Suppose a market has two firms, each of which has 2 strategies—high price or low
ID: 1120590 • Letter: S
Question
Suppose a market has two firms, each of which has 2 strategies—high price or low price. If
they both collude to keep price high, they can each earn $900. If they both compete on price
and charge low prices, they will each only earn $300. If one firm chooses to charge high
price and one a low price, the firm charging the high price will lose most of its customers to the low
price firm and will earn only $200.
a) Draw the payoff matrix for this oligopoly game, showing the players, strategies and payoffs. In
doing so, determine a value for the payoff to the “unilaterally defecting” firm (the one that charges a
lower price and steals most of the customers) that will make this game a prisoners’ dilemma. What
is the Nash equilibrium?
b) Explain fully how the structure of the payoffs makes this a dilemma.
Explanation / Answer
A) Matrix is shown below
Firm B
Firm A
High
Low
High
(900, 900)
(200, 1300)
Low
(1300, 200)
(300, 300)
Both firms have a dominant strategy of charging a low price and this is the Nash equilibrium. Now this is a Prisoner's dilemma game because a higher collusive outcome of 900 is not chosen
b)
Prisoners Dilemma has a Nash equilibrium where both prisoners have a dominant strategy to confess that does not minimizes (because payoffs are sentences for imprisonment) collective payoff. Both prisoners can choose a cooperative action of not to confess and get a lower terms for sentence but they choose a non-cooperative action as they cannot communicate/cooperate. The dilemma is about self-interest and collective interest. So they choose a lower payoff outcome
Here we can find the similar situation faced by A and B. A and B can earn a higher profit by charging a high price. But such collusion is not stable as an even higher one period profit is availble when any ofthe firm defects. Hence they end up in achieving a lower outcome at 300, 300.
Firm B
Firm A
High
Low
High
(900, 900)
(200, 1300)
Low
(1300, 200)
(300, 300)
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