Managerial Economics: Applying the Tools Topic 9, Part 2

1
Managerial Economics Applying the ToolsTopic
9, Part 2

• Brief review of competition
• Cooperative pricing
• Paul Kerin Sam WylieMBS Term 3, 2004

2
Game Plan

• Last topic a stand-alone topic (revealing
  pricing signalling)
  
• Well do that next week
• In our last class, we will
• provide information on the exam and exam tips
• review the whole course
• recap on concepts related to monopoly,
  competition, and collusion
  
• do some in-class practice, emphasising the
  necessary steps to answer a question

3
Recap competitive pricing

• Firms may compete in prices or in quantities
• Which one will it be?
• Its a function of the competitive conditions in
  the market
  
• ? Its pre-determined whether it will be price or
  quantity competition, by the time we compete
  
• If they can instantaneously meet any market
  demand at PMC, then its price competition
  (Bertrand) if capacity is fixed below the
  quantity where PMC, it is constrained Bertrand,
  with PMC P is where demand capacity
• If firms must decide how much to produce/stock
  before getting to market, then its quantity
  competition (Cournot)
  
• If firms have can decide/change their capacities
  before getting to market to produce, then its
  competition in capacities (choice of capacity
  choice of quantity Cournot)

4
Price versus quantity competition
P
Demand QD 1000 - P

• 
  
  
• Bertrand price competition each charge 200 ?
  sell 400
  
• Cournot quantity competition each sell 267
  units, for a total of 534
  
• units ? charge 466 each

Cournot
Bertrand
MC
Q
5
Competition versus collusion

• Bertrand Market price 200, Profits 0 each
• Cournot Market price 466, Profits 71,111
  each
  
• But under either set of competitive conditions,
  if they were to collude instead of competing,
  they would earn more!
  
• Collusion pricing higher than you would under
  competition.
  
• Under Bertrand competition, players are colluding
  if the price is any higher than 200 (and if no
  binding capacity constraint)
  
• Under Cournot, players are colluding if the
  market price is any higher than 466
  
• Perfect collusion is to behave exactly as if
  you were a monopoly
  
• Players are perfectly colluding if the price is
  the monopoly price, 600, each sell 200, and
  profits are 80,000 each

6
Comparison of outcomes
P
Demand curve
Monopoly or Perfect Collusion
Cournot
Bertrand
MR
MC
Q

• 
  
  
• Bertrand price competition each charge 200 ?
  each sell 400
  
• Cournot quantity competition each sell 267 units
  ? charge 466
  
• Perfect collusion each charge 600, sell 200
  each ½ monopoly profits each

7
How could collusion be sustained?

• Firms would like to collude
• But what is to prevent us from cheating on our
  collusive agreement?
  
• Cheating in a Bertrand environment
• undercutting your price
• Cheating in a Cournot environment
• selling extra quantity
• Clearly, we do not have a legally binding
  contract!
  
• What is keeping me from cheating?
• If anyone cheats, we will revert to
  competition, for the foreseeable future

8
Collusion in one-off repeated simultaneous
games a Cournot (quantity competition)
environment

• Mobil and Shell are in a Cournot environment
• Every month they choose the amount they produce
  (pump) before they get to market
  
• Mobil and Shell decide to collude at the monopoly
  output level
  
• produce half the monopoly quantity each lets
  call that Low Output
  
• Suppose there are only two choices of output
  High and Low

9
Cournot (quantity) environment
Well discuss where the numbers in the table come
from later
10
One-off game
Static Nash equilibrium
11
Repeated (dynamic) game can they agree to
cooperate?
Dynamic Nash Equilibrium???
12
Agreement to Cooperate (Collude)

• Mobil and Shell reach the following agreement
• if both of us chose Low Output last week, each
  of us will choose Low Output this week
  
• but if either player cheats on the agreement,
  well never collude again ? Well both choose
  High Output
  
• Question Is this agreement self-enforcing?
  (because we sure cant enforce it in court!)
  
• In other words, is it a Nash equilibrium?
• If the other player is following the agreement,
  is it my best response to stick to the agreement?

13
Nash equilibrium in repeated games

• To determine whether this is a Nash
  equilibrium
  
• Look at Mobils incentives
• If Mobil expects Shell to stick to the agreement
  ( not cheat), is Mobils best response to stick
  to the agreement?
  
• To answer this, you need to look at a decision
  tree for Mobil the payoff to cheat versus not
  cheat when Mobil knows that Shell is not
  cheating
• Then we look at Shells incentives in the same
  way
  
• If both would choose not cheat, its a Nash
  equilibrium
  
• But if either would prefer to cheat, its not a
  Nash equilibrium the agreement wont ever take
  place, because its not enforceable

14
The present value of profits from cooperating

• cooperate forever, given that
  Shell cooperates
  
• Mobil
• cheat today ? no cooperation ever
  after
  
• Note
• Which of these payoffs is bigger depends on the
  discount factor, d!
  
• If the discount factor is small enough (that is,
  if the discount rate is high enough) it will
  always be worthwhile to cheat

15
How to calculate the payoffs

• cooperate forever, given that
  Shell cooperates.
  
• Mobil
• cheat today ? no cooperation
  ever after
  
• Mobil cooperates if
• 80 19(1-?) 71 90 - 19?
• ? 0.5263
• Cooperate if the discount factor is above 0.5263
  ( discount ratebetween months below 90) ?
  pretty likely

d 1/(1r)
16
Cooperation from Shellboth players must want to
cooperate!

• cooperate forever, given that
  Mobil cooperates.
  
• Shell
• cheat today, then never
  cooperate
  
• This is the same condition as for Mobil
• ? Shell will want to cooperate if Mobil wants to
  cooperate
  
• But if there are asymmetries, you have to check
  both conditions

17
Practice (asymmetric) for what discount factor
can these players agree to cooperate?
18
Nash equilibrium in repeated games

• Cooperation is a Nash equilibrium only if both
  players find that their best response is to
  cooperate
  
• at ?0.4, Smitas best response to a cooperative
  agreement is to cooperate, but Ross would prefer
  to cheat
  
• at ?0.4, Smita doesnt believe that Ross will
  cooperate, so Smita doesnt enter a cooperative
  agreement
  
• No agreement
• at ?0.4, they play (Down, Right) every period
• But for any ?0.5, they would play (Up, Left)
  every period
  
• Cooperation is very likely, as ?0.5 means r

19
Bertrand (price competition) environment

• Two firms on the internet are selling identical
  software
  
• Every hour they can change their prices
• There is no real limit on the number of
  downloads
  
• unlimited capacity, and quantity is not
  pre-determined
  
• Bertrand competition
• Q 1000 P and MC 200
• If they collude
• They both charge 600, earn 80,000
• If someone cheats on the collusive agreement
• shell charge 599, earn 159,999
• If they are not cooperating (and both know the
  other is not cooperating)
  
• Theyll both charge 200, earn 0

20
gives the following payoff matrix
21
Determining whether a stable cooperative outcome
exists

• If youre not given a payoff matrix, construct it
  yourself
  
• Determine for what discount rates is collusion
  sustainable in this market- equate PV payoffs of
  collusion and cheating- solve for ? (and r)
  
• What is the answer here?

22
Cournot (quantity competition) environment

• Mobil and Shell pumping oil
• Q 1000 P and MC 200
  for each
  
• If they are competing (i.e. not colluding) their
  best response curves are
  
• QM 400 ½ QS
• QS 400 ½ QM
• and the intersection of those curves is QM
  266.66, QS 266.66, which means profits of
  71,111 each.
  
• If they cooperate, they each produce 200 and the
  market clearing price is 600 ? earn 80,000
  each
  
• But what are the payoffs if one player cheats?
• 90,000 to the cheater, and 60,000 to the
  other WHY?
  

23
gives the following payoff matrix
The cheater will choose her best response to the
amount produced by the other firm
This is where the numbers on page 9 come from
24
Tacit Collusion coordinating on high prices /
low quantities without communicating

• What makes collusion hard to achieve?
• Coordinating without directly communicating
• Ethical issues
• Why does knowing if it exists help?

25
1.a Collusion is impossible in a finite game

• Result from the centipede game
• If the game ends after a fixed number of periods,
  then no collusion can be sustained.
  
• Ex Generic drugs will flood our market in 2006
• Why? rollback
• In December 2005, no cooperation
• Can we agree to cooperate in November 2005,
  saying If you cooperate with me in November,
  Ill cooperate with you in December?
  
• Can we agree to cooperate in October?
• In the real world, you may cooperate for a
  while, but cooperation unravels when the end is
  apparent to all

26
1.b Impatience

• Anything that lowers your ? (raises your r) makes
  it harder to cooperate
  
• Suppose your initial discount factor is ?
• But now your firm is failing, and in every period
  there is a 20 chance that youll go bankrupt (it
  was approx. zero before)
  
• Then its your now discount factor is 0.8? ? a
  lower discount rateso more likely to cheat
  

27
1.c Costs benefits of cheating

• When the benefits to cheating are higher, youre
  more likely to cheat
  
• If it takes 3 periods for my competitor to
  realise that Im cheating
  
• because I get high profits for 3 periods
• Need to set up feedback mechanisms so that you
  hear about cheating quickly
  
• Example Kevin Smith Electronics offers to match
  the lowest price anywhere (a Meet the
  Competition clause), and a 15 rebate if the
  price is lower elsewhere
• Customers will inform Kevin Smith if his
  competitor has lowered the price.
  
• If you wont necessarily catch me cheating ?
  rebates, industry associations that share
  information

28
1.c Costs benefits of cheating (cont)

• Cheat if the benefits to cheating are high
  (cont)
  
• If its a really high demand period, or you have
  particularly low costs this period, you might be
  tempted to take advantage of that
  
• If your competitor will forgive you quickly
  (shell try to collude again)
  
• Cheat if the benefits to colluding are low
• If there are many firms in the market, then I am
  splitting the monopoly profits
  
• if its a Bertrand market, then I could undercut
  just a little and get the whole market profits
  
• Im more inclined to cheat than if there are 2 of
  us

29
1c. 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

30
1.d 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

31
2. Tacit collusion

• If you cant talk to each other, how do you agree
  on a price?
  
• Focal point something people gravitate to- if
  firms are identical, the monopoly price is an
  obvious focal point- but usually firms arent
  identical (different costs, products, etc) ?
  how do you coordinate?
• 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!)

32
3. Ethics of tacit collusion

• If customers are better off because of collusion,
  it may be 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
  (or less) prices (rather than monopoly prices)
  
• but such cases are rare

33
4. Why does knowing it exists help?

• 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?
• Sizable gap between P MC
• Prices dont change when costs or demand change
• Occasional price wars when prices go way down