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Part I Economics Coursework Assessment 1 18.11.11
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.
(9,3,9) Green

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):

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:…...

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