Delays and partial agreements in multi-issue bargaining

We model a situation in which two players bargain over two pies, one of which can only be consumed starting at a future date. Suppose the players value the pies asymmetrically: one player values the existing pie more than the future one, while the other player has the opposite valuation. We show that players may consume only a fraction of the existing pie in the first period, and then consume the remainder of it, along with the second pie, at the date at which the second pie becomes available. Thus, our model features a special form of bargaining delay, in which agreements take place in multiple stages. Such partial agreements arise when players are patient enough, when they expect the second pie to become available soon, and when the asymmetry in their valuations is large enough.