ECON 201
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OLIGOPOLIES & GAME THEORY
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EQUILIBRIUM IN A
CENTRALIZED
CARTEL
DUOPOLY
What are the strategic options and the
payoffs?
• Form a cartel
• Forego additional profits from increasing output beyond
assigned quota
• Cheat on the Cartel
• Increase production unilaterally (output effect)
• If only you increase output, price doesn’t fall too much (price effect)
• Compete on price
• Final equilibrium moves towards competitive market price
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• No monopoly rents (or + economic profits)
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
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• Firms are profit maximizers!
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FIGURE 12.7 XBOX
AND PLAYSTATION
DOMINANT STRATEGY
NASH EQUILIBRIUM
•
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
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Hence, a Nash equilibrium will be stable (once you get there!)
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)
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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
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
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• 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
PAYOFF TABLE
MULTIPLE NASH
EQUILIBRIA
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Requires collusion – agree no to compete in each other’s market
PRISONER'S DILEMMA
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A prisoner’s dilemma occurs when the dominant strategy
leads all players to an undesired outcome.
FIGURE 12.9
PRISONERS’ DILEMMA
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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Optimal - each would prefer to serve minimal time.
Each has to “not confess”
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
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• Why we keep suspects separated!
• Prevent collusive agreements
• In Economics – wiretaps, e-mail and Sherman Antitrust Act
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
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Prisoner’s
Dilemma
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
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• Competitors match price decreases
GAME THEORY: KINKED
DEMAND CURVE AND
NASH EQUILIBRIUM
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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Firm B
(Competitor)
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.
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• Firms have no incentive to change
their strategy.
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
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• Non-collusive
• Firms choose not to compete because of kinked
demand curve
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
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• 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
GAME THEORY
MODELS
OF OLIGOPLOY
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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.