250   Oligopoly and Strategic Interaction
We can illustrate the folk theorem using our Cournot duopoly example. If the two firm., collude to maximize their joint profits, they share aggregate profits of 2nm = fcs£/jr they act noncooperatively, they each earn nn = f"~';>2.1
The folk theorem says that any cartel agreement in which each firm earns more than and hi which total profit does not exceed can, at least in principle, be
sustained as a subgame-perfect equilibrium of the infinitely repeated game.
The folk theorem does not say that firms can always achieve total industry profit equal to that earned by a monopoly. It simply says that firms can do better than the noncooperative Nash equilibrium. The reason that exact duplication of monopoly may not be possible v.. that duplicating the monopoly outcome gives members a tremendous incentive to cheal unless the probability-adjusted discount factor is fairly large. However, the incentive to break the monopoly agreement does not mean that no cartel can be sustained. Firms-can still earn profits higher than the noncooperative equilibrium by means of a sustainable cartel agreement, even if they cannot earn the highest possible profits that the industry could yield. This is what the folk theorem says.
Before leaving this discussion of the feasibility of collusion we note that the foregoing analysis implicitly assumes that a fair bit of information is available lo all the firms, including typically information on rivals' prices. However, many if not most cartels involve upstream markets where the colluders are suppliers selling to industrial firms. In such cases, prices are often privately negotiated and therefore unobservable although market share data may be collected. Nevertheless, recent work by Athey arid Bagwell (2001) and Harrington and Skrzypacz (2007) show that collusion may still be sustained in such cases if punishments can be imposed asymmetrically so that the likely cheaters are treated more harshly than other firms unlike the symmetric punishments applied in the trigger strategies above.15 In sum, once we consider a framework of infinitely or indefinitely repeated interaction between firms, there is a real possibility for sustainable collusive behavior among these firms, so long as the discount factor is not too low and the probability of their continued interaction is not too low.
10.3   EMPIRICAL APPLICATION 1
Estimating the Effects of Price-Fixing
We have seen that both theory and evidence imply that the threat of cartels is a real one. Even so, that threat may be minimal from a policy viewpoint if, when they happen, cartels have only minor effects on prices and quantities. As we noted above, the folk theorem does not assert that the cartel can duplicate the monopoly profit. It only asserts that (he cartel members can do better than the one-shot Nash outcome. This leaves open the possibility that while cartels may be successful in raising prices above the noncooperative level, they may not raise them much higher. If that is the typical outcome, then there may still be little need to devote much effort to detecting and prosecuting such cartels.
15 An example would be the punishment scheme adopted in the lysine cartel in which a Arm that exceeded its production quota was required to buy that excess back from the other colluding firms. See Connor (2001).
Price Fixing and Repeated Games 251
, litis, to evaluate fully the cartel threat, we need to have evidence on how market prices .ybuld typically behave in the absence of (or "but for") the cartel.
' Unfortunately, the "but for" price is never truly observed. Instead, the best we can do is infer that price using what we know about the industry c°st and demand parameter. Thus, -,rb could try to build a Cournot model of the market using cost and demand estimates to approximate the noncooperative price that would have prevailed had there been no cartel. Second, and related, we could solve for the price using the Lemer index in combination ',.<ilh data on capacity utilization, fixed costs, and marginal costs. Third, we could use a belore-and-after approach. That is, identify a period during which the cartel was not active and generate a measure of the prices charged in that period. Fourth, we could specify and -stimate a reduced-form, time-series econometric model to estimate demand and supply interactions in the market and include a dummy or other variable to capture the impact ..f ihe cartel. Of these, the third and fourth are the most commonly used.16
One econometric technique frequently applied17 is to estimate some variant of the following reduced-form price equation:
Pit = a + j6y,-, + ywit + Ssit + XDU + su (10.16)
Here, Pu is price in region i at time t, yi, is a vector of variables that affect demand income, prices of other goods), w,-, is a vector of variables that affect supply (factor rices), sit is a vector of market structure variables (concentration, some measure of the ■liength of economies of scale), D,-, is a vector of dummy variables intended to capture I.10 impact of the cartel, and £„ is an error term. This is referred to as a reduced-form equation, since it is derived from an equilibrium condition equating demand and supply functions, which are functions themselves of underlying structural parameters that are not directly estimated.
A potential drawback of this approach is, of course, that it is very demanding on data. There need to be sufficient "before and after" the cartel observations to give reliable estimates of the dummy variables, and some of the variables in w„ such as factor costs :an only be obtained with the consent of the firms that are accused of being parties to he cartel. There may also be problems with the endogeneity of right-hand-side variables ■equiring that they be replaced by instruments when econometrically good instruments ire difficult to find.
There are, however, examples where a variant of the econometric technique has been used with great effect. One such example is Kwoka (1997), who estimated the price impact of a long-running cartel to rig prices in a particular set of real estate auctions held ■11 the District of Columbia.
The auctions related to properties that were either foreclosed as a result of mortgage default or were being sold under court supervision (the latter are referred to as nisi auctions). The cartel members constituted a relatively small and stable set of real estate investors who specialized in the purchase and subsequent resale of this type of property. They operated the cartel by designating a bidder who would submit an agreed winning bid at the auction, while the other cartel members either did not bid or deliberately bid low. A non-cartel member who turned up at such an auction was discouraged in various ways. For example the cartel members might make negative remarks about the property,
16 Connor (2001) provides a detailed discussion of the use of the before-and-after method in estimating the impact of the lysine cartel.
17 Baker and Rubiiifeld (1999) discuss the use of this method.
252   Oligopoly and Strategic Interaction
or the nonmember might be paid not to bid, or might be allowed to purchase one property. One measure of the success of this cartel at deterring entry and sustaining the cartel is that the cartel appears to have operated successfully for roughly 14 years, from January 1976 to August 1990.
At the end of the public auction the cartel members conducted a second, private, "knockout" auction among themselves to determine the final ownership of the property. Since this auction was conducted as a normal ascending bid auction, the property went to the high bidder—presumably, the cartel member who valued the property most highly. The winner of the public auction would then be reimbursed for the price that she had paid and the remaining difference between the public auction price and the knockout auction; price would be distributed as side payments to the members of the bidding ring.
To see how this collusive arrangement works among N members in the bidding ring, we denote the true value of the property by V, the public auction-wiririing bid by P, and the knockout auction bid by K. Only P and K are observable. There are N — 1 losing bidders who each receive a pay-off of S where
S =
K
N - 1
(10.17)
Every member of the ring knows that she will be paid at least S if she loses in the knockout, auction. The winner of the knockout gets V — K and so, in equilibrium, S = V — K. In other words, the true value of the property is V = K + S. Using equation (10.17), this condition implies that
K +
K
N
1     (N - 1)
-K -
(N-l)
= P +
N
(N-l)
(K-P)
(10.18)
Kwoka adds a bit more structure to the model by assuming that the fixed public auction price P on which the bidding ring agreed was a "constant fraction of a property's competitive valuation." If this fraction is 1//, then / = VjP. Substituting V =fP in (10.18) . and solving for K, we have the reduced form equation to be estimated at
K = P + (f -1)P
(N-l) N
(10.19)
where the independent variables in the regression are P and P(N — \)/N and / is to be estimated.
Members of the cartel kept detailed records of the identities of all the bidders in each auction and the payoffs that were made to each losing bidder. These records were central to the eventual prosecution of the cartel and are also essential to the estimation of the cartel's impact on prices. However, of.the 12 individuals that were charged with Sherman Act violations, 10 pleaded guilty before trial and so no data are available for these cases. This left Kwoka with data for 30 of the 680 properties affected by the cartel, all of which were auctioned between 1980 and 1988.
Summary statistics for these auctions are reported in Table 10.5. The average number of bidders was 4.6 and ranged from 2 to 9. The average knockout price was 28 percent in excess of the public auction price; or, alternatively, the rigged public auction price was on average 22 percent less than the knockout price.
Price Fixing and Repeated Games 253 Table 10.5   Summary statistics for the auction cartel
	Mean	Minimum.	Maximum
p	$25,800	$8,800	$44,800
K	$30,500	$10,800	$47,300
N	4.63	2	9
K/P	1.28	1.02	2.46
This is not, however, the full impact of the cartel, since we know that V = K + S. Moreover, it can be seen from Table 10.5 that there is considerable variance in K/P. Kwoka, therefore, estimated equation (10.19) directly, obtaining the results in column (a) of Table 10.6.
In the regression in column (a), observe that the coefficients on the two terms P and P(N - \)/N are significant, have the expected signs, and the fit is remarkable. In addition, the coefficient on P is (just) insignificantly different from unity, as required by equation (10.19). The coefficient on P(N - l)/iV is an estimate of / - 1, giving / = 1.86. Since P/V = l/f, this tells us that P/V = 0.54. In other words, the cartel results in public bid prices 46 percent lower than the true valuation of the properties being auctioned.
Kwoka then estimated two refinements on the simple model of equation (10.19). First, of the 30 properties in his sample, 19 were foreclosure auctions and 11 were nisi auctions held under court supervision as a condition to further legal action. It is possible that the cartel members would be more careful in their public auction bidding with a court watching. Suppose, therefore, that on nisi auctions we have that V/P = f — d. If we introduce a dummy variable D that takes the value of unity for nisi auctions and 0 otherwise the reduced form to be estimated then becomes
N N
(10.20)
The results are given in column (b) of Table 10.6. The coefficient on DP(N - 1)/JV is the estimate of d. It has the correct sign (negative) but is statistically insignificant.
The second refinement modifies the mechanism by which losing bidders in the cartel were compensated. In some auctions, losing bidders were compensated equally, while in others the compensation was based on each losing bidder's final (but losing) bid.
Table 10.6   Regression results
	(a)	(b)	(c)
P	0.519	0.520	0.703
	(2.18)	(2.15)	(4.47)
P(N - l)/N	0.860	0.879	0.481
	(2.58)	(2.58)	(2.01)
DP{N - l)/N		-0.045	0.014
		(0.51)	(0.23)
UNEQUAL			3,501
			(3.08)
R2	0.979	0.980	0.995
S	667	433	694
254   Oligopoly and Strategic Interaction
Price Fixing and Repeated Games 255
The impact of unequal compensation is potentially ambiguous. On the one hand, it might make bidders more aggressive to secure them a higher share. On the other hand, aggressive bidding might result in a bidder winning an auction that she did not want to win. To test for this impact, Kwoka added a dummy variable UNEQUAL to equation (10.20) and ran the regression for the 18 auctions in which it was possible to distinguish the compensation mechanism.
The results are given in column (c) of Table 10.6. The coefficient on UNEQUAL is positive and significant, implying that unequal compensation increased the subsequent knockout price. Moreover, the coefficient on P(N - 1)//V gives a revised estimate for 1// of 1.48, implying that the cartel rigged the public auction prices to 32.5 percent below the true property values. From this and the rest of Kwoka's (1997) results, this cartel is seen to have had an unambiguous and significant impact on the prices at which these properties were traded in the public auctions.
Kwoka's (1997) findings are broadly consistent with those of many other researchers. For example, Froeb, Koyak, and Werden (1993) found that a price-rigging scheme involved in supplying frozen fish to the U.S. mihtary raised prices by 23 to 30 percent. Connor (2001) found that the lysine cartel raised the market price by 17 percent, while Morse and Hyde (2000) argue the effect was twice as high at 34 percent. In the most exhaustive and complete review of the evidence that we have seen, Connor and Lande (2005) find that the median cartel price effect over all time periods and across all cartel types is 22 percent. They estimate that this effect is 18 percent for domestic cartels and 32 percent for international cartels.18
10.4   CARTELS IN PRACTICE: FACILITATING FACTORS AND PRACTICES
It seems clear in light of the foregoing that the threat of significant price distortion due to collusive behavior is a real one. In principle, a cartel can occur in almost any market. However, one suspects that it is more likely to occur in some markets than in others. Since the antitrust agencies have limited resources that make it impossible to patrol every industry and every market, they must focus on those settings where collusion is most likely to occur. : Thus, a natural question to ask is, what industry characteristics are most conducive to firms achieving a cooperative outcome? What market practices facilitate cooperative pricing? Such questions have been the focus of considerable theoretical and empirical research.19 We review some of the major findings of this research below.
10.4.1   Factors that Facilitate Collusion20
What factors make collusion easier and, therefore, more likely? Any factor that facilitates collusion must do one of two things. It must either reduce the critical probability-adjusted
18 Sproul (1993) is the one contrary study finding that industry prices rise slightly after an indictment, which he interprets as evidence that cartels keep costs low. Apart from notable dala problems, Sprout's (1993) analysis suffers from the difficulty that indictments only come after a long investigation. If the investigation itself niggers a breakdown in the cartel, then prices will fall long before the indictment. What happens at the indictment date then gives little guidance as to the actual carte! price effect.
19 Stigler (1964) is a classic in this field.
2(1   Morta (2004) provides an excellent and detailed discussion of these factors.
discount factor p* above which the cartel is potentially self-sustaining, or it must reduce the likelihood of profitable cheating by cartel members. We examine specific industry features to see whether and how they meet these criteria.
i. High Industry Concentration
We are more likely to find collusion in more concentrated markets for at least two reasons. First, increased concentration typically reduces the critical probability-adjusted discount factor p*. Take, for instance, a simple Bertrand model with N identical firms in the market. Each has profit n,H/N per period if it participates in the cartel. However, if one firm deviates, it can undersell all the others at just a bit lower price than the collusive one and therefore earn a one-period total monopoly profit it,,,. Deviation is not profitable, therefore, if
N
(1+p-rV
1 1
— >l-p=$. p(N)>l-- (10.21)
Clearly, p{N) is increasing in N:p*(2) = 0.5 as we noted above, p*(4) = 0.75, and p*(10) = 0.9. The intuition is clear. A firm in the cartel has to share the cartel's profits with other cartel members. As a result, the returns to collusion fall as the number of cartel members increases. By contrast, the reward for deviation is nm regardless of the number of firms N, The net gain from deviation is, in other words, more profitable as industry concentration falls. This result extends to the Cournot case as well as to the Bertrand case. Note, too, that detecting noncooperative behavior by arty one firm is more difficult when there are many firms. Since detection of cheating is essential for the success of the cartel, high concentration again makes collusion more likely.
Hay and Kelley (1974) provide compelling support for the proposition that industry structure matters for the likelihood of collusive arrangements. Their analysis of successful prosecutions of 62 cartels by the U.S. Department of Justice from 1963-72, summarized in Table 10.7, shows that the extent of collusive behavior depends substantially on the number of active firms.21
it Significant Entry Barriers
Easy entry undermines collusion. Suppose that an entrant does not join the cartel. Ease of entry weakens the ability of the cartel to maintain its goal of higher profit. Suppose,
Table 10,7   Cartels and industry concentration
Number of Conspirators 2	3	4 5	6 7	8 9	10   11-15   16-20 21-25	>25	Total
Number of Cases 1	7	8 4	10 4	3 5	7    5         2 -	6	62
Trade Association -	-	1 -	4 1	- 1	3    1         1 -	6	18
					Concentration Ratios		
Concentration (percentage)	0-	^25	25-	50	51-75 76-100		Total
Number of Cases	3		9		17 21		50
Source: Hay and Kelley (1974),
Concentration ratios were available for only 50 of Ihese cartels. We comment on the importance of trade associations.