Transcript TMP 38E050 Advanced Topics Economics of Competition and

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 > 5, best strategy in stage 1 is to stay out
– If n < 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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• How to punish?
3. Cartels and Collusion
• 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) < 1
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• Future matters but less than today: firms discount future
3. Cartels and Collusion
profits with discount factor 0 <  < 1
• Owners of firms value mt+1 = mt
1
1 P


1 r 1 k
• 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 stream
Vi = 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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• Examples of simple strategies:
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– 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 > 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-  > pM/2 (D: deviate or defect), hence
ViD = t t it(piD,pjM) > ViM = t t it(piM,pjM)
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•
•
•
•
 Strategy ”always monopoly price” is not in equilibrium
3. Cartels and Collusion
”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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• GS punishes defection forever
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• 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) < 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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• "Folk Therorem": Any outcome that leaves each player more
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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 here
ViC = ttit(piC,pjC) = piC/(1-)
as t dt = 1/(1-d) if |d| < 1
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• PV of deviation = profits reaped during deviation + present
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value of profits earned during punishment:
ViD = D + ttit(piP,pjP) = D +  piP/(1-)
– Note: here punishment assumed to be infinitely long
• Collusion is sustainable if
πiC
1 δ
>
πiD
+
δπiP
1 δ
 δ>
πiD  πiC
πiD  πiP
• 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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Homework
3. Cartels and Collusion
• Assume duopoly, c=0, 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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Collusion with Imperfect Information
3. Cartels and Collusion
• 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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Factors that Help Collusion
3. Cartels and 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:
M
M
1
p
Q
(
p
)
M
M
p Q( p ) 
N 1 
N
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1 
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• Product differentation works two ways
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– 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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• Free capacity
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– 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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• Firm symmetry
3. Cartels and Collusion
– 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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– Large firm has a lot more capacity available and can gain
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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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Collusion and Antitrust
3. Cartels and Collusion
• 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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– Asymmetry may be pro-competitive
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– 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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Detecting Collusion
3. Cartels and 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 firm’s ability to price above cost
• In oligopoly, supply behavior equation is aggregate firstorder 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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Example
3. Cartels and Collusion
• 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
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