Strategic Pricing

1
Strategic Pricing

• How to price in a game with competitors

2
Oligopoly

• Oligopoly Competition between multiple firms
  (still assuming mass market of buyers)
• Assume number of firms is fixed
• No immediate threat of entry
• Base-case homogeneous firms
• Production technologies identical (i.e., same
  cost structure)
• Products identical (i.e., same demand curve)
• Types of competition
• Price competition
• Quantity competition
• Extensions
• Product differentiation
• Tacit collusion

3
Class Experiment

• High or Low Production?

4
The Production Game

• Players approximately 76 of you
• Choices
• Capacity 2 units
• Choose 0, 1 or 2 units
• Payoffs
• No production costs
• Price 160 Total Production Quantity
• Profit Price x Quantity

5
Competition in mass markets with homogenous
products

• What happens when firms compete in quantity?
• What happens when firms compete in price?

6
Price vs. quantity competition

• Monopoly
• Firm can choose quantity or price
• Same answer either way
• Oligopoly
• Firms can still choose quantity or price
• Now, however, this matters
• Different models
• Different conclusions
• The key is capacity
• The price-competition model assumes all firms
  have sufficient capacity to serve the entire
  market
• The quantity-competition model is identical to
  the price competition model with the addition of
  capacity constraints
• So, the quantity competition model is good for
  situations in which firms are able to commit to
  production limitations (e.g., via capacity
  choices)
• We will see that
• For the same number of firms, price competition
  results in lower industry profits
• As the number of firms increases, profits under
  quantity competition converge to those under
  price competition (i.e., due to the more intense
  competition)

7
Tough price competition
8
Tough Price Competition

• CD ROM phonebooks
• 1986 Nynex charged 10,000 per disk for NY
  directory
• ProCD and Digital Directory Assistance
• Workers in China at 3.50 daily wage
• Outcome similar to Perfect competition
• Charge 200 each
• Price forced down to marginal cost

9
Same market assumptions as before

• Now, assume there are 2 firms F1 and F2
• Identical products costs
• Firms choose price

10
Competition in prices

• Firms post prices simultaneously, afterwards see
  what they sell
• P1 and Q1 denote F1s price and quantity,
  respectively
• P2 and Q2 denote F2s price and quantity,
  respectively
• Here, price is the choice variable, quantity is
  the outcome variable
• Goods are perfect substitutes (ex flour, sugar).
• Consumers buy from the firm with lowest
  price(provided price is less than their WTP)
• If firms set different prices, the low-price firm
  gets 100 share(implicit capacity assumption
  both firms can supply entire market)
• If firms set identical prices, firms get equal
  market shares
• This is known as the Bertrand model of
  oligopolistic competition

11
Informal analysis

• Suppose F1 believes that F2 will maintain price
• Assume the firms begin with identical prices of
  600
• At this price, 400 customers buy (note same as
  monopoly case)
• Firms
• Split the market (since prices are equal), 200
  units each
• Have identical profits of (600 200)200
  80k(note split the monopoly profit level)
• If F1 lowers the price a little, say to 590, it
  gets 100 market share
• No one buys from F2 (if price stays at 600)
• F1 gets Q1 1000 590 410 in sales (from
  demand equation)
• Profits are
• (590 200)410 159,900 for F1
• 0 for F2
• F1 wants to do this (ideally, cut price by 1
  cent!)

12
Nash equilibrium?

• It is not realistic for F1 to believe that F2
  will maintain price
• What is true for F1 is also true for F2
• If F1 cuts price a little, F2 loses everything
• Therefore, F2 will also cut price to match, if
  not exceed, F1s cut
• Each firms reaction to a price cut is to cut
  price where does it stop?
• To solve, use Nash equilibrium posted prices are
  stable when neither firm wants to change given
  competitors price
• If firms charge different prices, the high priced
  firm wants to switch to a lower price, so prices
  must be equal
• If common price above marginal cost, both firms
  prefer to shave price to gain 100 share, so
  price must be less than or equal to MC
• If common price is less than marginal cost, both
  firms prefer to exit the market and sell nothing
  at all, so price must equal MC

13
Outcome of pricing game

• Each firm has a marginal cost of 200
• So, both price at 200
• Quantity sold is 1000 200 800 units
• Each firm gets 50 share (400 units)
• Neither firm makes a profit
• This is an insidious outcome, neither firm can
  raise price without risking entire loss of share
• Actually, its worse than that

14
Price trap with no exit

• Since both firms earn 0 profit, each is
  indifferent to exiting
• But, is it a Nash equilibrium for one to exit
• If one firm exits, the other charges the monopoly
  price (600 is the best reply of the remaining
  firm to a competitor that stays out)
• But, if one firm stays and charges 600, the
  other firm wants to enter and charge slightly
  less
• This cannot be a stable situation (Nash
  equilibrium)
• Besides, who would volunteer to leave?
• It is only Nash for both firms to post P MC
• Otherwise, either someone wants to enter
• Or, someone wants to cut price

15
Usual objection

• But wont each firm realise that if it cuts its
  price the other firm will follow?
• (hold that thoughtwell address soon)

16
Fixed costs, exit and entry

• Outcome is P MC
• No fixed costs are covered
• If firms have no fixed costs, they earn zero
  profits
• If they have fixed costs, they have losses
• In the long run, firms w/fixed operating costs
  must exit
• Question is what happens then?
• If entry is free, price competition happens all
  over again (as discussed on previous slide)
• If entry is costly, no entry occurs
• The moment an entrant comes in, prices drop to MC
• Incumbent earns monopoly profit because the
  threat to cut price to MC is credible in this
  situation (i.e., it is a Nash equilibrium)
• This is why it may be rational for firms to try
  to hold out
• Need to be careful using this reasoning if it
  is rational for you to hold out, it is probably
  rational for your competitor to do so as well
• Amazon.com investors will never get a positive
  return on their investment
• Better differentiate your product

17
Softer, quantity competition
18
Competition in quantities

• Firms simultaneously choose quantities,
  afterwards see prices
• Think of this as choosing capacities
• Q1 denotes F1s quantity
• Q2 denotes F2s quantity
• The market-clearing price is P
• Here, quantity is the choice variable, market
  price is the outcome variable
• Again, goods are perfect substitutes (ex flour,
  sugar).
• However, there may not be enough capacity to
  serve entire market
• Since products are identical, prices are
  identical
• Capacity limitations imply higher market-clearing
  prices than price competition
• This is the Cournot model of oligopolistic
  competition

19
Informal analysis

• Assume the firms begin with identical capacities
  of 200
• To sell all their product (400 units, total),
  market price is 600 (again, same as monopoly
  case)
• Firms have identical profits of (600 200)200
  80k(split the monopoly profit level)
• Suppose F1 believes that F2 will maintain
  capacity
• What capacity should F1 choose? A partial
  schedule of outcomes is

20
F1s residual demand curve

• Preceding table shows F1s demand when F2
  maintains quantity/capacity
• It is D1 800 Q1 (just subtract Q2 200 from
  market demand schedule)

• What is F1s profit maximizing choice?
• Set MR MC!
• Now, MR 800 2Q1
• Solve 800 2Q1 200 ? Q1 300
• P 800 300 500

21
F1s reaction curve

• The preceding analysis can be done for any
  quantity choice by F2
• This results in a schedule of best responses for
  F1 given any Q2

This curve gives F1s optimal choice of Q1 for
any choice of Q2 (hence, the name reaction
curve)
800
800
If Q2 800, cannot produce profitably

MR200
Q2
D200 (i.e., F1 demand when Q2 200)
500
400
400
If Q2 0, choose monopoly quantity
D400
200
MC1
MR400
0
Q1
800
400
300
200
300
600
200
Q1
22
Equation of the reaction curve

• F1s MR when F2 chooses Q2 is MR (1000 Q2)
  2Q1
• So, if MR MC (1000 Q2) 2Q1 200
• Rearranging terms Q1 400 ½ Q2

800
Q2

• Check
• If Q2 800, Q1 0 ?
• If Q2 400, Q1 200 ?
• If Q2 200, Q1 300 ?
• If Q2 0, Q1 400 ?

400
200
0
400
300
200
Q1
23
Nash equilibrium

• F2 also has a reaction curve, which can be
  plotted along with F1s
• Nash equilibrium is the point of intersection
  both firms best reply

When Q1 Q2 267, neither firm wants to
change capacity

• To solve for the Nash equilibrium
• Plug F1s reaction equation into F2s reaction
  equation
• Solve for Q2
• Plug this value of Q2 into F1s reaction equation
• Solve for Q1

24
Outcome of pricing game

• Each firm chooses capacity of 800/3 ? 267
• Market price is 1000 1600/3 ? 467
• Each firm has profit (467 200)267 71,200k
• Much better outcome than price competition
• Not quite as good as sharing monopoly profit
• Firms would prefer to collude and profit more
• This is illegal
• Even if it werent, how would firms prevent
  cheating?
• At quantities of 200, both want to produce more
• Check the reaction curves!

25
MR in Monopoly vs. Cournot
MR falls more slowly why?
26
The 2 components of MR

• To sell one more unit, you have to
• Must sell to someone with lower WTP ? price drops
• This drops price to currently buyers
• If monopolist is selling 400 and wants to sell
  401, she must lower the price on 400 units
• Under Cournot, only consider effect on units YOU
  sell
• If firms sell 200 each, lower price effects you
  only through your existing 200 customers
• When making decisions, you dont care what
  happens to competitors profits
• Less downside for you (MR falls slower)
• You are more inclined to cut price (have more
  capacity)

27
Now, the general 2-firm Cournot case

• Demand P a bQ where a and b are constants
  and Q (Q1 Q2) is the market quantity
• Firms have identical, constant marginal costs C
• F1 profit maximized where MR1 MC1
• TR1 PQ1 (a bQ1 bQ2)Q1 (a bQ2)Q1
  bQ12
• MR1 ?TR/?Q1 (a bQ2 ) 2bQ1
• Setting MR MC (a bQ2 ) 2bQ1 C
• Rearranging terms gives reaction function for F1
• Since the firms are symmetric the reaction
  function for F2 is identical
• Solving two equations in two unknowns (use
  substitution as before)
• Check this against the results in our example
  (and use it for problems!)

28
The general n-firm Cournot case

• Keep the general case assumptions but assume
  there are n firms
• Nash equilibrium solution procedure the same
• But now there are lots of simultaneous reaction
  functions to deal with
• It can be shown that the amount produced by each
  firm i is
• The interesting thing is that the market price is
• So, as n ? infinity, P ? C because a/(n1) ? 0
  and n/(n1) ? 1
• In the limit, the same result as price
  competition!
• In mass, homogenous-good markets with lots of
  small competitors, firms earn zero profit

29
Competition in quantities Cournot

• 2 Possible scenarios
• Quantity decisions have to be made a long time
  before sale
• Firms choose the quantity they want to produce
  without knowledge of others choices
• After supply is determined, there is a market
  mechanism that finds the price at which Demand
  equals that available Supply
• Firms can limit their capacities
• Firms choose their capacity without knowledge of
  others choice of capacity
• Once they see each others capacity, they each
  charge the market clearing price

30
The Role of Tough Commitments
31
Quantity Pre-commitments

• Reaction curves are downward sloping
• The more F1 expects F2 to produce, the less F1
  wants to produce
• F2 should pre-commit to producing more than it
  would otherwise want to
• Example Investing in mass-production equipment
• Such pre-commitments cause rivals to back off and
  accommodate by producing less
• When are quantity increases credible?
• Reputation for high quantity
• Large supply or purchase contracts
• Cost leadership investments in lower unit
  production costs
• Irreversible capacity investments

32
Tough quantity competition
F2s output
B
F2s best response
A
F1s output
33
Pre-commitments

• A tough commitment means that F2 wants to produce
  more, at every output level of F1s the best
  response curve is shifted up.
• The commitment moves the equilibrium from A to B.
• CAREFUL! The commitment is only worth it if the
  firm earns more at B (after paying for the
  commitment) ? you have to check.

34
Pre-Emption

• Commitments change the game now one or the other
  will try to commit
• Either firm may commit...
• But what happens if you can commit first?
• Other firm observes your action before choosing
  their own
• ?You gain a first-mover advantage

35
Case Memory Chips

• Early 1980s market dominated by US firms
• mid 1980s Japanese firms (Toshiba, NEC)
  increased their investment in new capacity (while
  US firms didnt)
• late 1980s 80 of market controlled by Japanese
  firms
• 1990s massive investments by South Korean firms
  (Samsung, Hyundai) while the Japanese firms have
  not invested

36
Commitment and choosing capacities

• If capacities have to be chosen simultaneously,
  choose to build a plant whose capacity Cournot
  quantity
• BUT
• If one firm can choose capacity first, and can
  make sure the other firm sees its choice
• The second firm to build will choose its best
  response to the first firms capacity
• The first firm can profit by making a tough
  commitment in capacities build a large plant
• Both firms want to be first
• There may be a race to build first

37
Pre-emptive capacity building

• If firms were building at the same time, F2 would
  build a plant with capacity equal to the Cournot
  quantity Qc
• But if F2 builds first, it will build a larger
  capacity Q2

F2s output
F2s response curve after building capacity Q2
B
Q2
F2s best response curve in a simultaneous
game
QC
A
F1s output
38
Strategies to dampen competition
39
Return to price competition

• Even with only two firms P MC
• This is a very bad position in which to find
  yourself
• What can be done? Try to change the game!
• Merge (and earn monopoly profits)
• Differentiate your products (a common solution)
• Obtain a cost advantage (see Gans, p. 148 151)
• Collude (illegal and, in any event, hard to make
  work)

40
Niche market differentiation

• Go back to price (Bertrand) competition example
• Assume buyer demand is horizontal at
  1000(perfectly elastic)
• Suppose F1 can alter the design of its product
• The new product appeals to 40 of the market
• These customers are willing to pay a 50/unit
  premium for this product
• MC of this product is 225 (25 more expensive)
• Old product must be retired

41
Analysis

• F1 wishes to go to the new design
• Under old design, P1 MC 200
• With new design, F1 can post P1 250
• 400 units sold
• ?1 (250 225)400 10,000
• What is F2s best response?
• Since P1 gt 200, F2 can post P2 gt 200 as well
• For example, P2 201, ?2 (201 200)600 600
• What is Nash equilibrium?
• P2 201 ? P1 251
• So this is not Nash

42
Equilibrium in niche markets

• Calculating Nash is beyond the scope of this
  class
• Instead, look for undercut proof outcome
• Price difference must be 50,
• Any more and the 400 customers switch to F2
• Any less and F1 could earn more by raising price
• F1 must earn same or more profit as what could be
  obtained by undercutting P2 slightly
• If P2 gt 200, F1 can always
• Keep the old product
• Set P1 slightly below P2 and
• Get 100 of the market
• So, P2 cannot be too high, otherwise this option
  will be preferred

43
Compute the equilibrium

• The two requirements imply, respectively
• P1 50 P2
• (P1 225)400 (P2 200)1000
• Substitute first requirement into second
• P1 800/3 ? 267
• P2 650/3 ? 217

?1 if F1differentiates
?1 if F1just undercuts P2
These prices are undercut proof
44
Cooperation

• Collusive Pricing Can firms collude without
  communicating?

45
Large Electric Turbine Generators

• 1950s three producers of large electric turbine
  generators in the US
• GE, Westinghouse and Allis-Chambers
• Lots of profits low rivalry, high entry barriers
• Seem to maintain high prices during the 1950s
• Subject of antitrust investigation
• But how did collusion take place when there was
  no evidence of communication (let alone an
  agreement)

46
Celestial Coordination

• Competition on tenders from electricity utilities
• A formal solicitation of bids was released
• Based on the time of the formal document, each
  firm would consult the lunar calendar
• Days 1-17 of lunar month GE would own the
  contract (high bid with others bidding higher)
• Days 18-25 Westinghouses turn
• Days 26 to 28 A-Cs turn
• Gave market shares of 60, 30 and 10
  respectively.
• Why did A-C put up with this? Couldnt be taken
  to court for breaking a contract. That contract
  would be illegal.

47
Tacit collusion

• When interactions occur over many periods, firms
  can implement a wide range of outcomes
• Stay with price competition example
• Assume game is repeated indefinitely
• Firms have discount rate r
• Best case for firms is to post monopoly price
• Split market
• Split monopoly profit
• Problem strong incentive to cheat (shave price)
• Can this be overcome in repeated case?

48
Collusive strategies

• Consider this dynamic strategy
• Set price 600 (monopoly price w/P 1000 Q)
• If opponents price was 600 this period, set
  price 600 next period
• If opponents price was not 600 this period, set
  price 200 forever
• Both firms adopt this grim trigger strategy
• Does either wish to deviate?

49
Can F1 deviate profitably?

• Assume F2 follows the previous strategy
• If F1 also follows the strategy
• It gets (600 200)200 80k forever
• So, the PV of following the strategy is 80k/r
• Instead, F1 can undercut
• If it posts P1 599, ?1 (599 200)401 ? 160k
• But, in all following periods, P2 200 (by the
  strategy)
• The best response in those periods is P1 200
• So, F1 gets ?1 0 forever following a deviation
• It is not profitable to deviate from the strategy
  when
• If firms are sufficiently patient, collusion
  can be sustained

50
Cooperation in repeated interactions

• The previous type of result holds in most
  repeated situations
• That is, cooperation can be sustained in repeated
  transactions even though there are incentives
  to act opportunistically
• By cooperating, firms split the best outcome
  profit
• By deviating, a firm gets the short-run benefit
  but, when cheating is detected, play enters a
  punishment phase
• Punishment in future periods more effective with
  low discount rates(cheaters lost future
  benefits have greater value)
• There are many cases where reputation may be
  important
• Commitment issues (playing tough with entrants)
• Delivering high quality products (avoiding lemons
  problems)
• Delivering agreed upon effort in strategic
  alliances (no free riding)
• Even Prisoners dilemma can be resolved

51
Co-opetition Commitments that Facilitate
Collusion

• Most Favoured Customer Clause (MFC)
• Manufacturers of antiknock petrol additives (Du
  Pont, Ethyl) were brought before the US Federal
  Trade Commission for using MFCs.
• The seller will pay buyers the best price they
  pay to anyone.
• Commits to not offering selective discounts to
  attract customers from rivals
• Lowers the gain from cheating on price collusion.
• Meet the competition clauses
• With rebates, you find out quickly about cheating
• Commitment makes the price war more bitter
• Loyalty Programs
• harder to cheat by stealing customers from others

52
Trigger price strategies

• In some environments, you cant tell who has
  cheated
• Several firms
• You dont see how much theyve sold
• Variable demand ? when your price falls, you
  dont know if its because demand fell, or
  someone cheated.
• Results in this environment
• We cant collude at monopoly prices, because
  cheating is too tempting ? we have to charge
  mid-range prices
• There is a trigger price if the price falls
  below this trigger, we all revert to competition
  for a few periods (punishment), then we
  cooperate again.

53
Tacit collusion

• If you cant talk to each other, how do you agree
  on a price?
• Focal point something people gravitate to
• If the firms are identical, and can sustain
  collusion at monopoly price, that seems like an
  obvious focal point
• But usually firms have different costs, slightly
  different products ? how do you coordinate?
• Or you might have to charge a mid-range price (as
  in trigger strategies)
• ? what price should you charge? How do you reach
  agreement?
• One tactic Raise your price, hope the others
  follow
• Explains why its easier to coordinate on not
  cutting prices, than on raising prices
• (inflation is the customers friend!)

54
Ethics of tacit collusion

• If customers are better off because of collusion,
  seems ethically defensible
• Ex If firms compete Bertrand, one will leave the
  market, and the other will charge monopoly prices
• Customers are better off with two firms
  colluding, but only if theyre charging mid-range
  prices (rather than monopoly prices)
• no price wars
• But such cases are fairly rare
• What about in the other situations?

55
Why do you need to know?

• Suppose youre entering a market with 3 or 4
  producers.
• If theyre competing with very similar products,
  thats a pretty competitive market
• you would expect that prices wont fall
  drastically when you enter the market
• You enter so long as your marginal cost is less
  than the going price.
• But if theyre colluding
• The price could fall drastically after you enter,
  if they dont collude with you, or if there are
  now too many players to sustain collusion
• The going price is not enough information
• How would you pick up whether theyre colluding?
• Prices that dont change, when costs or demand
  changes
• In some mkts, occasional price wars when prices
  go way down.