Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Related questions
Question
![**Payoff Matrix Analysis for a Game with Players A and B**
The image depicts a payoff matrix for a game involving two players, A and B. The matrix shows the payoffs for each combination of strategies.
**Matrix Structure:**
- **Players:**
- Player A has two strategies: \(a_1\) and \(a_2\).
- Player B has two strategies: \(b_1\) and \(b_2\).
- **Payoff Combinations:**
- The payoff for each player is represented in the form \((x,y)\), where \(x\) is the payoff for Player A and \(y\) is the payoff for Player B.
**Payoff Matrix:**
\[
\begin{array}{c|c|c}
& b_1 & b_2 \\
\hline
a_1 & (2, 5) & (4, 2) \\
\hline
a_2 & (3, 4) & (1, 8) \\
\end{array}
\]
**Question:**
How many pure Nash equilibria does this game have?
- Options:
- 1
- 0
- 2
- 4
**Analysis:**
To determine the number of pure Nash equilibria, examine each strategy combination where neither player can unilaterally improve their payoff by changing their strategy.
- **Equilibrium Analysis:**
- \((a_1, b_1):\) Check if either player can benefit from switching strategies.
- \((a_1, b_2):\) Check value (4, 2).
- \((a_2, b_1):\) Check value (3, 4).
- \((a_2, b_2):\) Check value (1, 8).
After this evaluation, identify the Nash equilibria and count them accordingly.](https://content.bartleby.com/qna-images/question/88e84a40-2ab9-4b1b-97f3-40eaaaf2763c/84199985-bf86-47bf-94d4-c5ec304cf3cc/x340e4r_processed.jpeg)
Transcribed Image Text:**Payoff Matrix Analysis for a Game with Players A and B**
The image depicts a payoff matrix for a game involving two players, A and B. The matrix shows the payoffs for each combination of strategies.
**Matrix Structure:**
- **Players:**
- Player A has two strategies: \(a_1\) and \(a_2\).
- Player B has two strategies: \(b_1\) and \(b_2\).
- **Payoff Combinations:**
- The payoff for each player is represented in the form \((x,y)\), where \(x\) is the payoff for Player A and \(y\) is the payoff for Player B.
**Payoff Matrix:**
\[
\begin{array}{c|c|c}
& b_1 & b_2 \\
\hline
a_1 & (2, 5) & (4, 2) \\
\hline
a_2 & (3, 4) & (1, 8) \\
\end{array}
\]
**Question:**
How many pure Nash equilibria does this game have?
- Options:
- 1
- 0
- 2
- 4
**Analysis:**
To determine the number of pure Nash equilibria, examine each strategy combination where neither player can unilaterally improve their payoff by changing their strategy.
- **Equilibrium Analysis:**
- \((a_1, b_1):\) Check if either player can benefit from switching strategies.
- \((a_1, b_2):\) Check value (4, 2).
- \((a_2, b_1):\) Check value (3, 4).
- \((a_2, b_2):\) Check value (1, 8).
After this evaluation, identify the Nash equilibria and count them accordingly.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps
Knowledge Booster
Similar questions
- The biggest benefit of working for the Hamilton Manuf'g Co at Lowell was likely that: Group of answer choices eligible bachelors worked in the same factory the young men there earned valuable experience to make them better farmers the food was plentiful and delicious pay was steady and in casharrow_forwardWhat are the costs associated with downtime?arrow_forwardClarify or explain giving more details on what is meant by: 1.the risky-shift phenomenon 2.Evaluate the risky- shift phenomenon critically the likely standard of individual, compared with group or team performancearrow_forward
- Why can the group decision-making process be both efficient and effective? Please explain in detailarrow_forwardhow the heuristic and associated bias(es) play a part in an outcome. Explain how the biases could have been overcome to improve the decision.arrow_forwardIn a family business, the family's focus is on emphasizing all of the following EXCRPT Stability Cooperation Flexibility Unituarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Operations ManagementOperations ManagementISBN:9781259667473Author:William J StevensonPublisher:McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi...Operations ManagementISBN:9781259666100Author:F. Robert Jacobs, Richard B ChasePublisher:McGraw-Hill Education 
Purchasing and Supply Chain ManagementOperations ManagementISBN:9781285869681Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. PattersonPublisher:Cengage Learning
Production and Operations Analysis, Seventh Editi...Operations ManagementISBN:9781478623069Author:Steven Nahmias, Tava Lennon OlsenPublisher:Waveland Press, Inc.
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Operations Management
Operations Management
ISBN:9781259667473
Author:William J Stevenson
Publisher:McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi...
Operations Management
ISBN:9781259666100
Author:F. Robert Jacobs, Richard B Chase
Publisher:McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Cengage Learning
Production and Operations Analysis, Seventh Editi...
Operations Management
ISBN:9781478623069
Author:Steven Nahmias, Tava Lennon Olsen
Publisher:Waveland Press, Inc.