Question

Consider the following game.

		Player 2
		E		F	G	H
Player 1	A	2,0		4,2	3,1	-1,1
	B	1,1		1,0	2,0	4,2
	C	2,0		3,5	4,4	0,1
	D	1,-1		2,2	1,0	-1,1

Solve this one-shot simultaneous move game using the Iterated Deletion of Strictly Dominated Strategies.

Group of answer choices

(C,G)

This game is not solvable using IDSD

(D,F)

(C,F)

None of the other options

Answer 1

Using the iterated deletion of strictly dominated strategies, we will compare two strategies of a player at a time and find the strictly dominated strategy and remove the other one from the game and keep following the same method until we find one strategy that is not deleted.

For player 1, look at strategy C and D. C strictly dominates D, since the payoff that player 1 gets from playing C is always greater than playing D, no matter what player 2 plays. Hence we eliminate Row D from the game.

We are left with the following game .

PLAYER 1		PLAYER 2
		E	F	G	H
	A	2,0	4,2	3,1	-1,1
	B	1,1	1,0	2,0	4,2
	C	2,0	3,5	4,4	0,1

If we consider strategy E and H for player 2, we see that strategy H strictly dominates strategy E as the payoff from strategy H is always greater than from strategy E. So we will delete column E i.e strategy E for player 2.

We are left with the following table.

PLAYER 1		PLAYER 2
		F	G	H
	A	4,2	3,1	-1,1
	B	1,0	2,0	4,2
	C	3,5	4,4	0,1

Now we can see there is no strictly dominant strategy with any player. For instance, if player 1 plays A, player 2 plays F, but if player 1 plays B, player 2 no longer prefers F, but prefers playing H. Similarly if player 2 plays G, player 1 plays C, but if player 2 plays H, player 1 no longer prefers playing C but will play B. So none of the players have a strictly dominated strategy. We conclude that

This game is not solvable using Iterated Deletion of Strictly dominant strategy.