Without loss of generality, let cake 1 represent the most important issue (λ1 > 1 and
λ2 < 1), then if the between-cake discount factor of one player αi is sufficiently small,
that is, αi ≤ αi = ΦiΓi where
Γi =
(1 - λj)λi
(λ2λj - 1)
and Φi =
(1 - δiδj + αj(δi - δj))
(1 + δi)(1 - δj)
(36)
the Pareto superior agenda consists in discussing the most important issue first (see
Flamini 2001 for details).
3) In both agenda the SPE outcome is that player 1 demands xe1 (that is, max{g, q} <
αi < 1). Then, at the limit for ∆ → 0, the differences vi - ui are as follows
(λ1 - 1)α1r2
(37)
(38)
v1 — u1 = ------------
r1 + r2
(1 - λ2)(r1 + r2(1 - α2))
v2 — u2 = ----------------------
2 2 r1 + r2
Then, we can conclude that players who are sufficiently patient prefer to put the most
important issue first.
4) In agenda 1 player 1 demands the interior solution x1, but in agenda 2 he
obtains the entire surplus (i.e., b<αi <o). Then, at the limit for ∆ → 0, the
difference v1 — u1 is as follows
λ1((1 — α1)r2(r1 + Г2) + 2r1r2λ2α2) — (ri + Г2)2 — α1r2(r1 — Г2)
(ri + Г2)2
while v2 — u2 becomes
r1 [λ1λ2α2 (r1 — r2) + λ1(r1 + r2)(1 — α2) + 2α1r2
(40)
(r1 + r2)2λ1
22