Question

2. Iterative Deletion of (weakly) Dominated Strategies Consider the following two-player game 2 I c I T 1,1 0,1 3,1 1 M 1,0 2,2 1,3 D 1,3 3,1 2,2 (a) Are there any strictly dominated strategies? Are there any weakly dominated strategies? If so, explain what dominates what and how. (b) After deleting any strictly or weakly dominated strategies, are there any strictly or weakly dominated strategies in the reduced' game? If so, explain what dominates what and how. What is left? (c) Go back to your argument for deleting in the first round and recall what dominated what and how. Compare this with what was deleted in the "second round. Comment on how this might make you a bit cautious when iteratively deleting weakly dominated strategies?

Answer 1

a)

Player 1)

Taking up the first player, the strategy M has been weakly dominated by strategy D. ( 1,3, 2) = > (1,2,1).

There is no strictly dominated strategy.

Player 2)

Similarly, strategy C has been weakly dominated by strategy r. Thus, strategy C must be deleted.

This is no strictly dominated strategy.

b)

The reduced form of Game:

	I	R
T	1,1	3,1
D	1,3	2,2

Player 1)

D has been weakly dominated by the T,

For player 2, Similarly R has been weakly dominated by the I. R must be deleted.

c)

In the first round, M was dominated by the D. But in second round D has been dominated by the T,

Similarly. for player 2. C was dominated by the R and in second round R was dominated by the I.

In both cases, less powerful strategy in first round tends to be more powerful in second round.

Equilibrium occurs when ( T,I)

We must exercise the full iterative process to reach a rational conclusion.