Strategic Effects and Incentives in Multi-issue Bargaining Games

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 λ_i > 0 and for α₁ that varies in the intervals with extremes
0 ≤ bl ≤ gl ≤ 1, with

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
ye₂^l ≡ lim∆→0 ye2 =0.

2) If b_l ≤ α₁ ≤ g_l , the equilibrium demands are defined in (6) and (7) below

r2[(r1 + r2)λ2 + 2r1(α2λ1λ2 - αι)]
λ1(r1 + r2)²

r1[(r1 + r2)λ1 + 2r2(α1 - α2λ1λ2)]
λ1(r1 + r2)²

15

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