Finite horizon bargaining game. Consider an alternating offer bargaining game which has the same structure as the one described in the text except that there is a finite number T of bargaining...

Finite horizon bargaining game. Consider an alternating offer bargaining game which has the same structure as the one described in the text except that there is a finite number T of bargaining periods. If agreement is not reached by the end of period T the game terminates with neither player getting any pie. Show that the unique SPE of this game tends to the SPE of the finite horizon bargaining game as T → ∞. (Hint: work backwards from period T. What is the unique SPE of the single period game starting at date T ? Given this, what is the SPE of the two-period game starting at T 1? Carry on back to period 0. Now take the limit.)