Consider the following ultimatum game. There is a small pile of loonies. The number of loonies, nn 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.

1. What is your student number and your value for n?

2. How many coin combinations does the proposer have to choose from?

3. Carefully draw the game tree (marks for elegance).

4. (What is the equilibrium for this game if players care only about payoffs.

5. 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?

6. 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.

**Subject Mathematics Game Theory**