Download Oligoplies and Game Theory

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ECON 201
Oligopolies & Game Theory
An Economic Application of Game
Theory: the Kinked-Demand Curve
• Above the kink, demand is relatively elastic because all other firm’s
prices remain unchanged. Below the kink, demand is relatively
inelastic because all other firms will introduce a similar price cut,
eventually leading to a price war. Therefore, the best option for the
oligopolist is to produce at point E which is the equilibrium point
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Figure 12.4 Duopoly Equilibrium in a
Centralized Cartel
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Duopoly
• What are the strategic options and the payoffs?
• Form a cartel
• Forego additional profits from increasing output beyond assigned
quota
• Stable prices – don’t ever change (kinked demand curve)
• Cheat on the Cartel
• Increase production unilaterally (output effect)
• If only you increase output, price doesn’t fall too much (price effect)
• Hope competitor doesn’t change strategy
• Compete on price
• Final equilibrium moves towards competitive market price
• No monopoly rents (or + economic profits)
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Game Theory
• Game theory is a methodology that can be used to
analyze both cooperative and non-cooperative
oligopolies.
• Recognizes the interdependence of the firms’ actions
• Using a payoff matrix to describe options (strategies) and
payoffs
• Firms are profit maximizers!
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Jack and Jill’s Oligopoly Game
Jack’s decision
High production: 20M
Barrels
Jack gets
$1,600 profit
High
production:
Jill’s
Decision
13M
Barrels
Low
production:
7M Barrels
Low production: 13M
Barrels
Jill gets
$1,600 profit
Jack gets
$1,500 profit
Jill gets
$2,000 profit
Jack gets
$2,000 profit
Jill gets
$1,500 profit
Jack gets
$1,800 profit
Jill gets
$1,800 profit
In this game between Jack and Jill, the profit that each earns from selling oil
depends on both the quantity he or she chooses to sell and the quantity the other
chooses to sell.
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Nash Equilibrium
• Nash Equilibrium
– An economic decision maker has nothing to gain by
changing its own strategy without collusion
– Nobody wants to change their strategy given that the
other firm does not change their strategy
– A “stable” outcome where nobody wants to move from
their current position
– Often discussed with game theory, and easier to see
when games are drawn in matrix form
Nash Equilibrium
• If firm facing kinked demand curve tries to
raise price:
– Other firms do not
– As demand is highly elastic and other firms
are “close” substitutes
– Loses market share and revenues
• If firm lowers price
– Competitors match price decreases
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An Economic Application of Game
Theory: the Kinked-Demand Curve
• Above the kink, demand is relatively elastic because all other firm’s prices
remain unchanged. Below the kink, demand is relatively inelastic because
all other firms will introduce a similar price cut, eventually leading to a
price war. Therefore, the best option for the oligopolist is to produce at
point E which is the equilibrium point
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Figure 12.7 Xbox and
PlayStation
Dominant Strategy
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Nash Equilibrium
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Nash equilibrium
a solution to a non-cooperative game involving two or more players
• each player is assumed to know the equilibrium strategies of the other
players
• no player has anything to gain by changing only his own strategy
unilaterally
Hence, a Nash equilibrium will be stable (once you get there!)
A Dominant Strategy is one type of a Nash equilibrium – (a) no player has
any incentive to change – BUT (b) does not require collusion
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Determining the Dominate Strategy
(Single Nash)
• A dominant strategy occurs when one strategy is best for
a player regardless of the rival’s actions. (rival’s actions
don’t matter)
• Dominant strategy equilibrium—neither player has reason to
change their actions because they are pursuing the strategy that is
optimal under all circumstances.
• Here the dominant strategy is for each firm to advertise (it
is also a Nash Equilibrium)
• BUT there is no incentive for the firms to collude – hence
no Anti-trust violation! (at least on the cooperation side;
maybe still on anti-competitive pricing)
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Figure 12.7 Xbox and
PlayStation
Dominant Strategy
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Multiple Equilibria
• Sometimes there are come cases where there
are multiple Nash equilibria.
• In this case, the outcome is uncertain.
• Firms will have an incentive to collude.
• An example:
• Sony/Microsoft can add one of two new features
• One feature appeals only to YOUTH market
• Other feature appeals only to TEEN market
• Incentive to reach agreement on both firms offering the same
new (one only) feature
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Payoff Table
Multiple Nash Equilibria
Requires collusion – agree no to compete in each other’s market
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Prisoner's Dilemma
• A prisoner’s dilemma occurs when the dominant strategy
leads all players to an undesired outcome.
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Figure 12.9 Prisoners’ Dilemma
Optimal - each would prefer to serve minimal time.
Each has to “not confess”
But: if one does remains silent and the other does
confess -> not optimal. Hence each will choose to
confess -> sub-optimal
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Best Outcome
• Neither confesses
• But without collusion/agreement – how do you guarantee this
outcome?
• Enforcement issues (price, output, quotas)
• In our duopoly game:
• Each firm pursues “cheating” (here confessing) as can’t rely on other
firm not to cheat
• Supoptimal (from firm’s perspective) -> competitive equilibria
• Law & Order
• Why we keep suspects separated!
• Prevent collusive agreements
• In Economics – wiretaps, e-mail and Sherman Anti-trust Act
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An Economic Application of Game Theory: the
Kinked-Demand Curve:
Prisoner’s dilemma (sub-optimal)
• Above the kink, demand is relatively elastic because all other firm’s
prices remain unchanged. Below the kink, demand is relatively
inelastic because all other firms will introduce a similar price cut,
eventually leading to a price war. Therefore, the best option for the
oligopolist is to produce at point E which is the equilibrium point
Prisoner’s
Dilemma
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Nash Equilibrium
• If firm facing kinked demand curve tries to raise price:
• Other firms do not
• As demand is highly elastic and other firms are “close” substitutes
• Loses market share and revenues
• If firm lowers price
• Competitors match price decreases
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Game Theory: Kinked Demand Curve
and Nash Equilibrium
Firm B
(Competitor)
Firm A
(You)
Raise Price
Don’t Change
Lower Price
(-5%)
(-1%->+5%)
(-2%->+1%)
Raise Price
(A) -5%
(A) -5%
(A)-5%
(-5%)
(B) -5%
(B) +5%
(B)+1%
Don’t Change
(A) +5%
(A) 0
(A)-1%
(-1%->+5%)
(B) -5%
(B) 0
(B)+1%
Lower Price
(A) +1%
(A)+1%
(A) -2%
(-2%->+1%)
(B) -5%
(B) -1%
(B) -2%
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Features of a
Nash Equilibrium
• In a non-cooperative oligopoly, each firm has little
incentive to change price.
• This represents a Nash Equilibrium, where each firm’s
pricing strategy remains constant given the pricing
strategy of the other firms.
• Firms have no incentive to change
their strategy.
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Non-Cooperative Cartels
Either
• Some degree of price competition
• Firms engage in highly competitive pricing
• Similar outcome as perfect competition
• Firms have some market power
• Resembles monopolistic competition
• Bilateral monopoly with price competition
• or Stable prices prevail
• Non-collusive
• Firms choose not to compete because of kinked
demand curve
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Non-cooperative Oligopolies
• Competitive/psuedo-competitive behavior (non-
cooperative)
• Perfect Competition (almost): firms undercut each
other’s prices
• competition between sellers is fierce, with relatively low prices
and high production
• Outcome may be similar to PC or Monopolistic Competition
• Nash equilibrium
• Firms avoid “ruinous” price competition by keeping prices stable
and avoiding price competition (undercutting each others prices)
• May lead to product proliferation and/or extensive advertising
(non-price competition)
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U.S. 2003 Advertising-to-Sales Ratio for
Selected Products and Industries
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Game Theory Models
of Oligoploy
• Stackelberg's duopoly. In this model the firms move
sequentially (see Stackelberg competition).
• Cournot's duopoly. In this model the firms simultaneously
choose quantities (see Cournot competition).
• Bertrand's oligopoly. In this model the firms
simultaneously choose prices (see Bertrand competition).
• Monopolistic competition. A market structure in which
several or many sellers each produce similar, but slightly
differentiated products. Each producer can set its price
and quantity without affecting the marketplace as a whole.