demands are x1 =1and y2 = ye2 , where ye2 , defined in (3) is such that player 1 is
indifferent between accepting the demand ye2 or rejecting it to demand x1 =1. Since
α1 ≤ b and λ2 ≤ λ2,y2 < 1. Second, when b ≤ α1 ≤ g, then the solution of the system
(13) is given by the demands in (6) and (7), since these are interior, they are SPE
demands. Third, when g ≤ α1 ≤ 1, the equilibrium demands are y2 =1and x1 = xe1 ,
where xe1, defined in (10) is such that player 2 is indifferent between accepting the
demand xe1 or rejecting it to demand y2 =1. Following standard arguments (see for
instance, Osborne and Rubinstein, 1990), it can be shown that these solutions define
a unique SPE. ■
The equilibrium specified above has interesting characteristics. First of all, play-
ers’ demands in equilibrium are complicated functions of the parameters of the model
and typical results obtained in the context of bargaining over a single cake (for in-
stance a more patient player obtains a larger utility), may not exist in this game. The
following corollary presents some comparative statics. These results are immediate
consequences of Proposition 1. A discussion of these results follows.
Corollary 1 The equilibrium outcome defined in Proposition 1, part 2, is char-
acterised by the following:
1) if α1 increases, x1 decreases, v1 increases (decreases) if δ1 >δ2 ( δ1 >δ2
respectively) and v2 increases;
2) if α2 (or λ2) increases, x1 increases, v1 increases and v2 increases (decreases)
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