Strategic Effects and Incentives in Multi-issue Bargaining Games

_ly₂ > 1 and for λ > -⁺^^α^^+α), lУ2 < 0. Let α > 1/3, then, since

о < √ι+α -1 < P^α(^1+α)^{- α} < α+■.„.•. <¹⁺p(^1+α)
αα

the SPE demands are as defined in proposition 4, where the demand _lxe₁ and _lye₂
by player 1 and 2 respectively are such that the responder is indifferent between
accepting or rejecting the proposal so as to demand the entire surplus. ■

Similarly in agenda 2 where cake 2 is shared first the SPE is characterised by the
following proposition.

Proposition 5 In agenda 2, for ∆ → 0, the SPE demands are as follows: if λ< 1,

player demands the entire surplus, while player 2 demands a share _ag2 ye2 =

If λ> 1, player 2 demand the entire surplus, while player 1 demands the share

Proof. The solution of the indifferent conditions give demands:

(1 - δλ²)(1 - αδ²) + λ(1 - δ)(1 + αδ)
λ(1 + αδ)(1 - δ²)

λ(1 - δ)(1 + αδ) + (λ² - δ)(1 - αδ²)
λ(1 + αδ)(1 - δ²)

These are SPE demands if they are in (0,1). At the limit for ∆ → 0, the demands

_ag2x₁ and _ag2y₂ in (57) and (58) tends to sgn(1 - λ)∞ and sgn(λ - 1)∞ respectively.

This implies that the SPE demands in agenda 2 are as follows: if λ< 1, player 1

demands x₁ = 1 while Player 2 demands a share equal to _ag2ye₂ where _ag2 ye₂ is such

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