Part I Economics Coursework Assessment 1 18.11.11
SOLUTIONS
QUESTION 1 (8 points)
Consider the following three player game:

Find all Nash-equilibria in pure strategies in the game, and state what, if any, they are.
(Up, Left, Front) (2 points)
(Down,Right, Front) (2points)
(Down,Left,Back) (2 points)
Plus 2 points if no wrong equilibrium is given.

Grading recommendations:
To give ONLY the equilibrium payoffs instead of the equilibrium strategies: subtract 1 point per occurrence, i.e. if this is done for all 3 equilibria but everything else is correct the student gets 8-3=5 points in total.

QUESTION 2 (4 points)
Look at the following two-player game. Find all dominant strategies, and indicate what, if any, they are. | Player 2 | Player 1 | | Left | Middle | Right | | Up | (3,2) | (9,1) | (6,4) | | Down | (2,5) | (8,8) | (2,9) |

Player 1 has a dominant strategy: Up. (2 points)
Player 2 has a dominant strategy: Right. (2points)

QUESTION 3 (6 points)

Look at the following three player game in extensive form. The numbers 1,2 or 3 at each decision node indicate whose turn it is.
Top
Sky
Down
Sea
(7,9,8)
(3,5,4)
(0,7,1)
(2,7,9)
No
Yes
2
(9,3,9) Green
Red
1
3
3

Find the equilibrium by backward induction, and then state what the equilibrium is, and what the equilibrium payoff for each player is.
Note: You do not need to draw the game tree in the answer booklet or explain.

Equilibrium Payoff (2points):
(3,5,4)

Equilibrium (4points):
Player 1 chooses Top.
Player 2 chooses Sea.
Player 3 chooses Red (at decision node after 2 chooses Sky).
Player 3 chooses Yes (at decision node after 2 chooses Sea).

Grading guide:
Many students will not state “Player 3 chooses Red (at decision node after 2 chooses Sky).”, since this does never happen in equilibrium. Please subtract 3 points in this case: