Limit Solutions of a Bargaining Problem with a Finite Horizon

In this paper, we investigated the limit solution of the subgame perfect equilibrium of the sequential bargaining game with a deadline. The solution represents the bargaining outcome when players can exchange offers and counteroffers infinitely often within a limited amount of time. The outcome can be represented by a formula implying that under the random proposer protocol with an equal probability, the outcome is close to the Raiffa solution when the deadline is imminent, which we refer to as an end phase evaluation, and the solution tends toward the time preference Nash solution as the deadline is moved further ahead Different bargaining protocol yields different end phase evaluation. We also gave an axiomatic foundation for this solution which heavily utilizing symmetry property. Although one can obtain the Nash bargaining solution with respect to the best alternative outcome as an end phase evaluation under the IIA or its alternative axiom, its strategic foundation in line with the sequential bargaining game is yet to be found.