Strategic Effects and Incentives in Multi-issue Bargaining Games

see point 2 of Corollary 1). Given the structure of the game under agenda 1, the
parameters α2 and λ2 play exactly the same role under this agenda. When we con-
sider the equilibrium demand xe₁ defined in (10) the effects are all unambiguous. In
particular, an increase the between-cake discount factor α2 (or the parameter λ2)
has a positive effects on both players’ payoffs, regardless of players’ rates of time
preference. Instead, the effect of an increase in the relative importance of cake 1 to
player 1 (λ1) is unambiguous both in the case of corner solutions and in the case of
interior solutions. For the latter, player 1 is better off since he is able to extract a
larger share at the first division (point 3 of Corollary 1). In other words, if the first
issue becomes relatively more important to player 1, he is able to extract a larger
share at this stage. Again for the case of corner solutions (point 8 of Corollary 1),
the parameters interact in a less complicated way, in particular xe1 is unchanged but
obviously player 1 is better off.

The effects of a change in the within-cake discount factor δ_i on players’ payoffs
highlight much more complex relationships among the parameters (even for the case of
corner solutions). Indeed, these effects depend not only on the relationship between
players’ time preferences but also on players’ valuations of the second bargaining
stage. To be more precise, the effect of δ1 on player 1’s payoff is positive when player
1 is more patient than his opponent (δ₁ >δ₂) and he values the second bargaining
stage more than his opponent does, that is, α₁∕λ₁ ≥ α₂λ₂ (see points 4 of corollary

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