Cartel Stability: Trigger Strategies and Cheating Detection

Lecture 14 (II)Collusion in practice: Cartel stability ECON 312: Industrial Organization

Introduction • Cartel stability • Trigger strategies • The Folk Theorem • Cartel formation • Detecting cheating

Cartel Stability (cont.) • Analysis of infinitely or indefinitely repeated games is less complex than it seems • Cartel can be sustained by a trigger strategy • “I will stick by our agreement in the current period so long as you have always stuck by our agreement” • “If you have ever deviated from our agreement I will play a Nash equilibrium strategy forever”

Cartel Stability (cont.) • Take Example 1 but suppose that there is a probability r in each period that the market will continue: • Cooperation has each firm producing 30 thousand • Nash equilibrium has each firm producing 40 thousand • So the trigger strategy is: • I will produce 30 thousand in the current period if you have produced 30 thousand in every previous period • if you have ever produced more than 30 thousand then I will produce 40 thousand in every period after your deviation • This is a “trigger” strategy because punishment is triggered by deviation of the partner • Does it work?

Cartel Stability (cont.) • So there is a probability r in each period that the market will continue • And also a rate at which firms discount the future, that results in a discount factor R

Cartel Stability (cont.) • Profit from sticking to the agreement is: • PVC = 1.8 + 1.8 G + 1.8 G2 + … A cartel is more likely to be stable the greater the probability that the market will continue and the lower is the discount rate = 1.8/(1 - G) • Profit from deviating from the agreement is: • PVD = 2.025 + 1.6 G + 1.6 G2 + … = 2.025 + 1.6 G /(1 - G) • Sticking to the agreement is better if: • PVC > PVD 1.8 1.6 G this requires: > 2.025 + which requires G = rR> 0.592 1 - G 1 - G if r = 1 we need r < 86%; if r = 0.6 we need r < 13.4%

Cartel Stability (cont.) • This is an example of a more general result • Suppose that in each period • profits to a firm from a collusive agreement are pM • profits from deviating from the agreement are pD • profits in the Nash equilibrium are pN • we expect that pD > pM > pN • Cheating on the cartel does not pay so long as: There is always a value of G < 1 for which this equation is satisfied This is the short-run gain from cheating on the cartel This is the long-run loss from cheating on the cartel pD - pM G > pD - pN • The cartel is stable • if short-term gains from cheating are low relative to long-run losses • if cartel members value future profits (high probability-adjusted discount factor)

Cartel stability Same type of example now using directly Rr (same idea) • Expected profit from sticking to the agreement is: • PVM= 1800 + 1800Rr + 1800R2r2 + … = 1800/(1 - Rr) • Expected profit from deviating from the agreement is • PVD = 2025 + 1600Rr + 1600R2r2 + … = 2025 + 1600Rr/(1 - Rr) • Sticking to the agreement is better if PVM > PVD • this requires 1800/(1 - Rr) > 2025 + 1600Rr/(1 - Rr) • or Rr > (2.025 – 1.8)/(2.025 – 1.6) = 0.529 • if r = 1 this requires that the discount rate is less than 89% • if r = 0.6 this requires that the discount rate is less than 14.4% Chapter 14: Price-fixing, Repeated Games, and Antitrust Policy

Cartel Stability (cont.) • What about example with two trigger strategies? • two possible trigger strategies • price forever at $130 in the event of a deviation from $160 • price forever at $105 in the event of a deviation from $160 • Which? • there are probability-adjusted discount factors for which the first strategy fails but the second works • Simply put, the more severe the punishment the easier it is to sustain a cartel

Trigger strategies • Any cartel can be sustained by means of a trigger strategy • prevents destructive competition • But there are some limitations • assumes that punishment can be implemented quickly • deviation noticed quickly • non-deviators agree on punishment • sometimes deviation is difficult to detect • punishment may take time => rewards to deviation are increased!

Trigger strategies • The main principle remains • if the discount rate is low enough then a cartel will be stable provided that punishment occurs within some “reasonable” time • But problem: detection and punishment might not be easy, cheap,… or quick

Trigger strategies (cont.) • Another problem: a trigger strategy is • harsh • unforgiving • Important if there is any uncertainty in the market • suppose that demand is uncertain, and one cannot really observe others’ prices… A firm in this cartel does not know if a decline in sales is “natural” or caused by cheating Suppose that the agreed price is PC Price There is a possibility that demand may be low Actual sales vary between QL and QH And a possibility that demand may be high This is the expected market demand Expected sales are QE PC DH DL DE Quantity QL QE QH

Trigger strategies (cont.) • These objections can be overcome • limit punishment phase to a finite period • take action only if sales fall outside an agreed range • Makes agreement more complex but still feasible • Further limitation • approach is too effective • result of the Folk Theorem Suppose that an infinitely repeated game has a set of pay-offs that exceed the one-shot Nash equilibrium pay-offs for each and every firm. Then any set of feasible pay-offs that are preferred by all firms to the Nash equilibrium pay-offs can be supported as subgame perfect equilibria for the repeated game for some discount factor sufficiently close to unity.

The Folk Theorem • Take example 1. The feasible pay-offs describe the following possibilities p2 $1.8 million to eachfirm may not be sustainable but something less will be Collusion on monopoly gives each firm $1.8 million The Folk Theorem states that any point in this triangle is a potential equilibrium for the repeated game $2.1 If the firms collude perfectly they share $3.6 million $2.0 If the firms compete they each earn $1.6 million $1.8 $1.6 p1 $1.8 $1.5 $1.6 $2.0 $2.1

Stable cartels (cont.) • A collusive agreement must balance the temptation to cheat • In some cases the monopoly outcome may not be sustainable (the temptation to cheat is to strong!) • But the folk theorem indicates that collusion is still feasible • there will be a collusive agreement: • that is still better than competition • But it is not as good as to be subject to the temptation to cheat

Cartel Formation • What factors are most conducive to cartel formation? • sufficient profit motive • means by which agreement can be reached and enforced

Cartel Formation • The potential for monopoly profit • collusion must deliver an increase in profits: this implies • demand is relatively inelastic • restricting output increases prices and profits • you want to be able to raise the prices (cartelize the market for heroin for example, or for oil) • entry is restricted • high profits encourage new entry • but new entry dissipates profits (OPEC) • new entry undermines the collusive agreement

Cartel formation (cont.) • So there must be means to deter entry • common marketing agency to channel output (such as de Beers or the auctioneers Christie’s and Sotheby’s) • consumers must be persuaded of the advantages of the agency • lower search costs • greater security of supply • wider access to sellers • denied access if buy outside the agency (De Beers) • trade association (PEI mussels, Florida oranges, lawyers bars, doctors, professors, veterinaries, etc. ) They have persuaded consumers that the association is in their best interests. These associations might seem to be there only to protect quality and provide information…but they also facilitate collusion

Cartel formation (cont.) • Costs of reaching a cooperative agreement • even if the potential for additional profits exists, forming a cartel is time-consuming and costly • has to be negotiated • has to be hidden • has to be monitored

Cartel formation (cont.) • Costs of reaching a cooperative agreement • There are factors that reduce the costs of cartel formation • small number of firms (recall Selten) so negotiation is easier and cheating can be detected easily • high industry concentration • makes negotiation, monitoring and punishment (if necessary) easier • similarity in production costs (otherwise the firms need to produce different outputs, get different profits, and perhaps some might even need to close!!!) • product homogeneity lack of significant product differentiation (with differentiated products it is more difficult to get an agreement on prices and outputs, since there will be a variety of products, prices, and quantities to agree upon)

Cartel formation (cont.) • Similarity in costs • suppose two firms with different costs • if they collude they can attain some point on p*1p*2 p2 If all output is made by firm 2 this is total profit  p*1p*2 is curved because the firms have different costs pm  pmpm has a 450 slope and is tangent to p*1p*2 at M p*2 at M firm 1 has profit p1m and firm 2 p2m (joint profit is maximum) C p2C M If all output is made by firm 1 this is total profit p2m assume Cournot equilibrium is at C (inside the frontier, it was inefficient remember?) firm 2 will not agree to collude on M without a side payment from firm 1 p1 p1C p1m p*1 pm

Cartel formation (cont.) • Note that if the costs were the same for both, the curve would be more symmetric and the point M would be in the middle with equal profits for each, everyone would be happy  p2 pm Also, if the costs were not only equal but constant for each firm That frontier would be straight, It would not matter how much each Produced. Share it 50-50 and everyone is happy  45 degrees p*2 p2C M p2m C p1 p1C p1m p*1 pm

Cartel formation (cont.)  with side payments it is possible to collude to somewhere on DE (basically like trading) p2 pm  but side payments increase the risk of detection E B  without side payments it is only possible to collude to somewhere on AB p*2 C D p2C M p2m  this type of collusion is difficult and expensive to negotiate: e.g. possibility of misrepresentation of costs A p1 p1C p1m p*1 pm

Cartel formation (cont.) • Lack of product differentiation • if products are very different then negotiations are complex • need agreed price/output/market share for each product • monitoring is more complex • Most cartels are found in relatively homogeneous product markets • Or firms have to adopt mechanisms that ease monitoring • basing point pricing

Cartel formation (cont.) • Low costs of maintaining a cartel agreement • it is easier to maintain a cartel agreement when there is frequent market interaction between the firms • over time • over spatially separated markets • relates to the discussion of repeated games • less frequent interaction leads to an extended time between cheating, detection and punishment • makes the cartel harder to sustain

Cartel formation (cont.) • Stable market conditions • accurate information is essential for maintaining a cartel • makes monitoring easier • unstable markets lead to confused signals • makes collusion “near” to monopoly difficult • uncertainty can be mitigated • trade association • common marketing agency • controls distribution and improves market information (firms learn about each other and about each other’s costs, so they can detect cheaters easily)

Cartel formation (cont.) • Other conditions make cartel formation easier • detection and punishment should be simple and timely • geographic separation through market sharing is one popular mechanism • If we have many customers in the market it is easier to detect cheating

Cartel formation (cont.) • Other tactics encourage firms to stick by price-fixing agreements • most-favored customer clauses, which is a sales contract that guarantees that if I sell to you at a lower price I need to sell to everyone at that lower price • reduces the temptation to offer lower prices to new customers • meet-the competition clauses • makes detection of cheating very effective • if you find it cheaper we will give you twice the difference!!! This ad gives you info on someone cheating and pre-commits you to reduce the price as retaliation, even if it is not in your own interest

Meet-the-competition clause  the one-shot Nash equilibrium is (Low, Low)  meet-the-competition clause removes the off-diagonal entries  now (High, High) is easier to sustain Firm 2 High Price Low Price High Price 12, 12 5, 14 5, 14 Firm 1 Low Price 14, 5 14, 5 6, 6

Cartel Detection • Cartel detection is far from simple • most have been discovered by “finking” • even with NASDAQ telephone tapping was necessary • If members of a cartel are sophisticated they can hide the cartel: make it appear competitive • “the indistinguishability theorem” • The Cournot model illustrates this “theorem”

The Indistinguishability Theorem  start with a standard Cournot model: C is the non-cooperative equilibrium q2 R1  assume that the firms are colluding at M: restricting output  M can be presented as non-collusive if the firms exaggerate their costs or underestimate demand R’1 C  this gives the apparent best response functions R’1 and R’2 M R’2 R2  M now “looks like” the non-cooperative equilibrium q1

An Example  Suppose market demand is P = 100 - Q, that there are 3 firms and that each firm has true marginal costs of $20 The Cournot equilibrium market price and the outputs for each firm are given by the equations: qi = (A - c)/(N + 1); PC = (A + cN)/(N + 1) where we have that A = 100, c = 20, N = 3  So we have: qi = 20 and PC = $40  Suppose the firms are colluding on the monopoly price, which is (A + c)/2 = $60  What production cost 20 + f would make this look like a Cournot price? We need (100 + 3(20 + f))/4 = 60; so 160 + 3f = 240 which gives f = $80/3 = $26.67  The same result can be obtained by overestimating the reservation price (the 100 intercept in the demand curve)

Cartel detection (cont.) • Cartels have been detected in procurement auctions • bidding on public projects; exploration • the electrical conspiracy using “phases of the moon” • those scheduled to lose tended to submit identical bids • but they could randomize on losing bids! • Suggested that losing bids tend not to reflect costs • correlate losing bids with costs! There might also be a workable technical test against the indistinguisability theorem

Next • Contractual Relations between firms • Horizontal Mergers • Vertical and conglomerate mergers • Vertical price restraints • Read Ch. 16 and 17

Firm 1 $105 $130 $160 (7.3125, 7.3125) (8.25, 7.25) (9.375, 5.525) $105 $130 (7.25, 8.25) (8.5, 8.5) (10, 7.15) Firm 2 $160 (5.525, 9.375) (7.15, 10) (9.1, 9.1) Example 2: A Bertrand Game

Basing Point Pricing Then it was priced at the mill price plus transport costs from Pittsburgh Pittsburgh Suppose that the steel is made here And that it is sold here Birmingham Steel Company

Cartel Stability: Trigger Strategies and Cheating Detection