Problem Set 1
Ben Polak, Econ 159a/MGT522a. Four Questions due September 19, 2007.
1. Strictly and Weakly Dominated Strategies? What is the de nition of a strictly dominated strategy? What is the de nition of a weakly dominated strategy? Give an example of a two-player game matrix where one player has three strategies, one of which is strictly dominated; and the other player has three strategies, one of which is weakly (but not strictly) dominated. Indicate the dominated strategies. 2. Iterative Deletion of (weakly) Dominated two-player game 2 l c T 1; 1 0; 1 1 M 1; 0 2; 2 D 1; 3 3; 1 Strategies Consider the following r 3; 1 1; 3 2; 2
(a) Are there any strictly dominated strategies? Are there any weakly dominated strategies? If so,
…show more content…
Thus, for example, u1 (8; 8; 8) = _ _ 33:3 and u1 (7; 9; 9) = 73:3. Is strategy 1 dominated, strictly or weakly, by strategy 2. How about by strategy 3? Explain. Suppose we delete strategies 1 and 10. That is, we rule out the possibility of any candidate choosing either 1 or 10, although there are still voters at those positions. Is strategy 2 dominated, strictly or weakly, by any other (pure) strategy si in the reduced game? Explain. 4. \Strength can be weakness". A three-person committee has to choose a winner for a national art prize. After some debate, there are three candidates still under consideration: a woman who draws antelope in urban settings, a man who makes rectangular lead boxes, and a woman who sculpts charcoal. Lets call these candidates a, b and c; and call the committee members 1,2 and 3. The preferences of the committee members are as follows: member 1 prefers a to b and b to c; member 2 prefers c to a and a to b; and member 3 prefers b to c and c to a. The rules of the competition say that, if they disagree, they should vote (secret ballot, one member one vote) and that, if and only if the vote is tied, the winner will be the candidate for whom member 1 voted. Thus, it might seem that member 1 has an advantage. (a) Consider this voting game. Each voter has three strategies: a, b, or c. For each voter, which strategies are weakly or strictly dominated? [Hints.