ECS4862 Assignment 2 2025
Unique Number:
Due date: 17 June 2025
QUESTION 1
a.
i)
A dominant strategy is one that yields a higher payoff regardless of what the other player
does.
Purchaser:
Producer Strategy Buy (P1) Not Buy (P2)
High-Quality (Q1) 200 160
Low-Quality (Q2) 340 240
If the Producer chooses High-Quality, the Purchaser compares:
→ Buy (200) vs. Not Buy (160) → Buy is better.
If the Producer chooses Low-Quality, the Purchaser compares:
→ Buy (340) vs. Not Buy (240) → Buy is better.
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +27 81 278 3372
QUESTION 1
a.
i)
A dominant strategy is one that yields a higher payoff regardless of what the other
player does.
Purchaser:
Producer Strategy Buy (P1) Not Buy (P2)
High-Quality (Q1) 200 160
Low-Quality (Q2) 340 240
If the Producer chooses High-Quality, the Purchaser compares:
→ Buy (200) vs. Not Buy (160) → Buy is better.
If the Producer chooses Low-Quality, the Purchaser compares:
→ Buy (340) vs. Not Buy (240) → Buy is better.
Purchaser has a dominant strategy: Buy
Producer:
Purchaser Strategy High-Quality Low-Quality
Buy 160 80
Not Buy 280 200
If the Purchaser chooses Buy, Producer compares:
→ High-Quality (160) vs. Low-Quality (80) → High-Quality is better.
If the Purchaser chooses Not Buy, Producer compares:
→ High-Quality (280) vs. Low-Quality (200) → High-Quality is better.
Producer has a dominant strategy: High-Quality
, For additional support +27 81 278 3372
Both players have dominant strategies: Buy (Purchaser), Sell high-quality
(Producer).
ii)
A Nash equilibrium occurs when no player can improve their payoff by unilaterally
changing their strategy.
From (i), both players choose their dominant strategies:
Purchaser: Buy
Producer: Sell high-quality
Payoffs: (200 ; 160)
Check if either party has incentive to deviate:
If producer switches to low-quality → payoff becomes 80 < 160 ❌
If purchaser switches to not buying → payoff becomes 160 < 200 ❌
Yes, the game has a Nash equilibrium: (Buy, Sell high-quality goods) with
payoffs (200 ; 160). Neither player benefits from deviating.
iii)
This is not an example of a prisoner's dilemma. In a typical prisoner's dilemma,
players following their dominant strategies end up worse off. Here, both dominant
strategies lead to the best mutual outcome (200 ; 160), which avoids the dilemma
structure.
A prisoner’s dilemma arises when both players have incentives to choose strategies
that lead to a worse collective outcome, despite mutual cooperation being better.
In this game:
Mutual cooperation (Buy, Sell High-Quality) = (200 ; 160)
Unique Number:
Due date: 17 June 2025
QUESTION 1
a.
i)
A dominant strategy is one that yields a higher payoff regardless of what the other player
does.
Purchaser:
Producer Strategy Buy (P1) Not Buy (P2)
High-Quality (Q1) 200 160
Low-Quality (Q2) 340 240
If the Producer chooses High-Quality, the Purchaser compares:
→ Buy (200) vs. Not Buy (160) → Buy is better.
If the Producer chooses Low-Quality, the Purchaser compares:
→ Buy (340) vs. Not Buy (240) → Buy is better.
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +27 81 278 3372
QUESTION 1
a.
i)
A dominant strategy is one that yields a higher payoff regardless of what the other
player does.
Purchaser:
Producer Strategy Buy (P1) Not Buy (P2)
High-Quality (Q1) 200 160
Low-Quality (Q2) 340 240
If the Producer chooses High-Quality, the Purchaser compares:
→ Buy (200) vs. Not Buy (160) → Buy is better.
If the Producer chooses Low-Quality, the Purchaser compares:
→ Buy (340) vs. Not Buy (240) → Buy is better.
Purchaser has a dominant strategy: Buy
Producer:
Purchaser Strategy High-Quality Low-Quality
Buy 160 80
Not Buy 280 200
If the Purchaser chooses Buy, Producer compares:
→ High-Quality (160) vs. Low-Quality (80) → High-Quality is better.
If the Purchaser chooses Not Buy, Producer compares:
→ High-Quality (280) vs. Low-Quality (200) → High-Quality is better.
Producer has a dominant strategy: High-Quality
, For additional support +27 81 278 3372
Both players have dominant strategies: Buy (Purchaser), Sell high-quality
(Producer).
ii)
A Nash equilibrium occurs when no player can improve their payoff by unilaterally
changing their strategy.
From (i), both players choose their dominant strategies:
Purchaser: Buy
Producer: Sell high-quality
Payoffs: (200 ; 160)
Check if either party has incentive to deviate:
If producer switches to low-quality → payoff becomes 80 < 160 ❌
If purchaser switches to not buying → payoff becomes 160 < 200 ❌
Yes, the game has a Nash equilibrium: (Buy, Sell high-quality goods) with
payoffs (200 ; 160). Neither player benefits from deviating.
iii)
This is not an example of a prisoner's dilemma. In a typical prisoner's dilemma,
players following their dominant strategies end up worse off. Here, both dominant
strategies lead to the best mutual outcome (200 ; 160), which avoids the dilemma
structure.
A prisoner’s dilemma arises when both players have incentives to choose strategies
that lead to a worse collective outcome, despite mutual cooperation being better.
In this game:
Mutual cooperation (Buy, Sell High-Quality) = (200 ; 160)
