
1 demands (^2+λ)2(¹~^α), while in Agenda 2 player 1 obtains the entire surplus. In this
case player 1 obtains a larger payoff inagenda1ifλ is sufficiently large (at the
limit λ > λY_e with λY_e = ^α(^1+a)~¹⁺√√²_-~a,~^{2a +a +a} ), otherwise, he prefers agenda 2.

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