3 Cartels and Collusion Competition less than jointly

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 38 E 050 1 © Markku Stenborg 2005

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 HKKK TMP 38 E 050 2 © Markku Stenborg 2005

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 HKKK TMP 38 E 050 3 © Markku Stenborg 2005

• 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 HKKK TMP 38 E 050 4 © Markku Stenborg 2005

• 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 • 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 V i = t t i 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 HKKK TMP 38 E 050 5 © Markku Stenborg 2005

• Examples of simple strategies: 3. Cartels and Collusion – One-shot Bertand price always – Tit-for-Tat: do today what rival did yesterday – pi 1= p. M; pit= p. M if pjt-1= p. M, 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= p. M, what should i do? – Look at rf: i should choose pit= p. M- – If i deviates from p. M, it earns higher profits every period i. D = p. M- > p. M/2 (D: deviate or defect), hence Vi. D = t t it(pi. D, pj. M) > Vi. M = t t it(pi. M, pj. M) HKKK TMP 38 E 050 6 © Markku Stenborg 2005

• • Strategy ”always monopoly price” is not in equilibrium 3. Cartels and Collusion ”Grim Strategy” (GS): – Choose pi 1= p. M – Choose pit= p. M if pjt-1= p. M – 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 38 E 050 7 © Markku Stenborg 2005

• GS punishes defection forever 3. Cartels and Collusion • 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 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 38 E 050 8 © Markku Stenborg 2005

• "Folk Therorem": Any outcome that leaves each player more 3. Cartels and Collusion 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 Vi. C = t t it(pi. C, pj. C) = pi. C/(1 - ) as t dt = 1/(1 -d) if |d| < 1 HKKK TMP 38 E 050 9 © Markku Stenborg 2005

• PV of deviation = profits reaped during deviation + present 3. Cartels and Collusion value of profits earned during punishment: Vi. D = D + t t it(pi. P, pj. P) = D + pi. P/(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 HKKK TMP 38 E 050 10 © Markku Stenborg 2005

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 HKKK TMP 38 E 050 11 © Markku Stenborg 2005

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 period equil only possibility HKKK TMP 38 E 050 12 © Markku Stenborg 2005

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: HKKK TMP 38 E 050 13 © Markku Stenborg 2005

• Product differentation works two ways 3. Cartels and Collusion – 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 HKKK TMP 38 E 050 14 © Markku Stenborg 2005

• Free capacity 3. Cartels and Collusion – 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 HKKK TMP 38 E 050 15 © Markku Stenborg 2005

• 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 HKKK TMP 38 E 050 16 © Markku Stenborg 2005

– Large firm has a lot more capacity available and can gain 3. Cartels and Collusion 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 HKKK TMP 38 E 050 17 © Markku Stenborg 2005

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 HKKK TMP 38 E 050 18 © Markku Stenborg 2005

– Asymmetry may be pro-competitive 3. Cartels and Collusion – 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) HKKK TMP 38 E 050 19 © Markku Stenborg 2005

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 cost specification – “Wrong” model for demand and/or cost? HKKK TMP 38 E 050 20 © Markku Stenborg 2005

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 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 HKKK TMP 38 E 050 21 © Markku Stenborg 2005