,ECS4862 Assignment 2 (COMPLETE ANSWERS)
Semester 1 2025 - DUE 17 June 2025; 100% TRUSTED
Complete, trusted solutions and explanations.
QUESTION 1
(a) Suppose there are only two firms in a fast-moving consumer goods market.
The producer is deciding whether to sell high-quality or low-quality products. The
purchaser has two options either to buy or not buy. The annual profits associated
with each strategy are given in the table below:
Game Theory: Producer and Purchaser Decision
Producer \ Purchaser Buy Not Buy
High-Quality Goods (200 ; 160) (160 ; 280)
Low-Quality Goods (340 ; 80) (240 ; 200)
i) Determine whether either player has a dominant strategy. Explain. (4)
A dominant strategy is one that gives a player a higher payoff regardless of what the
other player does.
For the Purchaser:
If the producer sells high-quality:
o Buy = 160, Not Buy = 280 → Not Buy preferred
If the producer sells low-quality:
o Buy = 80, Not Buy = 200 → Not Buy preferred
→ Not Buy is a dominant strategy for the Purchaser
For the Producer:
If Purchaser Buys:
o High-Quality = 200, Low-Quality = 340 → Low-Quality preferred
If Purchaser Does Not Buy:
o High-Quality = 160, Low-Quality = 240 → Low-Quality preferred
→ Low-Quality is a dominant strategy for the Producer
✅Both players have dominant strategies
, ii) Determine whether there is a Nash equilibrium in this game. If so, what is it? If
not, explain. (4)
A Nash equilibrium occurs when both players choose strategies where no one has
an incentive to deviate.
From part (i), dominant strategies lead to:
Producer chooses Low-Quality
Purchaser chooses Not Buy
Payoff: (240 ; 200)
✅This is the Nash equilibrium since neither can improve their payoff by
changing strategies alone.
iii) Explain the concept of prisoner dilemma in game theory. Is this game an
example of the prisoners’ dilemma? Explain. (5)
The prisoner’s dilemma is a situation where individually rational strategies
lead to a worse collective outcome.
If both players cooperated (Producer sells high-quality and Purchaser buys),
payoff = (200 ; 160), better than the Nash equilibrium (240 ; 200 for
producer and 200 for purchaser).
However, both pursue self-interest:
o Producer cheats for higher gain (sells low-quality),
o Purchaser anticipates this and avoids buying.
✅Yes, this is a Prisoner's Dilemma — mutual cooperation gives better
outcomes, but dominant strategies drive them to a worse equilibrium.
iv) Assuming a sequential-move game in which the Purchaser chooses the
strategy first, determine the pure Nash equilibrium of this game. (4)
This is solved by backward induction.
Semester 1 2025 - DUE 17 June 2025; 100% TRUSTED
Complete, trusted solutions and explanations.
QUESTION 1
(a) Suppose there are only two firms in a fast-moving consumer goods market.
The producer is deciding whether to sell high-quality or low-quality products. The
purchaser has two options either to buy or not buy. The annual profits associated
with each strategy are given in the table below:
Game Theory: Producer and Purchaser Decision
Producer \ Purchaser Buy Not Buy
High-Quality Goods (200 ; 160) (160 ; 280)
Low-Quality Goods (340 ; 80) (240 ; 200)
i) Determine whether either player has a dominant strategy. Explain. (4)
A dominant strategy is one that gives a player a higher payoff regardless of what the
other player does.
For the Purchaser:
If the producer sells high-quality:
o Buy = 160, Not Buy = 280 → Not Buy preferred
If the producer sells low-quality:
o Buy = 80, Not Buy = 200 → Not Buy preferred
→ Not Buy is a dominant strategy for the Purchaser
For the Producer:
If Purchaser Buys:
o High-Quality = 200, Low-Quality = 340 → Low-Quality preferred
If Purchaser Does Not Buy:
o High-Quality = 160, Low-Quality = 240 → Low-Quality preferred
→ Low-Quality is a dominant strategy for the Producer
✅Both players have dominant strategies
, ii) Determine whether there is a Nash equilibrium in this game. If so, what is it? If
not, explain. (4)
A Nash equilibrium occurs when both players choose strategies where no one has
an incentive to deviate.
From part (i), dominant strategies lead to:
Producer chooses Low-Quality
Purchaser chooses Not Buy
Payoff: (240 ; 200)
✅This is the Nash equilibrium since neither can improve their payoff by
changing strategies alone.
iii) Explain the concept of prisoner dilemma in game theory. Is this game an
example of the prisoners’ dilemma? Explain. (5)
The prisoner’s dilemma is a situation where individually rational strategies
lead to a worse collective outcome.
If both players cooperated (Producer sells high-quality and Purchaser buys),
payoff = (200 ; 160), better than the Nash equilibrium (240 ; 200 for
producer and 200 for purchaser).
However, both pursue self-interest:
o Producer cheats for higher gain (sells low-quality),
o Purchaser anticipates this and avoids buying.
✅Yes, this is a Prisoner's Dilemma — mutual cooperation gives better
outcomes, but dominant strategies drive them to a worse equilibrium.
iv) Assuming a sequential-move game in which the Purchaser chooses the
strategy first, determine the pure Nash equilibrium of this game. (4)
This is solved by backward induction.
