3. Cartels and Collusion
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1 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 - c i )/p = s i /e? If p, s i and e known, make inference on p - c i Often not practical: p, c i 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
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 56
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 57
4 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 Π it = p it q it (p it, p jt ) Bertrand equil price for one-shot game = 0 Each period t each firm chooses price p it knowing all previous prices p it-s, s = 1,2,3, No end-game problem: repeat per-period game infinitely many times Or: Prob(next period is last) < 1 58
5 Future matters but less than today: firms discount future profits with discount factor 0 < δ < 1 Owners of firms value m t+1 = δm t 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 V i = Σ t δ t π 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 59
6 Examples of simple strategies: One-shot Bertand price always Tit-for-Tat: do today what rival did yesterday p i1 = p M ; p it = p M if p jt-1 = p M, else p it = 0 Equilibrium: No incentive to change strategy Is "always one-shot Bertrand equil behavior" still an equil strategy? Yes: if i always chooses p it = 0, best j can do is to choose p jt = 0 Π it = 0 Both always charge monopoly price and earn Π it = Π im /2 > 0 equilibrium? If j always charges p jt = p M, what should i do? Look at rf: i should choose p it = p M - ε If i deviates from p M, it earns higher profits every period Π i D = p M - ε > p M /2 (D: deviate or defect), hence V i D = Σ t δ t Π it (p id,p jm ) > V i M = Σ t δ t Π it (p im,p jm ) 60
7 Strategy always monopoly price is not in equilibrium Grim Strategy (GS): Choose p i1 = p M Choose p it = p M if p jt-1 = p M Else always choose p it = 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
8 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 Π M /2 each period Temptation: gain Π M - Π M /2 - ε = Π M /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
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 V C i = Σ t δ t Π it (p ic,p jc ) = p ic /(1-δ) as Σ t d t = 1/(1-d) if d < 1 63
10 PV of deviation 3. = Cartels profits reaped and during Collusion deviation + present value of profits earned during punishment: V D i = Π D + Σ t δ t Π it (p ip,p jp ) = Π D + δ p ip /(1-δ) Note: here punishment assumed to be infinitely long Collusion is sustainable if C i P i π D δπ > πi + δ > 1 δ 1 δ π π D i D i π π C i P i 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
11 Homework Assume Bertrand duopoly, c=0, mkt demand q = p, and price must be integer (100, 99, 98,...) Assume punishment: p t = 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
12 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 66
13 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/N th share of total monopoly profits Collusion sustainable if one shot defection followed by punishment leaves less profits that staying on collusive path: p M Q( p M ) < 1 N p M Q( p 1 δ M ) N 1 < 1 δ 67
14 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 68
15 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 69
16 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 70
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 and capacities make collusion more difficult 71
18 Collusion and Antitrust Read Motta Ch 4, Europe Economics report, UPM/Haindl decision p. 18-, and browse my forest paper Joint dominance, coordinated effects are legal jargon ~ collusion in econ jargon How to identify collusion or separate collusion from competition? Authorities/customers need to argue that collusive equilibrium is being played Suspected firms want to argue that behavior is as if noncooperative Cournot or Bertrand equil is being played 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 technical (Nevo, Slade) See my forest paper 72
19 Core of policy problem: Collusion arises as an equilibrium behavior Hard to prohibit or deal with ex post Solution: try to prevent collusion, ban business practices and mergers that help facilitate collusion 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 tend to predict that a more symmetric industry is more likely to be more competitive Analysis instead suggest that asymmetry may be procompetitive 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 73
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