Two players are trying to divide one unit of ice cream between themselves. At

period 1, player 1 makes an offer of division to player 2. If accepted, players

get the proposed division and the game is over. If rejected, period 1 ends and

the game moves to period 2. In period 2, player 2 makes a proposal of division,

and so on. Letting x denote the unit of ice cream, assume that for each player

u(x) = x.

Suppose the players do not discount their payoffs. However, at the end of each

period, 1/3 unit of ice cream melts so that in the beginning of period 2, only

2/3 unit of ice cream is left, and in the beginning of period 3, only 1/3 is left,

and nothing is left at the beginning of period 4. Assume that when players are

indierent between accepting and rejecting, they accept. Find the subgame

perfect Nash equilibrium in this alternating offers game.