1. 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

2. 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

3. 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

4. 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
3. Cartels and Collusion

5. 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 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
3. Cartels and Collusion

6. 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 > 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)
3. Cartels and Collusion

7.  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
3. Cartels and Collusion

8. 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
3. Cartels and Collusion

9. "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 here ViC = ttit(piC,pjC) = piC/(1-) as t dt = 1/(1-d) if |d| < 1
3. Cartels and Collusion

10. PV of deviation = profits reaped during deviation + present 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
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
3. Cartels and Collusion

11. 3. Cartels and Collusion Homework
Assume duopoly, c=0, mkt demand q = 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
3. Cartels and Collusion

12. 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
3. Cartels and Collusion

13. 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:
3. Cartels and Collusion

14. 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
3. Cartels and Collusion

15. 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
3. Cartels and Collusion

16. 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
3. Cartels and Collusion

17. 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
3. Cartels and Collusion

18. 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
3. Cartels and Collusion

19. 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)
3. Cartels and Collusion

20. 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 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?
3. Cartels and Collusion

21. 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