Strategic Effects and Incentives in Multi-issue Bargaining Games

and the equilibrium payoffs are as follows:

3) If g ≤ α_i ≤ 1, the equilibrium demands are y₂ =1 and x_i = xe^l_i ≡ lim_∆→0 xe_i =
0.

Corollary 3 For riτ small with i =1, 2, demand lxi defined in (20) is strictly
increasing (decreasing) in τ when r_i > r₂λ_i λ₂ (r_i < r₂λ_i λ₂, respectively), payoff _lv_i
is strictly decreasing (increasing) in τ when ri < r2(1 + 2λi λ2) (ri > r2(1 + 2λi λ2)
respectively) and lv2 is strictly decreasing (increasing) in τ when r2 <ri (2 + λi λ2) (
r₂ >r_i (2 + λ_i λ₂) respectively).

Proof. When riτ is small, the between-cake discount factor αi can be approximated
by 1 — r_iτ. The results then follow directly from Corollary 2. ■

In Corollary 3 the focus is on the SPE demands defined by interior solutions, since
for the other cases the demands are extreme (simply 0 or 1). When the interval of time
∆ tends to zero, obviously we can re-establish some of the results of the comparative
statics presented in corollary 1 (with reference to —ri rather δi). However, as Corollary
3 shows, additional effects on the equilibrium outcome can be highlighted in the case
of small interval of time (for ∆ that tends to zero and r_iτ is small). First of all, if
the interval τ increases, that is, the future payoffs are discounted more strongly by
both players, and players have the same rate of time preference (r_i = r₂), then, as

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