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Wize University Microeconomics Textbook > Oligopoly

Game Theory and Nash Equilibrium

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Oligopoly and Game Theory

  • Oligopoly - A market in which only a few sellers offer similar products Examples:
  • Credit card companies: MasterCard, Visa, American Express.
  • Aircraft manufacturer: Boeing and Airbus

  • Duopoly - An oligopoly that consists of only two firms that dominate the market Example: Apple and Android dominate the smartphone market.
  • Game Theory – A game in which there are players (firms) and payoffs (profits). It studies how people behave in strategic situations and can be seen in a payoff matrix like the one below. The outcomes are interdependent (which means profit for one company depends on what the other company does)
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Dominant Strategy

A dominant strategy is your best strategy no matter what the other firm (player) does. The firm does not necessarily have a dominant strategy. Dominant Strategy for Wize
  • In the diagram above, the payoffs (profits) for Wize are the numbers in red.
  • If XYZ does a promotion then Wize should do
    a promotion
    because they would make
    $10
    instead of
    $5
    .
  • If XYZ does no promotion then Wize should do
    a promotion
    because they would make
    $25
    instead of
    $20
    .
  • No matter what XYZ does it is better for Wize to do a promotion therefore doing a promotion is Wize's dominant strategy.

Dominant Strategy for XYZ
  • In the diagram above, the payoffs (profits) for XYZ are the numbers in green.
  • If Wize does a promotion then XYZ should do
    a promotion
    because they would make
    $10
    instead of
    $5
    .
  • If Wize does no promotion then XYZ should do
    a promotion
    because they would make
    $25
    instead of
    $20
    .
  • No matter what Wize does it is better for XYZ to do a promotion therefore doing a promotion is XYZ's dominant strategy.
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Nash Equilibrium

The Nash equilibrium is a sustainable point where neither player has an incentive to cheat (change their strategy).
  • In the diagram above, this would occur when both firms are doing
    a promotion
    with a payoff of
    $10
    each.
  • If we are in the top left box and Wize decides to cheat (change their strategy) and do no promotion, their profit would drop to
    $5
    .
  • If we are in the top left box and XYZ decides to cheat and do no promotion, their profit would drop to
    $5
    .
  • Neither player has an incentive to cheat that is why it is the Nash equilibrium

Collusion

The outcome with collusion is also called the mutually beneficial outcome or the outcome with commitment or a cartel.
  • In the diagram above, the outcome with collusion would be where both firms are doing
    no promotion
    with a payoff of
    $20
    each.
  • However, this point is not sustainable because there is an incentive to
    cheat
    .




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Example: Oligopoly and Game Theory

The diagram above shows the payoff matrix for Wizedemy and ABC Inc showing their profits based on whether they spend on advertising or not.

a) Does ABC Inc have a dominant strategy? If yes, what is it?

Yes, ABC's dominant strategy is to advertise because no matter what Wizedemy does, ABC makes more profit when they advertise (160>150 and 130>125)

b) Does Wizedemy have a dominant strategy? If yes, what is it?

No. If ABC does no advertising then its better for Wizedemy to not advterise (140>130) but if ABC advertises it is better for Wizedemy to advertise (120>110). Since the strategy changes it means Wizedemy does not have a dominant strategy.

c) What is the Nash equilibrium? What are their total combined profits at Nash equilbrium?

They both advertise and make profits of (120, 130). The combined profits are 120 + 130 = $250.

d) Do the two firms have a reason to collude? If yes, what would be the combined profits at this outcome?

Yes, compared to the Nash equilibrium they are both better off doing no advertising and making profits of (140, 150). Their combined profits would be 140 + 150 = $290

Practice: Oligopoly and Game Theory

Which of the following statements is true about the Nash equilibrium?
Extra Practice
Game Theory
Suppose the Canadian live-sports broadcasting industry is a duopoly consisting of TSN and SportsNet. The broadcast rights for NHL games is coming up and both firms must decide how much to bid for NHL broadcasting rights. Each network can submit low-bid or high-bid for the rights. The revenues (in millions) are summarized below.
Practice Question: Game Theory 3
If firms in an oligopoly market are in a Nash equilibrium,
a) Firms will not take into account the strategies of competing firms.
b) Each firm will have its own market price
The main feature of an oligopolistic market is that:
Consider the following game
Two firms, Appl Inc. and Samsoo Inc. can choose to keep price at $800 per smartphone or charge less to capture a larger share of the market.
Their market shares (payoffs) are listed in both cases
Which of the following is incorrect about oligopoly?
Practice Question: Game Theory
Two firms in a duopoly are trying to decide if they should form a cartel by limiting output so that each can charge a high price along their demand curve and thereby increase their profits. The following payoff matrix shows their payoffs in millions when they cooperate (CO) and when they don’t cooperate.
Practice Question: Game Theory - Two Nash Equilibria
Numbers listed in the table are payoffs.
Consider the following game
Two firms, Appl Inc. and Samsoo Inc. can choose to keep price at $800 per smartphone or charge less to capture a larger share of the market.
Their market shares (payoffs) are listed in both cases