Question

In this game, Ann first offers to split $15 in one of three ways: (14,1), or (8,7), or (1,14), where the first number shows Ann's share, the second shows Bob's share. After Ann makes the offer, Bob can choose to Accept it (and the offer is implemented), or Reject it (and both get 0), or grab a handful of quarters and run with it, in which case he gets $2 and Ann gets $13, i.e. (13,2) is the payoff.

What is Ann's payoff in the subgame perfect equilibrium?

Answer:

Answer 1

Ann's payoff is 13

the subgame perfect equilibrium for the game is for Ann to offer (14,1) and for Bob to choose grab and run, giving Ann 13 and Bob 2

By backward induction we can see that,

If ann offers (8,7), Bob will accept the offer giving Ann 7. She can do better.

If ann offers, (1,14) Bob will accept the offer giving Ann 1. She can do better.

Thus, Ann offers (14,1) and Bob's best strategy is to Garb and run to maximize his profits. This gives a payoff of 13 for Ann and she can not do any better than this.