MBA201a: The Bertrand Trap
Recap of the “Bertrand trap”
– Even with two firms, price is driven down to the competitive
price (marginal cost).
• Economic profits are zero,
• Accounting profits could be negative if there are sunk
costs.
– Note that neither higher demand nor lower costs (if both
firms have the same cost) increase profits.
– Examples: fiber-optic cable, railroad grain rates.
– First piece of advice: Avoid this game if you can!
Professor Wolfram
MBA201a - Fall 2009
Page 1
Avoiding the Bertrand trap
Option 1: Be the cost leader.
P1
MC2
45°
BR2
BR1
P* = c2 - ε
MC1
P2
Remember: cost advantage must be sustainable.
Professor Wolfram
MBA201a - Fall 2009
Page 2
Additional ways to avoid the Bertrand trap
– Option 2: Limit capacity
• In the example we did on the board, imagine that the two
firms each had maximum capacity of 20.
– Option 3: Product differentiation and branding (moderates
impact of price competition)
• Create switching costs
– Option 4: Collude
• This is illegal in the U.S. and many other countries, more
on that later.
Professor Wolfram
MBA201a - Fall 2009
Page 3
Option 5: leverage repeated interactions
– If firms interact repeatedly, they can use the future as source
of leverage: threaten to punish rival if it behaves noncooperatively.
– Topsy-turvy principle: if price wars lead to a really bad
situation, it is easier to deter non-cooperative behavior!
– This is called tacit collusion.
Professor Wolfram
MBA201a - Fall 2009
Page 4
The repeated Bertrand price game
– In the Bertrand price game, we contrasted
• The “cooperative” outcome: set the monopoly price, split
the market, and make M/2 (M = monopoly profits).
• The Nash equilibrium: price at MC, make zero.
– Claim: in the repeated game, the cooperative outcome (set
the monopoly price) can be a Nash equilibrium.
– Equilibrium strategies:
• If all firms have set the monopoly price in the past, stick
to it.
• If one firm ever sets price different from monopoly price,
revert to pricing at marginal cost forever. (This
“punishment” is what supports the equilibrium.)
Professor Wolfram
MBA201a - Fall 2009
Page 5
How is cooperation an equilibrium?
– If firm sets monopoly price, expected payoff is M/2 + V,
where V is discounted future profit along the monopoly
pricing path.
– If firm undercuts rival, then expected payoff is approximately
M + 0. (This assumes firm sets price just below rival and
takes all of the market—for one period.)
– If follows that monopoly pricing is an equilibrium if
M/2 + V > M + 0, or simply V > M/2.
Profits from
cooperating
Professor Wolfram
Profits from
cheating
MBA201a - Fall 2009
Page 6
Tacit collusion in words
In words, “if the future is sufficiently important, then cooperation
is an equilibrium.”
• Temptation: deviate and capture all the monopoly profits
right now.
• Carrot: if you don’t deviate, you get the monopoly profits
in the future.
• Stick: if you do deviate, you get 0 profits in the future,
forever…
Professor Wolfram
MBA201a - Fall 2009
Page 7
When is cooperation easier?
– Market growth (firms care more about the future)
– Likelihood of survival (ditto)
– Speed of response (future is close)
– Market structure (numbers and symmetry)
– Multimarket contact (harsh punishments)
– Probability of detection
Professor Wolfram
MBA201a - Fall 2009
Page 8
Comments
– Punishment/retaliation is a disciplinary device that supports
“cooperation.”
– Along the “equilibrium path,” price wars do not actually take
place, only the threat.
– Explicit price-fixing is illegal, but an understanding of
repeated games may produce a similar outcome legally.
Professor Wolfram
MBA201a - Fall 2009
Page 9
Price wars
Price wars are supposed to be “off the equilibrium path,” but they
happen in many industries on occasion. Why?
– High demand
– Low demand and imperfectly observable strategies
– Financial distress
– Signalling strength
Professor Wolfram
MBA201a - Fall 2009
Page 10
Professor Wolfram
MBA201a - Fall 2009
Page 11
The fine print
Retail Store Price Match Guarantee
If you find a lower advertised price on the same
available brand and model prior to your purchase or
during the exchange and return period, we will match
that price. Simply bring in the ad of the local retail
competitor or Best Buy, while the lower price is in
effect and receive your price match.
The guarantee does not apply to our competitors' website pricing and the guarantee does
not apply to our or our competitors':
•
Offers that include financing, bundling of items, free items, pricing errors and mail-in offers
•
Items that are limited-quantity, out of stock, open-box, clearance, Outlet Center,
refurbished/used items and items for sale Thanksgiving day through the Saturday after
Thanksgiving
Professor Wolfram
MBA201a - Fall 2009
Page 12
Other “facilitating practices”
– Most-favored customer clauses
• GE and Westinghouse
• Medicaid reimbursement rules
Professor Wolfram
MBA201a - Fall 2009
Page 13
U.S. antitrust laws
The Department of Justice (DOJ) and the Federal Trade Commission (FTC)
have missions to “promote and protect the competitive process.”
Laws concerning:
– Price-fixing (Sherman Act of 1890, Section 1).
– Monopolization (Sherman Act of 1890, Section 2).
– Mergers.
– Price discrimination, exclusive dealing, tying.
Some things are per se illegal. In other cases, the courts apply a rule of
reason.
Enforcement involves:
– Both private party and government initiated proceedings.
– Civil and criminal cases.
Professor Wolfram
MBA201a - Fall 2009
Page 14
Competition policy outside the U.S.
All 30 OECD countries have some antitrust authority:
– European Union laws very similar to U.S..
– Member countries have their own competition commissions.
– Japan Fair Trade Commission.
As do a number of non-OECD countries:
– For example, Argentina, Brazil, and India.
Professor Wolfram
MBA201a - Fall 2009
Page 15
Antitrust and price discrimination
US law* forbids “discriminat[ing] in price between different purchasers”
where the effect “may be substantially to lessen competition” unless:
– price differences are based on costs, or
– price differences were needed to “meet the competition.”
Two categories of cases:
– “Primary line discrimination”: seller practicing discrimination harms
its rivals.
– “Secondary line discrimination”: injury to competition takes place in
the buyers’ market.
“One often hears of the baseball player who, although a weak hitter, was also a poor
fielder. Robinson-Patman is a little like that. Although it does not prevent much
price discrimination, at least it has stifled a great deal of competition.”
- Robert Bork
* The Robinson-Patman Act.
Professor Wolfram
MBA201a - Fall 2009
Page 16
Takeaways
– Price competition can be severe, even with a small number
of firms.
– Avoid hazards of price competition by
• Having lower costs
• Limiting capacity
• Differentiating your product
– Repeated interaction provides firms with strategic leverage
over each other that may encourage cooperation.
Professor Wolfram
MBA201a - Fall 2009
Page 17