Question

1. Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure:

                                First, Max eliminates one of three choices.

Then, Sally decides among the two remaining choices.

Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining).

1. Write down the extensive form (game tree) to represent this game.

2. If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be?

Answer 1

Let us analyse the situation with all three choices:

1) Suppose Max eliminates A, then the remaining choices are B and C. Sally prefers B over C and hence the final choice is B.

2) Suppose Max eliminates B, then the remaining choices are A and C. Sally prefers A over C and hence the final choice is A.

3) Suppose Max eliminates C, then the remaining choices are A and B. Sally prefers B over A and hence the final choice is B.

Now Max is only concerned about the final result, and Max prefers A over B. Hence the decision Max chooses is the eliminate B and get the final choice as A, which he prefers over B.

a)

The extensive form of the game is as follows: (the thick lines represent the decision Sally takes)

b)

If Max acts non-strategically and makes a decision to eliminate his least desirable choice of C, then Sally chooses between A and B and since she prefers B over A, the final choice made is B.