In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.

GAME 3

Player B

B1

B2

B3

Player A

A1

10, 12

8, 8

12, 10

A2

9, 3

7, 6

11, 8

A3

8, 10

9, 4

14, 5

In Game 3 above,

Question

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.

GAME 3
 
	
 
	
Player B
 
	
 
	
B1
	
B2
	
B3

Player A
	
A1
	
10, 12
	
8, 8
	
12, 10

A2
	
9, 3
	
7, 6
	
11, 8

A3
	
8, 10
	
9, 4
	
14, 5

In Game 3 above,

BlackTom AI · Accepted Answer

We start by restating the setup: in Game 3, payoffs are listed as (row player's payoff, column player's payoff). The matrix is:

- If A1 is played by Player A: against B1 -> (10, 12), against B2 -> (8, 8), against B3 -> (12, 10)
- If A2 is played: against B1 -> (9, 3), against B2 -> (7, 6), against B3 -> (11, 8)
- If A3 is played: against B1 -> (8, 10), against B2 -> (9, 4), against B3 -> (14, 5)

We examine whether either player has a dominant strategy, meaning a single action that yields the highest payoff regardless of the other player’s choice.

First, assess Player A (row player):
- Look at A1 across B1, B2, B3: payoffs for A are 10, 8, 12 respectively.
- Look at A2 across B1, B2, B3: payoffs for A are 9, 7, 11 respectively.
- Look at A3 across B1, B2, B3: payoffs for A are 8, 9, 14 respectively.
To have a dominant strategy, one row would need to give the highest payoff than the other rows for every column of B. Comparing column by column:
- For B1, A1 (10) is best among A1/A2/A3 (10 vs 9 vs 8).
- For B2, A3 (9) is best among the three (9 vs 8 vs 7).
- For B3, A3 (14) is best among the three (14 vs 12 vs 11).
Since no single row beats the others in all three columns (A1 wins at B1, but A3 wins at B2 and B3), Player A does not have a dominant strategy.

Next, assess Player B (column player):
- Consider B1 as a column: payoffs to B across A1/A2/A3 are 12, 3, 10 respectively.
- Consider B2 as a column: payoffs to B across A1/A2/A3 are 8, 6, 4 respectively.
- Consider B3 as a column: payoffs to B across A1/A2/A3 are 10, 8, 5 respectively.
For a dominant strategy for B, one column would need to yield the highest payoff for B regardless of A’s move. Checking each row of A:
- If A plays A1, B1 (12) is best among B1/B2/B3 (12 vs 8 vs 10).
- If A plays A2, B3 (8) is best among B1/B2/B3 (3 vs 6 vs 8).
- If A plays A3, B1 (10) is best among B1/B2/B3 (10 vs 4 vs 5).
There is no single column that is best for B across all three possible A moves (A1 favors B1, A2 favors B3, A3 favors B1). Therefore, Player B also does not have a dominant strategy.

Putting these observations together, neither player has a dominant strategy in Game 3.

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second. GAME 3 Player B B1 B2 B3 Player A A1 10, 12 8, 8 12, 10 A2 9, 3 7, 6 11, 8 A3 8, 10 9, 4 14, 5 In Game 3 above,单项选择题

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