Suppose there are two players, 1 and 2. Player 1 just baked a delicious cake. She
can offer player 2 some infinitely divisible amount of the cake. Player 2 can then
accept or reject her offer of the cake. Suppose 2 accepts, when indifferent. If 2
accepts, 1 keeps the rest of the cake. If 2 rejects, 2 gets half the cake, and 1 gets
half the cake. Draw this game in the extensive form, and solve for subgame-perfect
Nash Equilibria. How much cake does each player get?
Now suppose there are three players, 1, 2, and 3. 1 has again baked a delicious cake. First, player 1 offers 2 some cake and 2 accepts or rejects. If 2 rejects, half the cake is transferred to 2. Whether 2 accepts or rejects, 2 must then offer 3 some cake, and 3 accepts or rejects (and accepts when indifferent). If 3 rejects, each player receives a third of the original cake. Draw this game, and solve for subgame-perfect Nash Equilibria. How much cake does each player get?
