Strategic Effects and Incentives in Multi-issue Bargaining Games

to the value that α_i assumes (see Proposition 1 and 2), then we need to consider the
following seven cases:

1) In both agendas the SPE outcome is that player 1 demands the entire surplus
(that is, αi < min{b, o}). In this case, player 1 prefers agenda 1 (2 respectively) if

(^λ1 ^{- 1})(^{1 - δ}1^δ2 ^{- α}1^δ1(^{1 - δ}2))_n∕∩        ɪʌ             ∕O₉∖

-------------1 + δ δ-------------- > 0(< 0, respect.)             (32)

while player 2 prefers Agenda 1 if

α₂(1 - δ₁)(1 - λ₂)

----------——------>> > 0(< 0, respect.)                      (33)
1+δ₁δ₂

At the limit for ∆ → 0, expression (32) is positive when λ₁ > 1. Then both players
prefer the agenda that sets the most important issue first (e.g., agenda 1 if λ1 > 1
and λ₂ < 1).

2) In both agendas the SPE outcome is that player 1 demands the interior solution
of the system of indifference condition (that is, max{b, o} <αi < min{g, q}). In this
case, agenda 1 is preferred by player 1 when (34) below is positive and vice-versa
agenda 2 is favoured when (34) below is negative.

/₁ л л ²2 ʌ [(^λ1^λ2 ^{- 1)(1 + δ}2)^α2(^{1 - δ}1) ^{+ λ}2(^λ1 ^{- 1)(1 - δ}1^δ2 ^{+ α}1(^δ2 ^{- δ}1))] ⁽³⁴⁾
(1 - δ₁δ₂)²λ₂

Similarly, agenda 1 (2) is preferred by player 2 when (35) below is positive (negative,
respectively):

∕₁ ²^_{χ χ} 42). ^{[(1 - λ}2^λ2)(¹ + ^δ1)^α1(^{1 - δ}2) + ^λ1(^{1 - λ}2)(^{1 - δ}1^δ2 + ^α2(^δ1 ^{- δ}2))] ⁽³⁵⁾

(1 - δ1δ2)²λ1

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