3. Cartels and Collusion

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3. Cartels and Collusion

• Competition ? less than jointly max profit ?
  firms have incentives to avoid competition
• These incentives are basis for competition policy
• Explicit cartels, implicit tacit collusion
• How would these show up in reaction fn picture?
• Detect Cartels and Collusion?
• Hard to do w/ econ alone
• Lerner Index L (p - ci)/p si/e?
• If p, si and e known, make inference on p - ci
• Often not practical p, ci and e not known
  accurately enough
• But with good enough data this can be done
• Identical prices?
• Not evidence for cartel
• Perfect competition ? identical prices

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3.1 Explicit Cartel

• Intuition
• Few competitors ? easy to form cartel/collude
• Many competitors ? hard to form cartel/collude
• Selten (1973) 4 is few, 6 is many
• Intuition w/ 6 competitors staying outside
  cartel gives more than joining cartel w/ 5 other
  firms
• Result from 2-stage model
• 1. Decide to join/stay out
• 2. Choose output
• If n gt 5, best strategy in stage 1 is to stay out
• If n lt 5, best strategy in stage 1 is join cartel

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3.2 Tacit Collusion

• Implicit agreement or understanding not to
  compete
• Eg. firms "agree" on monopoly price and output
• Unstable cheating and undercutting gives even
  higher profits than collusion, if rivals adher to
  agreement
• Need mechanism to remove incentives for cheating
• "Stick-and-Carrot" Theory
• Cheating draws punishment and low profits in
  future
• Collusion draws rewards (high profits)
• Deters from cheating on promise to fix prices
• Future reward ? Collude now
• Requires that future matter

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3. Cartels and Collusion

• How to punish?
• Price war
• Punishment will also hurt the punisher
• Need incentives to punish
• Collusion in Bertrand Competition
• Read Motta Ch 4
• Model firms interact repeatedly
• Assume c 0, mkt demand q a - bp
• Per period profits now ?it pit qit(pit, pjt)
• Bertrand equil price for one-shot game 0
• Each period t each firm chooses price pit knowing
  all previous prices pit-s, s 1,2,3,
• No end-game problem repeat per-period game
  infinitely many times
• Or Prob(next period is last) lt 1

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3. Cartels and Collusion

• Future matters but less than today firms
  discount future profits with discount factor 0 lt
  ? lt 1
• Owners of firms value mt1 ?mt
• where r is discount (or interest) rate, P
  probability that game ends after this period and
  k firm's marginal cost of capital
• Firm goal max present value of per-period profit
  streamVi ?t ?t?it
• Strategy?
• Plan ahead how to play entire game
• What per-period moves to choose after any history
• Think players desing strategy before game starts
  and then leave computers to execute strategy

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3. Cartels and Collusion

• Examples of simple strategies
• One-shot Bertand price always
• Tit-for-Tat do today what rival did yesterday
• pi1 pM pit pM if pjt-1 pM, else pit 0
• Equilibrium No incentive to change strategy
• Is "always one-shot Bertrand equil behavior"
  still an equil strategy?
• Yes if i always chooses pit 0, best j can do
  is to choose pjt 0 ? ?it 0
• Both always charge monopoly price and earn ?it
  ?iM/2 gt 0 equilibrium?
• If j always charges pjt pM, what should i do?
• Look at rf i should choose pit pM- ?
• If i deviates from pM, it earns higher profits
  every period ?iD pM- ? gt pM/2 (D deviate or
  defect), henceViD ?t ?t ?it(piD,pjM) gt ViM
  ?t ?t ?it(piM,pjM)

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3. Cartels and Collusion

• ? Strategy always monopoly price is not in
  equilibrium
• Grim Strategy (GS)
• Choose pi1 pM
• Choose pit pM if pjt-1 pM
• Else always choose pit 0
• Suppose j knows i plays GS what is best for j?
• GS is best reply (among others)
• ? GS is a best reply against itself
• ? Both firms using GS is an equilibrium
• Punishment needs to be credible, otherwise it is
  only empty threat
• There must be incentives to start punishment
• Punishment must be part of equilibrium path from
  that moment onward, so that no firm will want to
  deviate from punishment
• One-shot Nash equil behavior always credible
  punishment

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3. Cartels and Collusion

• GS punishes defection forever
• Punishment "too hard", lesser punishment suffices
• Optimal punishment shortest number of periods T
  such that extra profits gained by defection are
  vanished
• Stay on intended equil path earn ?M/2 each
  period
• Temptation gain ?M - ?M/2 - ? ?M/2 - ? during
  defection
• Punishment earn zero profits long enough so that
  profits (defect punishment) lt profits
  (collusion)
• Minimum length of sufficient punishment depends
  on discount factor ?
• Often optimal punishment is minimax strategy of
  per period game, ie tougher than one-shot equil
  behavior
• GS easy to use
• Point here collusive outcome, not details how one
  supports outcome

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3. Cartels and Collusion

• "Folk Therorem" Any outcome that leaves each
  player more than one-shot minmax is sustainable
  as an equil outcome in infinitely repeated game
• There are many equilibrium strategies
• "Anything" is in equil
• No predictive power w/o more assumptions
• Generally collusion is sustainable if temptation
  to defect is low enough and punisment following
  the deviation strong enough
• Firm wants to keep colluding if present value of
  devi-ating is smaller than present value of
  adhering to collusive agreement
• PV of collusion hereViC ?t?t?it(piC,pjC)
  piC/(1-?)as ?t dt 1/(1-d) if d lt 1

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3. Cartels and Collusion

• PV of deviation profits reaped during deviation
  present value of profits earned during
  punishmentViD ?D ?t?t?it(piP,pjP) ?D ?
  piP/(1-?)
• Note here punishment assumed to be infinitely
  long
• Collusion is sustainable if
• Incentive to deviate depends on discount factor
• If discount factor is too low to support
  collusion, either toughen up punishment or try to
  lower degree of collusion
• Longer or harder price war
• Reduce collusive prices from monopoly price
• Note punisments are never observed
• None used since threat is enough

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3. Cartels and Collusion

• Homework
• Assume duopoly, c0, mkt demand q 100 - p, and
  price must be integer (100, 99, 98, ...)
• Assume punishment pt 0 ( c)
• What is optimal punishment strategy for
• ? 0.5
• ? 1
• Need to find i) monopoly price and profits and
  ii) optimal one-period defection for i if j
  charges monopoly price
• Then calculate how long price war needed to make
  defection unprofitable

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3. Cartels and Collusion

• Collusion with Imperfect Information
• What if firms cannot observe rivals' exact prices
  nor quantities sold?
• ? Don't know if rival defected ? don't know when
  to start price war
• No threat of price war ? collusion not
  sustainable?
• Use other info Sales were less than expected
• Think Bertrand oligopoly with identical goods and
  with stochastic demand
• Firm has 0 demand today somebody deviated and
  stole customers or shift in demand?
• Start price war when price or demand drops
  "enough"
• Start price war even if you know nobody deviated,
  as nobody has incentives to deviate
• Intuition no punishment ? no firm has incentives
  to collude ? per period equil only possibility

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3. Cartels and Collusion

• Factors that Help Collusion
• General idea stronger, earlier and more certain
  punishment increases possibilities to collusion
• Topsy-Turvy principle the more firms have
  opportunities for aggressive competition, the
  less competition there is
• Public prices and other market transparency
• Easy to observe deviation
• Size of cartel
• N equally sized firms
• Each firm receives 1/Nth share of total monopoly
  profits
• Collusion sustainable if one shot defection
  followed by punishment leaves less profits that
  staying on collusive path

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3. Cartels and Collusion

• Product differentation works two ways
• More products are differentiated, the larger
  price decrease needed to
• steal mkt share
• punish deviator
• More products are differentiated, less incentive
  to cheat and try to steal mkt share
• More products are differentiated, less price war
  by rivals affects profits
• Introduces non-price competition more variables
  to monitor and more ways to cheat
• Cost conditions and capacity utilization
• Capacity constraint or steeply rising MC reduce
  profit margin for extra output
• Reduce incentive to cheat
• Reduces possibilities and incentives to punish

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3. Cartels and Collusion

• Free capacity
• Increases temptation to cheat
• Allows harsher punishment ? increases
  possibilities and incentives to punish
• Elasticity of firm demand
• Inelastic firm demand ? more mkt share means
  significant reduction in price ? less incentive
  to cheat
• More elastic demand is, the harder it is to
  sustain collusion
• Multimarket contact
• Firms produce several competing goods or operate
  on several geographic mkts
• More opportunities to cheat
• Price war on all mkts ? allows more severe
  punishments

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3. Cartels and Collusion

• Firm symmetry
• Firms have different shares of a specific asset
  (capital) which affects marginal costs
• Joint profit maximization output is shifted away
  from small (inefficient) firms towards large
  (efficient) firms
• Smallest firm has highest potential to steal
  business of its rivals and, has highest
  incentives to disrupt collusive agreement
• Incentives to deviate are reversed when
  equilibrium calls for punishments
• Largest firm loses most at punishment phase, it
  will have highest incentives to deviate from
  punishment
• Capacity constraints
• Incentives to stay in collusive equilibrium are
  very different for large and small firms
• Small firm will have some incentive to cheat in
  short run, as it can only increase its sales
  marginally up to capacity level

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3. Cartels and Collusion

• Large firm has a lot more capacity available and
  can gain more customers with same price deviation
  from collusive norm
• Large firms tend to have a greater incentive to
  deviate from collusive price
• Asymmetry in capacities will also have an
  important effect on effective punishments
• Worst punishment firm can impose on its
  competitors is to produce up to full capacity
• Small firm that is already producing at almost
  full capacity has low possibilities to punish
  rivals that do not follow collusive norm
• Large firm competing with small firm will have
  large incentives to deviate from any collusive
  norm without this being disciplined threat of low
  prices in future
• Increases in asymmetries in capacities make
  collusion more difficult

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3. Cartels and Collusion

• Collusion and Antitrust
• See Motta Ch 4, Europe Economics report,
  UPM/Haindl and Gencor/Lonrho decisions, and
  browse my forest paper
• Joint dominance and coordinated effects in legal
  jargon collusion in econ jargon
• Core of policy problem Collusion arises as
  equilibrium behavior
• Hard to prohibit or deal with ex post
• Solution try to prevent collusion, ban business
  practices and mergers that help to facilitate
  collusion see above
• Analyses of asymmetry in assets and capacity
  constraints suggest merger guidelines that differ
  from traditional wisdom
• For a given number of firms, Herfindahl and other
  concentration tests predict that more symmetric
  industry is more competitive

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3. Cartels and Collusion

• Asymmetry may be pro-competitive
• Asymmetric industry may even more than compensate
  for reduction in number of firms in merger
  involving large firm
• Increased asymmetry hurts collusion and may
  benefit competition
• How to identify collusion?
• Possible to detect collusion from behavior alone?
• Firms have more mkt power than one shot equil?
• Estimate cost, demands and reaction fns and
  compare actual behavior to non-cooperative and
  collusive equil
• Doable, but gets technical with differentiated
  products (see Nevo, Slade)

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3. Cartels and Collusion

• Detecting Collusion
• Inferences about competition from price and
  quantity data rest on assumptions on 1) demand,
  2) costs, and 3) nature of firms unobservable
  strategic interactions see Market Power above
• Demand specification plays critical role in
  competition models
• Demand position, shape and sensitivity to
  competitors actions affects firms ability to
  price above cost
• In oligopoly, supply behavior equation is
  aggregate first-order condition for
  profit-maximization, not aggregate MC curve
• Mark-up supply MC depends on firms
  competitive interactions
• Data can be consistent both with collusion and
  competition, depending on demand and cost
  specification
• Wrong model for demand and/or cost?

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3. Cartels and Collusion

• Example
• Constant elasticity industry demand curve at each
  period t
• 1 ln Qt a e ln Pt b Zt ut,
• where e is demand elasticity, Zt vector of
  demand shifters and ut error term
• Constant elasticity variable cost function
• Ci(qit) ci qdit
• FOC for maximizing per period profits by choosing
  qit
• 2 pt(1 e/?it) ci qdit
• where ?it is CV parameter (?Qt/?qit) (qit/Qt)
• Recall, for cartel ?it 1, ?it 1/N for
  symmetric Cournot
• Observing ?it close to one or much above 1/N
  indication for collusion
• We only observe (Qt,Pt) pairs that solve true
  1 and 2, not functions themselves, so
  assumptions on functions and stochastics (ut)
  matter