Warm-Up 5, Due Thursday, March 7, 12:00.

Warm-up questions usually either address material we handled during last class, or material you were to read in preparation for class, or you are supposed to answer questions based on your common sense alone. Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try to tell me why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

Your Name:

7 EQUAL PIRATES: Seven pirates without a hierarchy (A, B, C, D, E, F, G) have to decide decide how to distribute 10 gold coins they have found. They do it according to the following rules.

In each round they sit in a circle and rotate a bottle of rum. The one to which the bottle points has to propose a distribution of the coins. This proposal is voted on, with the proposer voting too, and even deciding in case of a tie. That implies that in case of only two pirates, the proposal will always win, and in case of four pirates, the proposer needs only one of the others voting for the proposal.
If the proposal wins, everything is settled. If not, the proposer is thrown into the water and dies, and the next round starts.

Assume that the pirates value their life worth 20 gold coins, and prefer throwing somebody overboard if everything else is equal (are playing the “hostile” variant).

Question 1

What would you propose if the bottle points on you and there are 7 pirates left?

Question 2

What would you propose if the bottle points on you and there are 5 pirates left?

Question 3

What would you propose if the bottle points on you and there are 3 pirates left?

Question 4

Is the game sequential? With or without randomness?