# Lecture: Dynamics of Pricing

```STR 421
Economics of
Competitive Strategy
Michael Raith
Spring 2007
Course structure
Part I: Obtaining and Sustaining a Competitive Advantage
Part II: Strategic Interaction
4. Dynamics of price competition
5. Strategic commitments
6. Technological competition
Today’s class
4. Dynamics of price competition
4.1 Shrimp game wrap-up
4.2 Logic of cooperative pricing
4.3 Factors hindering and facilitating coordination (next class)
Shrimp game:
example of a Cournot market
 Price (Bertrand) competition: firms set prices, quantities
sold are functions of prices
 Quantity (Cournot) competition: firms choose how much
to produce, market price is set so that demand = supply
 Applications:
– (Oligopolistic) commodities markets: oil (OPEC), aluminum
– Long-run competition: think of quantities as capacities
Monopoly solution
= perfect collusion
 Demand: P = 45 -.2 QTotal
 MR = 45 -.4 QTotal, set equal to MC=5
 Optimal QTotal = 100, so QA = QB = QC = 33.33
– Price is 25
– Profit is 666.7 for each firm = 2000 for industry
Independent decisions:
look for Nash equilibrium
 First: find best response for each player
– Find quantity that maximizes my profit given what I think my
rivals are doing
 Demand: P = 45 -.2 (QA + QB + QC)
 Arnold’s MR, taking QB and QC as given:
MR = 45 -.2 (QB + QC) - .4QA
 Set equal to MC = 5, solve for QA:
QA = 100 – (QB + QC)/2
The more the others produce,
the less you want to produce:
QA
100
75
QA=100 - (QB + QC)/2
25
QB +QC
50
150
200
Static Nash equilibrium
 Nash equilibrium: each player chooses best response
to other players’ quantities
 Solution: QA = QB = QC = 50
– Corresponding price is 15
– Profit is 500 for each firm = 1500 for industry, less than with
perfect collusion
 At Nash equilibrium, no firm has incentive to change its
quantity
 But with repeated interaction, strategic interaction gets
very complicated:
Example of prices in shrimp game:
Prices over time
30
25
20
Price
Series1
Series2
15
Series3
Series4
Series5
10
5
0
1
2
3
4
Round
5
6
7
Some worlds did better than static
Nash equilibrium, others worse
 Failed attempts to cooperate: incentive to be mean
greatest when others are nice:
Arnold Beatrice Charlotte
Quantity
33
33
66
Profit
449
449
898
 Trying to beat others in industry?
Arnold Beatrice Charlotte
Quantity
50
50
65
Profit
350
350
455
Moral: competitive mindset can be
very destructive
 Least profitable firm in nicest world almost always has
higher profit than most profitable firm in meanest world
 Avoiding price wars more important than outperforming
competitors
 With repeated interaction, competitors can and will
 How do firms manage to cooperate?
Today’s class
4. Dynamics of price competition
4.1 Shrimp game wrap-up
4.2 Logic of cooperative pricing
4.3 Factors hindering and facilitating coordination
Cooperation in
the shrimp game
 Suppose:
– Firms expect to play this game forever, choose quantities
weekly
– Future profits are discounted by 20% annually ≈ 0.35% weekly
 Possible strategy for the repeated game:
– If no one has deviated so far, produce 33 and get profit of 667
– If someone deviates and it is observed by others, switch to
static Nash equilibrium (Q=50) forever, and get profit of 500
 Suppose deviations are observed with ¼ probability
Key to coordination is a long
 Equilibrium?
– Payoff from cooperating: \$667/0.0035 = \$190,571
– Payoff from cheating: 889
(this week)
+ 0.998 *
(discount from next week)
(3/4 * 667/0.0035 +
(deviation is not detected)
1/4 * 500/0.0035)
= 179,175 < 190,571
 No incentive to deviate!
(deviation is detected)
 In our game, last round mostly uncooperative
 In rounds right before last, when cooperation worked, you didn’t
know that game would end very soon
 Airlines that are on the verge of bankruptcy cut prices. Why?
Tit-for-tat pricing
 Problem with “trigger” strategy above: threat of price war forever is
very costly if followed through
 Alternative: “tit-for-tat” pricing = Match price that rival charged in
previous period
 Axelrod (1981): experimentally, best strategy to induce cooperation
 Why does it work? Axelrod argues: Tit for tat is
–
–
–
–
nice: never the first to start price war
provokable: immediately matches a price cut
easy to understand (“We will match our competitors’ prices”)
 Problem (see BDSS): misperceptions can lead to large losses
– Possible solution: “forgiving” TFT = Wait until it is clear that defection
taking place
An Example: Airlines in 1998
March
Northwest begins sale on 14-day advance purchase fares. Others match
April
Continental twice tries to raise leisure fares by \$20 per round-trip. Other
carriers match, but Northwest blocks both attempts
May
Northwest initiates 25 % sale on 21 -day advance-purchase fares. Others
match. Later, Continental tries 5% increase on non-sale leisure fares. United,
American, Delta and USAir match, but not Northwest. Increase is rolled back
July
Continental raises leisure fares \$20 round-trip; Northwest blocks
August 11 Delta and American raise fares by 4%, Northwest blocks
August 14 American raises fares by 4% in markets not served by Northwest; carriers
other than Northwest match
August 17 Delta rolls back the increases; other airlines follow
August 18 Northwest raises fares by 4%. All other carriers match the increase
August 19 Northwest rescinds fare hike; US Airways and TWA match same day
August 20 American, Delta, Continental match reversal; other carriers follow
August 21 Northwest hikes fares by 4%, other carriers match
Remark: Collusion and product
differentiation are conceptually different
 Both lead to P > MC, lower internal rivalry, but:
 Product differentiation: At Nash equilibrium, cutting
price not profitable even if rivals don’t respond
 Collusion: At cooperative price, cutting price not
profitable because others are expected to retaliate
– Cutting price is profitable in short run, i.e. before rivals can
respond
Antitrust restrictions
 Goal of antitrust laws is to promote efficiency
 Price-fixing agreements are per se illegal in U.S.
– Recent international cases: Lysine cartel, vitamin cartel (late
90s), Sotheby’s and Christie’s (2001), Samsung in DRAMs
(2005), L’Oreal, Chanel and 11 others in perfumes
 Parallel behavior in oligopolies not sufficient for antitrust
violation; evidence of explicit agreement is required
– Tacit collusion is currently not considered illegal in U.S.
– E.g. Jewel’s and Dominick’s high milk prices in Chicago in late
90s: lack of evidence of conspiracy
Today’s class
4. Dynamics of price competition
4.1 Shrimp game wrap-up
4.2 Logic of cooperative pricing
4.3 Factors hindering or facilitating coordination
What determines ability to
coordinate prices?
1. How easy is it for firms to tacitly agree on prices?
2. How effectively can deviations from an agreement be
deterred? Need, for each firm,
Profit under continued cooperation
> Gain from deviating today
+ Probability of detection * Profit in a price war
Effectiveness of retaliation
1. Can firms agree on a price?
 Finding a (tacit) agreement more difficult
– the more firms there are
 Main reason why we care about concentration in 5 forces:
collusion in aluminum, infant formula industries?
– the more products there are, and the more heterogeneous the
products
– If there are cost asymmetries
So what can firms do about it?
 Price leadership: if one firm is accepted by all as price
leader, then it’s easier for all to coordinate prices
 Pricing rules to price large number of products
– E.g. per-pound price rule for electrical equipment used by GE
and Westinghouse in 1960s
 Information exchange, e.g. through trade association
– about which products are substitutes
2. Are there strong incentives to
deviate?
 Gain from deviating is larger….
– the more firms there are
– if orders are lumpy
 Commercial aircraft: Boeing vs. Airbus
 Industries with large business customers: e.g. CCS
– if firms have excess capacity
How can firms reduce the incentive
to cut price?
 Advance announcement of price raises: if rivals don’t
match, just rescind
 Exclusive territories for retailers
 Most-favored customer clauses
– “If I sell to any other buyer at a lower price, I will also charge
you the lower price (or pay you a rebate)”
– Reduces the own temptation to cut price!
 Meet-the-competition clauses
– “If any other seller offers you a better price, I will match it”
– Makes it unprofitable for rivals to cut price
3. How effective is retaliation
against deviating firms?
 Factors making retaliation more difficult
– Lack of price transparency
 Retail gasoline, vs. corporate discounts in express mail industry
– Demand fluctuations: were your sales low because of low
demand or because someone stole your customers?
– Product differentiation between firms
 Multi-market contact actually facilitates collusion, since cutting
price in one market may trigger price war in all markets
– Argument against merger of Union Pacific and Southern Pacific
Railroads in mid-90s: multi-market contact with large rival
How can firms make retaliation
more effective?
 Sometimes excess capacity can help: punishing
deviations requires some unused capacity
– Saudi-Arabia’s capacity to flood market as way to discipline
OPEC members
 Increase market transparency
– Through information exchange
– By standardizing products
– Through pricing formulas
The “topsy-turvy principle” of
collusion
 “Factors/practices that lead to intense competition if
firms don’t cooperate often actually facilitate
coordination.”
 Examples:
– High market transparency
– Low degree of product differentiation
Antitrust restrictions II
 Warning: many/most of the practices mentioned raise
suspicions with antitrust authorities
 Many practices facilitate collusion, but also increase
market efficiency among non-colluding firms
– e.g. information exchange
 In evaluating facilitating practices, courts weigh proand anti-competitive effects
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