1. Four dwarves, Dopey, Sleepy , Mushy and Grubby, have been left four items which they value differently.

Dopey, Sleepy, Mushy, Grubby
rubber duck 20 2 18 21
Cinderella’s brush 50 50 50 40
Scrooge McDuck’s hat 10 20 20 50
Walt’s Watch 100 101 102 103

Use the method of sealed bids to determine an allocation.

2. Consider the following ultimatum game. There is a small pile of loonies. The number of loonies, n is equal to the first digit from the right in your student number that exceeds 5. (If there is no such number then it is equal to the first sum that exceeds five and is less that 10) The proposer moves first and proposes a division of the pile. He or she may keep any number of loonies from 0 to n inclusive. The responder can choose to accept of reject.

(a) What is your student number and your value for n?
(b) How many coin combinations does the proposer have to choose from?
(c) Carefully draw the game tree (marks for elegance).
(d) What is the equilibrium for this game if players care only about payoffs.
(e) Say the proposer knows that the responder will accept any offer of 3 or more and reject any offer of 2 or less. What is the proposers best strategy?
(f) In laboratory experiments players often do not play the subgame perfect strategies. Proposers usually offer between 2 and half of the loonies. Responders frequently reject offered of 2 and even 3. Explain why this might occur.

3. Define the following properties with respect to division problems
a proportionality
b equability
c super-additivity d envy-freeness

4. Describe a situation in which you would find one of the division techniques described in the text useful.

1. Four dwarves, Dopey, Sleepy , Mushy and Grubby, have been left f...