3. Cartels and Collusion

HKKK TMP 38E050

© Markku Stenborg 20051

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

HKKK TMP 38E050


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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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) < 1

HKKK TMP 38E050


3. Cartels and Collusion• Future matters but less than today: firms discount future profits with discount factor 0 < < 1

• Owners of firms value mt+1 = 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 ti

t

• 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

kP

r

11

11

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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 = i

M/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(pi

D,pjM) > Vi

M = t t it(piM,pj

M)

HKKK TMP 38E050


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

HKKK TMP 38E050


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) < 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

HKKK TMP 38E050


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 hereVi

C = ttit(piC,pj

C) = piC/(1-)

as t dt = 1/(1-d) if |d| < 1

HKKK TMP 38E050


3. Cartels and Collusion• PV of deviation = profits reaped during deviation + present value of profits earned during punishment:Vi

D = D + ttit(piP,pj

P) = 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

1 1 C P D C

Di i i ii D P

i i

π δπ π π> π + δ >

δ δ π π

HKKK TMP 38E050


3. Cartels and CollusionHomework• 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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3. Cartels and CollusionCollusion 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

HKKK TMP 38E050


3. Cartels and CollusionFactors 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:

1)(1)(

MMMM pQp

NpQp

11N

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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

HKKK TMP 38E050


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 CollusionCollusion 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 CollusionDetecting 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 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?

HKKK TMP 38E050


3. Cartels and CollusionExample• 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 functionCi(qit) = ci qd

it

• FOC for maximizing per period profits by choosing qit:[2] pt(1 + e/it) = ci qd

it 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

3. Cartels and Collusion

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