Strategic Effects and Incentives in Multi-issue Bargaining Games

In this case, if r₁ >r₂ , that is, player 1 is more patient than player 2, then player 2
always prefers agenda 1 (even for λ2 > 1), while player 1 has the same preferences
when λ₁ is sufficiently large, so that expression (39) is positive. In other words,
players can agree over agendas even when they do not agree over the importance of
the issues.

5) In agenda 1 player 1 demands the entire surplus, while in agenda 2 he obtains
the interior solution x1 (i.e., o<αi <b). Then, at the limit for ∆ → 0, the difference
v₁ - u₁ is as follows

λ1λ2((r1 + r2)² + α1r2(r1 - r2)) - λ2r2(r1 + r2)(1 - α1) - 2α2r1r2
(r1 + r2)²λ2

while v₂ - u₂ is the following:

-r1 [2α1r2λ1λ2 + λ2(r1 + r2)(1 - α2) + α2(r1 - r2)]
(r1 + r2)²

When r1 >r2 , player 2 always prefers agenda 2, while player 1 has the same preference
only if λ₁λ₂ is sufficiently small. That is, player 2’s relative valuation of cake 1 is
larger then player 1 (λ₁ < 1∕λ₂). In this case, it does not matter what is the important
issue, only the product λ1λ2 is relevant.

6) Player 1 obtains xe₁ in agenda 1 and the interior demand x₁ in agenda 2. In
this case, at the limit for ∆ → 0, player 1 prefers agenda 1 if

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