asks for the entire surplus at the initial stage.
To investigate further the subtle effects of the parameters on the equilibrium
outcome of the bargaining game we focus on the case in which the interval of time
between a rejection and a new proposal, ∆, tends zero.
Corollary 2 Under the conditions specified in Proposition 1, in the limit as ∆
tends to zero, that is, for λi > 0 and for α1 that varies in the intervals with extremes
0 ≤ bl ≤ gl ≤ 1, with
bl ≡ lim b =
∆→0
λ1(2α2λ2r2 - (ri + r2))
2r2
lim g =
∆→0
λ1(2α2λ2r1 + ri + r2)
2r1
there is a unique SPE in which the agreement is reached immediately over the partition
of every single cake. At the second stage, player i demands the Rubinsteinian share
(r1+r2 with i,j = 1, 2 and i = j) while in the first stage the SPE demands by player
1 and 2 respectively are as follows.
1) If 0 ≤ α1 ≤ bl , then the equilibrium demands at the first stage are x1 =1 and
ye2l ≡ lim∆→0 ye2 =0.
2) If bl ≤ α1 ≤ gl , the equilibrium demands are defined in (6) and (7) below
lx1
ly2
r2[(r1 + r2)λ2 + 2r1(α2λ1λ2 - αι)]
λ1(r1 + r2)2
(20)
(21)
r1[(r1 + r2)λ1 + 2r2(α1 - α2λ1λ2)]
λ1(r1 + r2)2
15
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