ECS4862 Semester 1 2025 Assignment 2

ECS4862
ASSIGNMENT 2 2025

UNIQUE NO.
DUE DATE: 17 JUNE 2025

,ALTERNATIVELY;

ECS4862 – ASSIGNMENT 02 SOLUTIONS

Due Date: 17 June 2025
Total Marks: 85

QUESTION 1

(a) Game Theory Problem

Payoff Matrix (Producer ; Purchaser)


Sell High-Quality Sell Low-Quality

Buy (200 ; 160) (340 ; 80)

Not Buy (160 ; 280) (240 ; 200)




i) Dominant Strategies (4)

 A dominant strategy is one that yields a higher payoff for a player regardless of
what the other player does.

Producer:

 If Purchaser buys:
o High quality: 200
o Low quality: 340 → prefers low
 If Purchaser does not buy:
o High quality: 160
o Low quality: 240 → prefers low
✅ Low quality dominates

, Purchaser:

 If Producer sells high quality:
o Buy: 160
o Not buy: 280 → prefers not to buy
 If Producer sells low quality:
o Buy: 80
o Not buy: 200 → prefers not to buy
✅ Not to buy dominates


✔️ Answer:
Yes, both players have dominant strategies:

 Producer: Sell low-quality goods
 Purchaser: Not buy




ii) Nash Equilibrium (4)

A Nash equilibrium is a situation where no player has anything to gain by changing
only their own strategy.

From dominant strategies:

 Producer → Low quality
 Purchaser → Not buy
→ Outcome: (240 ; 200)


✔️ Answer:
✅ Yes, the Nash equilibrium is:
Producer sells low-quality, Purchaser does not buy → Payoffs (240 ; 200)