# 3. Cartels and Collusion Competition  less than jointly max profit  firms have incentives to avoid competition These incentives are basis for competition.

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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

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

3.2 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

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

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

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

 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

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

"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

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

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

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

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

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

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

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

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

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

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

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

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

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