Question

Perform IDSDS on the game below Player 2 Player 1 0, 4 2, 2 0, 2 1, 2 3, 0 Which strategy profile(s) survive IDSDS? А.а.x C. a,z D.b.x E. b.y F. b,z G. C,X H. C.y L. C,Z

Answer 1

Solution:

Correct answer: E) b,y

IDSDS is Iterated Deletion of Strictly Dominated Strategies. Strictly dominated strategies are the strategies which a player never chooses under any circumstance. This means that, given another player's strategy, a player always has a better strategy to choose (one which gives a higher payoff), thus, the strategies which are strictly dominated are deleted (since, they will never be chosen).

			PLAYER 2
		x	y	z
	a	1, 3	1, 1	0, 4
PLAYER 1	b	3, 1	2, 2	1, 0
	c	0, 2	1, 2	3, 0

Strategy profile(s) surviving IDSDS is(are) the ones which stays till the end, that is, the one which doesn't get deleted. So, we proceed as follows:

If player 2 chooses strategy x, best response of player 1 would be to choose strategy b (since, 3 > 1(from a)and 3 > 0(from c)). If player 2 chooses strategy y, best response of player 1 would be again, to choose strategy b (since, 2 > 1(from a)and 2 > 1(from c)). Similarly, if player 2 chooses strategy z, best response of player 1 would be to choose strategy c (since, 3 > 0(from a)and 3 > 1(from b)). Notice, that whatever strategy player 2 chooses, player 1 chooses either strategy b or c, thus, strategy a is never chosen. Hence, deleting this strictly dominated strategy. So, our payoff matrix reduces to:

			PLAYER 2
		x	y	z
PLAYER 1	b	3, 1	2, 2	1, 0
	c	0, 2	1, 2	3, 0

Now, if player 1 chooses strategy b, best response of player 2 would be to choose strategy y (since, y gives the highest payoff comparatively: 2 > 1(from x) and 2 > 0(from z)). If player 1 chooses strategy c, best response of player 2 would be to choose strategy x or y (since, both gives the highest (and equal) payoff comparatively: 2 > 0(from z)). In this case, player 2 never chooses strategy z, thus this is deleted/eliminated. Our payoff matrix reduces to:

		PLAYER 2
		x	y
PLAYER 1	b	3, 1	2, 2
	c	0, 2	1, 2

Further, if player 2 chooses strategy x, best response of player 1 would be to choose strategy b (since, this gives highest payoff comparatively: 3 > 0(from c)). Similarly, if player 2 chooses strategy y, best response of player 1 would be to choose strategy b (since, 2 > 1(from c)). Thus, eliminating strategy c, since it is never chosen. Further, reducing the payoff matrix we get:

		PLAYER 2
		x	y
PLAYER 1	b	3, 1	2, 2

Finally, if player 1 chooses strategy b, best response of player 2 would be to choose strategy y (since, y gives the highest payoff comparatively: 2 > 1(from x)). So, we lastly eliminate strategy x. So, we remain with:

		PLAYER 2
		y
PLAYER 1	b	2, 2

So, finally the strategy profile remaining is strategy b for player 1 and strategy y for player 2.

Thus, the only strategy profile surviving IDSDS is E. (b,y). (so, the chosen option is the correct one).