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
(41)
(42)
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
r2
λ1λ2α1 (r1 - r2) - λ2 (r1 + r2)(1 - α1) - 2α2r1
(r1 + r2)2λ2
>0
(43)
23