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.

ECON_104B_001_25S Chapter 14 Practice Problems -- Multiple-Choice

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,

View Explanation

Log in for full answers

Similar Questions

In a market with two firms, a firm that has a dominant strategy will do which of the following?

Question at position 31 Section 1: What is Walmart's dominant strategy? (none of the choices listed here)Price HighWalmart does not have dominant strategyPrice Low

Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the answers that are consistent with it. (multiple correct answers may be possible)

Table 17-8This table shows the payoffs for a game played between two players, A and B.Refer to Table 17-8. Which of the following statements regarding this game is true?

Consider the following game. Terry and Kerry are roommates who must make decisions about cleaning simultaneously. Terry’s payoff is the first number in each cell and a higher number is a better outcome: Kerry Clean Don’t clean Terry Clean ( 8, 2 ) ( 3, 5 ) Don’t clean ( 10, 3 ) ( 4, 1 )

Two companies, Acme and Pinnacle, each decide whether to produce a good-quality product or a poor-quality product. In the figure, the dollar amounts are payoffs, and they represent annual profits (in millions of dollars) for the two companies. The dominant strategy for Acme is to

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler