ECS4862
Assignment 2 2025
Unique #:
Due Date: 17 June 2025
Detailed solutions, explanations, workings
and references.
+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
Both players have dominant strategies: Buy (Purchaser), Sell high-quality
(Producer).
Varsity Cube 2025 +27 81 278 3372
, 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)
If both deviate (Buy, Sell Low) = (340 ; 80):
o Purchaser gets better payoff (340), but Producer worse (80)
No mutual incentive to defect and end up worse off.
Varsity Cube 2025 +27 81 278 3372
Assignment 2 2025
Unique #:
Due Date: 17 June 2025
Detailed solutions, explanations, workings
and references.
+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
Both players have dominant strategies: Buy (Purchaser), Sell high-quality
(Producer).
Varsity Cube 2025 +27 81 278 3372
, 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)
If both deviate (Buy, Sell Low) = (340 ; 80):
o Purchaser gets better payoff (340), but Producer worse (80)
No mutual incentive to defect and end up worse off.
Varsity Cube 2025 +27 81 278 3372
