Strategic Effects and Incentives in Multi-issue Bargaining Games

Without loss of generality, let cake 1 represent the most important issue (λ₁ > 1 and
λ2 < 1), then if the between-cake discount factor of one player αi is sufficiently small,
that is, α_i ≤ α_i = Φ_iΓ_i where

the Pareto superior agenda consists in discussing the most important issue first (see
Flamini 2001 for details).

3) In both agenda the SPE outcome is that player 1 demands xe₁ (that is, max{g, q} <
αi < 1). Then, at the limit for ∆ → 0, the differences vi - ui are as follows

(λ1 - 1)α1r2

v₁ — u₁ = ------------

r1 + r2

(1 - λ₂)(r₁ + r₂(1 - α₂))

v₂ — u₂ = ----------------------

^{2    2}                r1 + r2

Then, we can conclude that players who are sufficiently patient prefer to put the most
important issue first.

4) In agenda 1 player 1 demands the interior solution x1, but in agenda 2 he
obtains the entire surplus (i.e., b<αi <o). Then, at the limit for ∆ → 0, the
difference v₁ — u₁ is as follows

λ1((1 — α1)r2(r1 + Г2) + 2r1r2λ2α2) — (ri + Г2)² — α1r2(r1 — Г2)
(ri + Г2)²

while v2 — u2 becomes

r1 [λ1λ2α2 (r1 — r2) + λ1(r1 + r2)(1 — α2) + 2α1r2

(r1 + r2)²λ1

22

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