There is a cake of size 1 to be divided between Alf and Bill. In period t 1 Alf offers player Bill a share: Bill may accept now (in which case the game ends), or reject. If Bill rejects then, in period t 2 Alf again makes an offer, which Bill can accept (game ends) or reject. If Bill rejects, the game ends one period later with exogenously fixed payoffs of r to Alf and 1 - r to Bill. Assume that Alf and Bill's payoffs are linear in cake and that both persons have the same, time-invariant discount factor o 1.
1. What is the backwards induction outcome in the two-period model?
2. How does the answer change if the time horizon increases but is finite?
3. What would happen if the horizon were infinite? (Rubinstein 1982, Stahl 1972, Sutton 1986)