This assignment is designed to provide you with the opportunity to communicate about technical and abstract
material in a clear and straightforward manner. You will spend some time each week writing up a response to a
question/prompt, and then posting that on a discussion board that your peers will review. By doing this each
week, you’ll get practice writing about technical matters.
Directions
Here is the prompt. In 500 words, write an answer to the following question:
Discussion Prompt
Consider a scenario with the following game tree:
U
+-------> (x1) 2, 6
| Y
| +-------> (x5) 2, 0
| B |
1---+ (x0) +-------> 2---+ (x3)
| | . |
| | . +-------> (x6) 2, 1
| | . X
+-------> 1---+ (x2) .
D | . Y
| . +-------> (x7) 1, 4
| . |
+-------> 2---+(x4) 5, 2
A |
+-------> (x8) 3, 4
X
This is an ascii-art version of an extensive-form game. The players are labeled 1 and 2, the nodes are labeled
x0, x1, and so on through x8, the strategies are U, D, A, B, X, and Y, and they are written by each branch. The
payoffs are listed at each leaf node. There is a dotted line for Player 2 connecting their move at x3 and x4.
Player 1 can choose U or D at x0, then A or B at x2. Player 2 does not know if they are at x3 or x4 (as
indicated by the dotted line), so they can choose only X or Y.
What are the subgame-perfect Nash equilibria for this game?
In your answer, be sure to complete the following tasks:
Explain why backward induction does not work for games of imperfect information.
Explain what a subgame is.
Explain why a subgame does not split up information sets.
Explain what a subgame-perfect Nash equilibrium is.
Explain the procedure for finding subgame-perfect Nash equilibria
Sample Solution