Strategic Effects and Incentives in Multi-issue Bargaining Games

one would expect, both players are worse off (since the frictions to reach the second
bargaining stage increase). More interestingly, the effect on the SPE initial division
is more subtle. The share that player 1 obtains at the first stage _lx₁ decreases, if the
relative importance of cake 1 to player 1, λ1, is larger than the relative importance
of cake 1 to player 2, 1 /λ₂ (and vice-versa). In other words, player 2 is able to
obtain a more profitable initial agreement when he minds relatively less about the
initial issue and despite the fact that player 1 minds more about the initial issue is
unable to extract a larger surplus. The intuition is that when player 2’s relatively
more important issue is discussed second and the payoffs obtained at the second
bargaining stage are discounted more strongly, he is able to play in a "tougher" way
at the initial stage.

When players have different time preferences, some of the previous effects are
reversed. In particular a player could obtain a larger payoff when the frictions (τ )
increase. Let player 1 be more patient than player 2 (r₁ < r₂) then player 1 obtains a
smaller share at the initial division, when the relative importance of cake 2 to player
1 is larger than the relative importance of cake 2 to player 2 (i.e., 1∕λ₁ > λ₂). Under
these circumstances the effect of an increase in the interval of time τ on player 2’s
payoff is ambiguous. Indeed, there is a trade-off, on one hand, player 2 is worse off
since the payoff obtained from future negotiations are discounted more strongly when
τ increases; on the other hand, player 2 is better off since he can get a larger share at

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