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 55 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 56 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 57 •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 Πit = 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 58 • Future matters3. but Cartels less than and today: Collusion firms discount future profits with discount factor 0 < δ < 1 • Owners of firms value mt+1 = δmt 1 1− P δ = = 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 t t Vi = Σt δ πi •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 59 • Examples of simple3. Cartels strategies: and Collusion – One-shot Bertand price always – Tit-for-Tat: do today what rival did yesterday M M M – pi1= p ; pit= p if pjt-1= p , 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 ⇒ Πit = 0 M • Both always charge monopoly price and earn Πit = Πi /2 > 0 equilibrium? M –If j always charges pjt= p , what should i do? M –Look at rf: i should choose pit= p - ε –If i deviates from pM, it earns higher profits every period D M M Πi = p - ε > p /2 (D: deviate or defect), hence D t D M M t M M Vi = Σt δ Πit(pi ,pj ) > Vi = Σt δ Πit(pi ,pj ) 60 • ⇒ Strategy ”always3. Cartels monopoly and price” Collusion is not in equilibrium • ”Grim Strategy” (GS): M – Choose pi1= p M M – Choose pit= p if pjt-1= p – 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 61 • GS punishes defection3. Cartels forever 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 ΠM/2 each period – Temptation: gain ΠM - ΠM/2 - ε = ΠM/2 - ε during defection – Punishment: earn zero profits long enough so that profits (defect + punishment) < profits (collusion) • Minimum length of sufficient punishment depends on discount factor δ • 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 62 • "Folk Therorem":3. Cartels Any outcome and th Collusionat 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 C t C C C Vi = Σtδ Πit(pi ,pj ) = pi /(1-δ) t as Σt d = 1/(1-d) if |d| < 1 63 • PV of deviation3. = Cartels profits reap anded duringCollusion deviation + present value of profits earned during punishment: D D t P P D P Vi = Π + Σtδ Πit(pi ,pj ) = Π + δ pi /(1-δ) – Note: here punishment assumed to be infinitely long • Collusion is sustainable if π C δπ P π D − π C i > π D + i ⇒ δ > i i i D P 1 − δ 1 − δ πi − πi • 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 64 Homework 3. Cartels and Collusion • Assume Bertrand 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 – δ = 0.5 – δ = 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 65 Collusion with 3.Imperfect Cartels Information 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 66 Factors that Help3. CartelsCollusion 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: 1 p M Q( p M ) 1 p M Q( p M ) < ⇒ N < N 1−δ 1−δ 67 • Product differentation3. Cartels works and two Collusionways – 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 68 • Free capacity3. 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 69 • Firm symmetry3. 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 70 – Large firm3.