Hi can anyone help me with my homework in this subject? :)
Can you post it?
It will be really hard to post it here since it's in a file...
Oh well.. I'll try..
Suppose Lasse and Morten have a cake with 2 pieces and trying to come up with ways
to share it. Each like to eat as many pieces of cake as possible. Each has a plate to put the pieces
of cake, i.e. that is there are two plates and one belongs to Lasse while the other belongs to Morten.
Consider the following sharing mechanism. First, Lasse distributes the pieces of cake on each plate.
Then, Morten can accept or reject this offer of Lasse. If Morten accepts the offer, they eat the pieces
of cakes on their plates and derive a utility equal to the number of pieces of cake they eat. If Morten
rejects however, the process goes on. However, in case Morten rejects, they loose a piece of cake. That
is, after a rejection of Lasse’s first offer, the total number of available cake pieces drop to one. Then
Morten distributes the remaining piece of cake on the two plates. Given Morten’s offer, Lasse can
decide to either accept this offer or reject this offer. If Lasse accepts the offer, then they eat the pieces
of cakes on their plates and derive a utility equal to the number of pieces of cake they eat. If Lasse
rejects the offer, neither of them get any cake. Throughout this process, if any player is indifferent
between accepting or rejecting an offer, they accept the offer.
(a) Draw the game tree for this strategic interaction.
(b) Write the down the set of players. Given that their strategy sets are rather large, write one
possible strategy for each player. [Hint: In writing these strategies, start from highest node for
each player in the game tree and go from left to right at each decision level.]
(c) Find the subgame perfect equilibrium strategy profile of this game.