A game show has two contestants, Alice and Bob. The host offers them £100 to split between them using these rules: Alice proposes a split (she decides how much she gets and how much Bob gets) Bob can either accept or reject the proposal If Bob accepts, they both get the money according to Alice's proposal If Bob rejects, they both get nothing Both players want to maximize their own money Bob will accept any offer where he gets at least some money (even £1), but will reject if he gets £0 Alice knows all of Bob's decision rules If Alice plays optimally to maximize her own earnings, how much will she offer to Bob?