Managerial Economics: Applying the Tools Topic 8, Part 2

1
Managerial Economics Applying the Tools Topic
8, Part 2

• Short-run competition
• Applying game theory to analyse mass markets with
  a few competing suppliers (oligopoly)
• Paul Kerin Sam Wylie
• MBS Term 3, 2004

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BEST RESPONSE.

• This is the main thing to take away from our
  introduction tosimultaneous game theory, A best
  response is determined this waysuppose I knew
  that player B was going to play Scissors, what
  is my best response to her strategy?
• You need to figure out your best response to
  every strategy that other players could follow
• Example Im a member of OPEC. If I knew that
  Kuwait would produce 20 million barrels of oil
  and Saudi Arabia would produce 30 million barrels
  and Nigeria and what would I want to produce?
• What I choose to do depends on what I expect the
  other player(s) to do. Its strategic!

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Nash Equilibrium ALL playing a BEST RESPONSE

• Imagine that each player has chosen her strategy
• If every players strategy is a best response to
  the other players strategies, its a Nash
  equilibrium
• Looking at a table
• Each box is a choice of strategy for each player
• For example, in the top right box, Conductor has
  chosen Hold out and Tchaikovsky has chosen
  Confess
• Is that box a Nash equilibrium?

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Intuition for Nash Equilibrium

• My expectations about the other player will be
  consistent Im not expecting him to behave
  irrationally, in response to my choice
• Its a self-fulfilling agreement If Oscar and
  Felix decide to clean 3 and 9 hours each
  respectively, theyll both go through with it
• I cant do better by unilaterally changing my
  choice
• A Nash equilibrium can also be an outcome that
  weve settled into after repeating a situation
  many many times.

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Oligopoly

• Oligopoly competition between a few producers
• (not perfect competition)
• Assumes high entry barriers
• no more entrants
• set of competitors is given
• Well deal with markets in which oligopolists
  produce exactly the same thing homogeneous
  products - extreme assumption
• There are (optional) readings on markets in which
  oligopolists produce differentiated products

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Competition in mass markets with homogenous
products

• What happens when firms compete on
• Price?
• Quantity?

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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

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Our favourite market demand curve, but now with 2
firms

• 
  QD
• In algebra demand (QD) is QD 1000 - P

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Competition in Prices Bertrand

• Firms post prices simultaneously, afterwards see
  what they sell
• The goods are perfect substitutes (ex flour,
  sugar).
• Consumers will buy from the firm with the lowest
  price
• If two firms set different prices, then the
  low-price firm gets the entire demand
• The firms are not capacity constrained they can
  meet the whole markets needs
• ? e.g. Either firm can supply 800 or more units
  to the market (why 800?)

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Nash equilibrium

• Each firm has a marginal cost of c
• This is a simultaneous game (but there are too
  many price choices to draw table)
• Is there a Nash equilibrium(a)?
• The only Nash Equilibrium in this market is that
  both firms will sell for a price of c, and make
  zero profit (P MC)

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Bertrand competitionNash equilibrium price MC

• What is my best response to my competitor
  charging a price P2 that is greater than c?
• I want to charge a price P1 just below P2.
• But then is my competitor at a best response?
• No, he wants to price just below P1
• What if your competitor charges c (marginal
  cost)? Then your best response is to charge c as
  well
• ? The only Nash equilibrium is P1P2c

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Usual objection

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

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Bertrand competition versus perfect competition

• Oddly enough we get the same result as in a
  market with a huge number of sellers (perfect
  competition) P MC
• Yet there may be very few sellers in the market
  maybe only 2
• if they found another way to increase price,
  theyd earn profits
• likely to try and change the game
• Differentiate their products most common tactic
• Differentiating the products softens price
  competition price no longer falls to MC
• Merge (then theyd earn monopoly profits)
• Collude (illegal) or tacitly collude
• Limit their capacity looking at this next

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What if firms have limited capacities? a
credible commitment

• Galleria and Travelite are competing in the
  market for Melbourne souvenir Tee-shirts the
  Tee-shirts are identical, from the point of view
  of a tourist
• The demand curve is Q1000 P per month, and
  marginal cost of each firm is 200 per 10
  Tee-shirts
• (This is just so that we can retain our
  favourite demand curve think of our graph as the
  price for 10 T-shirts, and the quantities in tens
  of T-shirts 20 per Tee-shirt is the opportunity
  cost of re-selling them in bargain shops, so 200
  per 10 is the marginal cost)
• What happens if Galleria stocks 400 (in tens of
  T-shirts) per month, and Travelite stocks 300 per
  month?

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The new capacity game

• Galleria has capacity 400, Travelite has capacity
  300
• Suppose the firms are currently charging 600,
  and selling 200 each is this a Nash equilibrium?
• No, each firm has a incentive to undercut the
  price and thereby sell 100 or 200 more
• Price falls lower
• Suppose the market price falls to 300
• Each firm could sell 350, if they had the
  capacity
• In fact, Travelite doesnt have the capacity
• Travelite sells 300 and Galleria sells the rest
  (400)
• Is 300 a Nash equilibrium? Or does price fall to
  200?

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What if total capacity is more than 800?

• (800 is the quantity demanded where PMC)
• Suppose Galleria has a capacity of 500 and
  Travelite has a capacity of 400
• What is the Nash equilibrium?
• Is the equilibrium price 300?
• Is the equilibrium price 200?
• Is the equilibrium price 100?

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Binding capacity constraint raises price

• If total capacity is less than demand at PMC
• Firms will produce up to full capacity, and
  charge the market-clearing price
• no incentive to under-cut each other, as
  they cannot sell more by doing so
• they choose their capacity, knowing that that is
  the amount they will choose to produce
• it becomes a new game competition in capacities
  like competition in quantities.
• both firms are better off P gt MC
• They want to restrict capacity
• Remaining question if they can choose their
  capacities, what capacities do they choose?...

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Competition in quantities Cournot

• 2 possible scenarios in which Cournot may be
  relevant
• 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

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Oil refining example

• Only 2 producers Shell and Mobil
• Each chooses simultaneously whether to have high
  production or low production
• Afterwards, see what the world-market-clearing
  price is for the total oil produced
• If you are Shell, what do you do?

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First rough approximation
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Tough quantity competition
Unique Outcome
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Competitive Equilibrium

• Both choose high production
• just like Prisoners Dilemma
• More generally
• Total profits are maximised when they each
  produce ½ of monopoly output
• If Mobil and Shell can independently choose from
  a range of production levels, both will choose
  relatively higher production than ½ of monopoly

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The problem negative spillovers (externalities)

• Shell is creating a negative spillover for Mobil
  when Shell increases its quantity, price falls
  for Shell but also for Mobil
• ? Shell increases quantity more than it would if
  Shell owned Mobil

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Marginal Revenue under Monopoly vs. Cournot
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The 2 components of MR

• To sell one more unit, a monopoly
• has to sell to people with lower WTP ? price of
  the last unit is lower, so less revenue
• has to lower the price to everyone you were
  currently selling to.
• if the monopolist is selling 400, and wants to
  sell 401, she has to lower the price on 400 units
• BUT under Cournot, you only consider the effect
  on units YOU sell
• if youre selling 200 and competitor is selling
  200, to sell one more unit, you lower the price
  to your 200 buyers
• less downside for you
• MR falls more slowly (so produce more)

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Mathematics of Cournot competition(you do not
need to know how to do this)

• BEST RESPONSE If Mobil knew that Shell would
  produce an amount QS, how much would Mobil
  produce?
• Example Demand (Q) is Q 1000 P, and MCM
  200.
• Demand is met by both producers, so Q QM QS
• Rearranging the demand equation gives us
• P 1000 (QM QS)
• Firm M maximises its profits
• TRM P?QM
• 1000 (QM QS)?QM
• Take the derivative, as in a monopoly problem,
  but treat QS as a constant (because Mobil thinks
  its fixed)
• MRM 1000 2QM QS

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While each player assumes no reaction, is that
what really happens?

• QM 400 ½QS (best response curve)
• If Shell increases its output, Mobil reduces its
  output
• Reason to keep market price high
• If Shell produces nothing, Mobil produces 400
• If Shell produces 200 million, Mobil produces 300
• If Shell produces 400 million, Mobil produces 200

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Best response curve
Mobils output

• The equation QM 400 ½QS is a best
  response or reaction curve it expresses what
  quantity Mobil will want to produce, for any
  given quantity Shell produces

400
Mobils best response curve
Shells output
800
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Nash equilibrium in Cournot competition

• A Nash equilibrium occurs when both players are
  playing their best response to the other player
• the intersection of the best response curves is a
  Nash equilibrium
• Mathematically we found QM 400 ½QS
• Suppose Shell has MCS300
• Then we can calculate Shells best response
• QS 350 ½QM
• and solve the 2 equations at once for QM and
  QS

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Best response Nash equilibrium
Mobils output

• Nash equilibrium where Shell and Mobil are
  playing a best response
• the intersection of the two reaction curves

Shells best response
700
400
Mobils best response
QM 300
350
Shells output
800
200QS
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Cournot outcomes

• From the reaction curves, we see that each firm
  produces less than it would if it were a monopoly
• But each firm produces more than half the
  monopoly quantity
• Adding their output together, the firms produce
  more than a monopolist would
• Each earns less than half of monopoly profits
• Competing in quantities yields low profits,
  although not zero profits
• its better than price competition

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The Role of Tough Quantity Pre-commitments

• Reaction curves are downward sloping
• The more Shell expects Mobil competitor to
  produce, the less Shell wants to produce
• Mobil 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

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Commitment shifts your best response and
therefore rivals decision
Mobils output
Shells best response
B
Mobils best response
A
Shells output
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Pre-commitments a warning!

• A tough commitment means that Mobil wants to
  produce more, at every output level of Shells
  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

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Pre-emption

• Commitments can change the game in your favour
• if so, each firm will want to commit
• What happens if you can commit first?
• Rival observes your action before choosing her
  own
• ?You gain a first-mover advantage

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Example Memory Chips Commitment Industry
Leadership

• 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

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Commitment choosing capacities

• If capacities have to be chosen simultaneously,
  choose to build a plant capacity equal to the
  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

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Pre-emptive capacity building
Gallerias output
Ts best response

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

Gs response curve after building capacity QG
Gs response curve after building capacity QG
Gs response curve after building capacity QG
B
QG
Gs best response curve in a simultaneous game
QC
A
Travelites output