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Pay off table for oligopoly competition

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1. Alpha and Beta, two oligopoly rivals in a duopoly market, choose prices of their products on the first day of the month. The following payoff table shows their monthly payoffs resulting from the pricing decision they can make.

Alpha's price
High Low
High $200,$300 $50, $350

Beta's Price
Low $300,$150 $75, $200

a) Is the pricing decision facing Alpha and Beta a prisoners' dilemma? Why or why not?
b) What is the cooperative outcome? What is the non-cooperative outcome?
c) If Alpha and Beta make their pricing decision just one time, will they choose the cooperative outcome? Why or why not?
d) Can Alpha make a credible threat to punish Beta with a retaliatory price cut? Can Beta make a credible threat of a retaliatory price cut?
e) For each of the following events, explain whether Beta would be more or less likely to cooperate:
i. Beta expects to be able to cheat for more than two months before getting caught by Alpha.
ii. Alpha announces that it will match any price cut by Beta, and it will do so immediately following any price cut by Beta.
iii. Alpha hires a new CEO who has a reputation for relentlessly matching price cuts by rivals, even after rivals are ready to resume cooperative pricing.
iv. Alpha alters the design of its product to make it more desirable to some consumers than Beta's product.

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Solution Preview

We can find the dominant strategy by indicating each player's best move, given the other's, with (d):

Alpha's price
High Low
High $200,$300 $50, $350 (d)

Beta's Price
Low $300(d), $150 $75 (d), $200 (d)

Both players have the dominant strategy of pricing low.

A prisoner's dilemma occurs when each player's attempts to maximize his payoff, given the other player's choice, does not result in the maximum total payoff for both players. In this case, Beta and Alpha's best choices regardless of the other's choice is to price low. But, they are both better off pricing high. This is therefore a prisoner's dilemma.

If ...

Solution Summary

Pricing decisions and game theory in oligopoly