Ann and Bill are trying to divide one ice cream cake between themselves. At period 1,

Ann makes an offer of division to Bill. If accepted, they will get the proposed division

and the game is over. If rejected, period 1 ends and the game moves to period 2. In

period 2, Bill makes a proposal of division, and so on.

Suppose that Ann and Bill do not discount their payoffs in the future, i.e. ice cream in

the next period is valued as much as ice cream in the current period. However, at the

end of each period, of ice cream melts so that in the beginning of period 2, only

unit of ice cream is left, and in the beginning of period 3, only unit of ice cream is

left. Assume that when players are indifferent between accepting and rejecting, they

accept. Find the subgame perfect Nash equilibrium in this alternating offers game.

Explain.