Assignment 2: Centipede Games and Symmetric.

2×2 Games

1. Solve the following centipede game. S stands for Stop and C stands for continue. There are two players, 1 and 2, and the player that chooses at each node

is indicated by number.

S S S S S S

1 C 2 C 1 C 2 C 1 C 2 C

1, 0 0, 2 3, 1 2, 4 5, 3 4, 6

6, 5

2. In the preceding game what do you think of the solution you found? Can you

think of anything to improve the result?

3. What is a centipede game? Why is a centipede game interesting?

4. Replace the Xs in the following centipede game with payoffs that will induce a solution at the 5th exit (Player 1 will choose S at the 5th leg of the

centipede).

S S S S S S

1 C 2 C 1 C 2 C 1 C 2 C

X, X X, X X, X X, X 5, 5 X, X

X, X

10 CONTENTS

5. Which of the symmetric, 2×2, strictly ordinal game interests you most? Why?

6. Choose any of the 7 non-boring symmetric games and create a payoff matrix

for it with values that differ from the standard 1, 2, 3, 4 used in Chapter 8 of

the most recent version of the text.

7. Sketch your values in payoff space.

8. By swapping values in your payoff matrix or sketch, convert the game to one

of its symmetric neighbours.

9. Make up a story to fit the payoffs you have developed.

10. Create a version that is not symmetric in terms of the actual payoffs but is still

ordinally symmetric.

11. Create a version that is not ordinally symmetric.

12. Sketch the game from the previous question in payoff space.

Assignment 2: Centipede Games and Symmetric.