Rubenstein Bargaining Solution

What if there is no deadline? What if we allow for an infinite number of steps? What is the solution then?
Assume that 1's discount rate is d₁ and 2's is d₂.
Rubenstein's bargaining solution tells us that the solution is for agent 1 to get (1 - d₂)/(1 - d₁d₂) and agent 2 gets the rest.
This agreement will be reached on the first round.

Proof:

Offerer's maximal acceptable claims in a finite game.
Round	1's share	2's share	Offerer
t-2	1 - d₂(1 - d₁P)		1
t-1		1 - d₁P	2
t	P		1

As the number of times goes to infinity the difference between successive steps goes to 0, so we can say that P = 1 - d₂(1 - d₁P) and solve for P.