# Assignment 2: Centipede Games and Symmetric.

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
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.