Collusion in the Champagne Fairs : Controlling Law Merchants Brishti Guha 1 Singapore Management University

Transcription

1 Collusion in the Champagne Fairs : Controlling Law Merchants Brishti Guha 1 Singapore Management University 1 Department of Economics, Singapore Management University, 90 Stamford Road, Singapore bguha@smu.edu.sg. I am indebted to Ashok Guha for helpful discussions, in particular about the role of competing fairs.

2 Collusion in the Champagne Fairs : Controlling Law Merchants In Milgrom, North and Weingast s 1 seminal 1990 paper about the role of the law merchant 2 and the Champagne fairs in the revival of medieval trade, the authors concede the possibility that the law merchant (LM) or private judge adjudicating disputes among pairs of traders may be dishonest. The paper also contains a rigorous discussion of extortion, deriving parameters over which the LM will not attempt to extort bribes from honest traders by threatening to falsely smear their reputations. However, the authors do not analyze the possibility of collusion between the LM and a dishonest trader (though they mention that this is a possibility). This begs the question of why a trader who has cheated his partner and not paid a fine cannot bribe the LM to conceal this fact from prospective future partners who query the LM about him. In fact, there is nothing to prevent this from happening in the MNW model. In the present paper we first summarize key aspects of MNW s paper (in Section 1). In Section 2 we discuss why their model is not collusion-proof. In Section 3 we propose an extension to their paper, which involves some modifications in the light of actual practice at the Champagne fairs, and derive conditions under which the system is collusion-proof. Section 4 concludes. 1. Key Results in MNW MNW model the institution of private judges or Law Merchants at the Champagne fairs that were the focus of international trade in Medieval Europe. A trader could apply to the LM (after paying a fee Q) for information about the past of a potential trading partner. He then traded (provided the information was satisfactory) and, if he believed himself to have been cheated in the trade, could appeal to the LM at a personal cost C. The LM would deliver a judgment J in his favor if his appeal was valid, but 0 if it was not. The accused party, if the judgment went against him, could then pay at a personal cost f(j) or refuse to do so. If he refused, the fact was recorded by the LM and reported to any trader who inquired about him in future. The LM earned a revenue of ε from each trader who queried him. MNW derive parameters for which there always exists a judgment J* such that in equilibrium, each trader who has no unpaid judgments outstanding against him queries the LM 1 Denoted in the rest of this paper by MNW. We summarize the key aspects of MNW s paper in Section 1. 2 Law merchant is often used in the sense of the informal code of mercantile law which governed medieval traders notions of what constituted cheating. MNW, however, use the term interchangeably with the private judges who kept records of traders past transgressions and adjudicated disputes between them, and we follow their terminology. 1

3 about his partner. If each is assured that his partner has no outstanding judgments, the pair trade honestly. Honesty is ensured by the credible threat that, in the event of cheating, the injured party will appeal to the LM, who will award a judgment J* against the cheat, the cost of which to him, f(j*), exceeds what he might gain by cheating. Appealing remains credible as long as the cost of appeal, C, is less than the judgment J* that the plaintiff expects to be awarded. Moreover, no one can gain by first cheating and then disappearing without paying the fine, as this would then be recorded by the LM and reported to future partners, and the value of future trading opportunities exceeds that of a one-time cheating gain. Throughout, each merchant s payoffs from honesty and cheating have the traditional prisoner s dilemma structure and are constants. The main role of the LM in MNW s paper is thus to provide a centralized source of information where each trader can access records of a potential partner s history. This provided a mechanism whereby a cheat could be punished by all potential future matches, without the need for continuous multilateral information exchange. For the bulk of their paper, MNW assume that the LM is honest. But they also provide a rigorous treatment of conditions under which the LM will not extort where extortion implies that the LM would threaten to smear an honest trader s reputation (by falsely reporting a past misdeed when queried about him) unless bribed. While collusion is mentioned as a possibility, it is not addressed in their model. We now turn to a discussion of why the MNW model is not collusion-proof. 2. A Mechanism to Deter Collusion? In the MNW paper, the LM is the source of all information. In every period, each merchant gets information about his prospective trading partner by querying the LM (for a fee of Q). In this system, any collusion of the sort described above would be undetectable. The LM merely has to accept a bribe from a merchant who has cheated and not paid a fine, agreeing to suppress this information from any one who queries about the dishonest merchant. The LM s transgression would remain unknown: if a merchant transacted with the dishonest merchant on the basis of the LM s information of a clean previous record, and were subsequently cheated, no blame would 2

4 attach to the LM. In keeping with the strategy outlined in MNW 3, the cheated merchant would then appeal to the LM, who would then order the cheat to pay a fine an order which, however, could not be forcibly implemented. Throughout, there is no way of detecting collusion by the LM. But if merchants are able to collude with the LM by cheating and offering him a portion of their cheating gains and subsequently suffer no penalty (as the law merchant erases any records of their cheating), they would certainly have an incentive to do so. The LM would also have an incentive to collude, as his income would increase while he would suffer no penalty. Thus the system is not collusion-proof and will unravel. 3. Collusion-Proofing the model: Fairs, Guilds and Competition Actual practice at the Champagne fairs was somewhat different from the MNW model (as the authors themselves point out). The fair authorities, who played the LM s role, controlled entry to the fair. If any one cheated another merchant at the fair and escaped without paying a fine, the fair authorities would, if honest, debar him from future fairs. Collusion in this context would be tantamount to letting the offending merchant attend future fairs, in exchange for a bribe. Unlike collusion in the MNW model, collusion in the actual Champagne fairs of the sort just described - would very likely have been detectable with some probability. We modify the assumptions of MNW s model below to analyze the situation. Our assumptions differ in three main ways from MNW s. 1. While MNW consider payoffs in a traditional prisoner s dilemma game where each merchant s payoff was unaffected by the number of merchants in our modified faircentric model, we make payoffs to attending a fair a function of the number of merchants at that fair. There is good reason to make this assumption, as network effects are likely to be of importance in attending an event such as a trade fair: the larger the number of others at the event, the more worthwhile is it for an individual merchant to attend the event. 2. We introduce an element of competition by assuming the presence of more than one fair. 3. We also allow merchants to belong to a guild. As Greif, Milgrom and Weingast (1994) point out, the merchant guild played an important role in sustaining medieval trade: 3 This strategy involves a pair of traders approaching the LM for information about each other s past records : they trade only if the LM reports that both have clean records. Subsequently if one of the two cheats, the other appeals to the LM who orders the miscreant to pay a fine. Though the miscreant may flee without paying the fine, this would be noted in the LM s record and could be revealed to future partners. 3

5 moreover the existence of merchant guilds overlapped with the time period when the Champagne fairs were important. We do not, however, assume that all merchants who attended one fair (say the Champagne fair) must belong to the same guild this in fact would be highly unlikely. 3.1 A Model As in MNW s paper, we assume that the LM earns 2ε per contract out of the 2Q that the pair of querying merchants pays for the cost of the query. Let the total number of merchants be N, where N is large but finite. Of these N merchants, at t = 0, a number M (to be endogenized shortly) attends the Champagne fairs. In the interests of simplicity, we assume competition from only one other fair. We also assume that each merchant transacts with only one other merchant at the fair. 4 Then if the LMs at the Champagne fair are honest, they earn a per period revenue of R(M) = εm (1) This is provided the M merchants continue to patronize the Champagne fair: if not, the revenue will be ε times the number of patrons in the relevant period. An individual merchant s per period payoff from attending the Champagne fair and being honest is a function H(M) of the number of traders attending the fair. This could be so for several reasons. First of all, if the number of participants is large, each trader has a larger choice set in terms of whom to trade with and this makes him better off. Secondly, attending a fair with a large number of merchants would enable each of these merchants to cultivate valuable contacts even if he can trade with only one of these at the fair. Such contacts might help him in his business later or provide lines of credit or letters of introduction to their own networks. Thus H(M)>H(M-1) for all possible values of M. The trader s one-period payoff from cheating is α(m) > H(M) for all M (so that in a one period game, merchants would always want to cheat). We now endogenize M. Let the returns that an honest merchant at the rival fair could earn be a function β(n), where n is the number of merchants attending the rival fair, and 4 This assumption is made for simplicity. Alternatively, if there were no restriction on the number of merchants one could trade with in one period, the fair s expected payoff would be proportional to the number of potential pairings, M C 2, while each merchant s expected payoff would be proportional to the number of other merchants at the fair, M- 1. Nothing of essence would change if this were so in fact our results would be reinforced. 4

6 β(n)> β(n-1) for all n in the interval (2,N) 5. However, there is, in addition, a merchantspecific cost to attending this rival fair relative to the Champagne fair (the cost could reflect a composite of locational factors, that would be individual-specific, and may be negative for low values of n) 6. These merchant specific costs are denoted by C n, n = 1 to N, with C 1 denoting the lowest cost, and C N the highest. Therefore, the n-th merchant will choose the rival fair over the Champagne fair if and only if β(n) H(N-n + 1) > C n (2) The left hand side of (2) is increasing in n. As the number of traders at the rival fair increases and the number at the Champagne fair falls, the rival fair becomes increasingly profitable relative to the Champagne fair (not accounting for merchant specific costs). We already know (by construction) that the right hand side is also increasing in n. We may plot both the LHS and the RHS against n (which measures the number of merchants choosing the rival fair). Consider the class of functions which satisfy the following properties: 7 (a) H(N) > C 1 (b) β(n) H(1) > C N (c) There exists some n between 1 and N for which β(n) H(N-n+1) < C n Lemma 1: If properties (a) to (c) are satisfied, there is an even number of intersections between the two functions of n representing the LHS and the RHS of inequality (2). A necessary condition for properties (a) to (c) to hold is that the LHS be steeper than the RHS over some range, or more formally, [β(n) β(n-1)]- [H(N-n+1)-H(N-n)] > C(n)-C(n-1) for some n (3) An example of functions which are described by properties (a) to (c) and which, therefore, satisfy Lemma 1 is shown in Figure 1. The RHS is plotted as a dashed step function, while the LHS (plotted by the solid step function) has 2 intersections with the RHS. As n measures the number of merchants who might join the rival fair, n cannot exceed N, the total number of merchants. Of the two intersections, the first one (for the smaller value of n) is a stable 5 β(0)= β(1)=0. If there is only one trader at a fair, he has no one to trade with and cannot reap any benefits. 6 Indeed C 1 must be negative so that in a situation where all the other merchants were at the Champagne fair, one merchant would prefer to be at the rival fair simply due to the expense of being at Champagne. For example, Italian merchants might have lower costs of attending an Italian fair, while Flemish merchants would prefer to attend one in Flanders. If this were not so, no competition between fairs could emerge in our model, as Champagne presumably had the first mover advantage over rival fairs, and our analysis would become uninteresting. 7 This condition reflects footnote 7 in a situation where all N merchants are at the Champagne fair, one must strictly prefer to be at the rival fair instead. 5

7 Figure 1 β(n)- H(N-n+1), Cn N-M N* n N

8 equilibrium: for values of n to the right of this point, the LHS is less than the RHS, so (2) is not satisfied. Hence at this point no more merchants want to go over to the rival fair. In contrast, the second intersection (at N* in the diagram) is unstable, because if we move to the right of this point the LHS exceeds the RHS so, once n reaches N*, it would jump all the way to N with all the merchants going over to the rival fair. Since history has established that the Champagne fair was the dominant trade fair at the relevant period (perhaps due to first mover advantage), we assume that the initial division of merchants between the two fairs is represented by the first (stable) equilibrium: this fixes the number of merchants at the Champagne fair at M, while the number in the rival fair is a small number, N-M. For the rest of this paper, we focus on cases with only 2 intersections between the LHS and the RHS of (2), as depicted in Figure 1. However, this is done merely for the sake of simplicity. In the appendix we discuss how the analysis might be modified to accommodate a larger number of intersections (whether even or odd) our qualitative results are not dependent on the restrictive functional forms assumed here. 3.2 Detecting Collusion and the role of the Guild Now suppose the LM at the Champagne fair were to collude with a trader with a past history of cheating and not paying fines. The LM would, in exchange for a bribe, let this trader attend future fairs. However, there is a finite probability that a merchant he has cheated in the past also attends the Champagne fair in the future, and sees the trader who had cheated him. He could then infer that the LM (ie the authorities at the Champagne fair) had been involved in collusion. Now suppose this previously cheated merchant belongs to a merchant guild (a highly likely event in view of the importance of merchant guilds around the time of the Champagne fair). This merchant would then be able to spread information about the Champagne fair s unreliability to the other guild members. A question might arise at this point: if communication between merchants were feasible, what purpose does the LM at a trade fair play? Wouldn t it be possible to enforce honesty in all transactions through a multilateral punishment system such as the one among the Maghribi traders described in Greif (1993)? However, we argue that LMs and trade fairs would still serve a purpose: merchant guilds might not be able to keep track of the history of 6

9 individual merchants, especially those from outside their guilds, but it would be much easier to keep track of the activities of fairs, particularly major trade fairs like the Champagne fairs. Obviously the number of fairs would be very much smaller than the number of merchants, so this is not an unrealistic assumption. Moreover, we have modeled the fair as providing a stream of benefits arising simply from the fact that a large number of merchants congregated there (so a merchant s payoff from attending the fair is a function of the total number of attendees). Returning to our analysis, let the total number of guild members who used to attend the Champagne fair be G. We assume that the guild can solve collective action problems to the extent of being able to organize a collective boycott of future Champagne fairs by its members when one member reports collusion on the part of the Champagne fair authorities. What conditions would then rule out a deviation by an individual guild member? Proposition 1: If G N*-(N-M), no guild member has an individual incentive to deviate from the policy of collective boycott of the fair. Proof: If the number of guild members who regularly attended the Champagne fairs is large enough, a collective boycott of the Champagne fairs and a collective switch to the rival fair would actually ensure that individual payoffs from attending the rival fair became higher than those from continuing at the Champagne fairs. If G N*-(N-M), a collective boycott moves n past N*, the value of n at the second (unstable) intersection at this point, (2) holds and the rival fair yields higher payoffs. So no individual merchant has an incentive to deviate from the collective punishment. The self-enforcing nature of the punishment does not, therefore, depend on a belief that the authorities of the Champagne fairs must continue to collude in future periods. Nor does it depend on a belief that any guild member who deviates and goes to the Champagne fairs will be punished by other guild members. What about the other merchants at the Champagne fair who were not members of the cheated merchant s guild? Once the guild members boycott the Champagne fair, then provided G N*-(N-M), these other merchants would also benefit from switching to the rival fair. However, this could happen with a lag: the other merchants might not know because of communication difficulties with members of other guilds about the guild s intention to boycott the fair. However, they would observe the low attendance at the next fair, 7

10 and would respond to this by switching to the rival fair from the following period (we implicitly assume that the merchants have static expectations, i.e E(n t ) = n t-1 (4) 3.3 Conditions Under Which the LM Will Not Collude The discussion in the preceding sub section showed that there is a finite probability of collusion by the LM being detected. Denote this probability by p. Let δ denote the discount factor. Then we have the following proposition : Proposition 2: The LM will not collude if α(m) H(M) Q < p[δεg + δ 2 εm/(1-δ)] (5) Proof: The term on the LHS of inequality (5) is the maximum bribe that might be offered to the LM by a cheating merchant (since it represents cheating gains net of the cost of querying). If even the maximum bribe is less than the present discounted value of the losses that the LM expects on account of collusion, he will not collude. These expected losses are captured by the terms on the RHS of inequality (5). If the LM s collusion is detected which happens with probability p he loses the custom of the G guild members in the next period, and from the period after that he loses the custom of all M merchants forever (as every one switches to the rival fair). 4. Discussion and Conclusion We have modified and extended MNW s model with the objective of deriving conditions under which the Champagne fairs could function without collusion. We have pointed out that collusion was undetectable in MNW s model, and that therefore there was no mechanism to deter the LM from engaging in collusive behavior, which would have led the system to unravel. To achieve our objective, we have altered the model so that it, in our view, represents the reality of the Champagne fairs more closely than MNW s model did. When we consider the way in which collusion actually took place at these fairs, it is not hard to conceive of mechanisms which would allow it to be detected. Moreover, we introduce two other institutions into the picture: a competing fair, and a merchant guild which could organize collective boycotts. We derive conditions under which a transgression against one trader by the LM would lead to a collective boycott from which no one guild member would 8

11 want to deviate. We also show how the presence of a rival fair would encourage even merchants outside the guild to abandon the colluding fair. Appendix We now look at how the above analysis might be modified when there are more than 2 intersections between the functions on the LHS and RHS of (2), when both of these are plotted against n. We first look at the case where the number of intersections is even, as in Appendix Figure 1. This is an instance where there are 4 intersections (again, with the dashed step function depicting the RHS of (2), while the solid step function represents the LHS). As before, we assume that the initial division occurs at the (stable) equilibrium with the smallest value of n, so that a large number (M) of the merchants go to the Champagne fair, while N-M go to the rival fair. Now, just as before, suppose the LM were to collude by letting in a trader who had cheated a merchant, and that this merchant observes this in a future fair, and reports the LM s collusive behavior to his guild. Now supposing the number of guild members G who are regular attendees of the Champagne fair is such that G N*-(N-M) (A1) then the collective boycott by these members would push the number at the rival fair beyond N*. At this point, no individual member would have an incentive to deviate, as their payoff from attending the rival fair is higher than from attending the Champagne fair. What is more, the other merchants remaining at the Champagne fair all find it in their interest to join the rival fair. Now the analysis follows that in the text and the LM s no collusion condition continues to be given by (5). What if G is smaller? If N*-(N-M) > G N 1 -(N-M) (A2) then the collective boycott takes the number at the rival fair beyond N 1. At this point, again, the payoffs to joining the rival fair are higher than those from deviating to the Champagne fair. Moreover, some other merchants outside the guild are also induced to switch from the 9

12 Appendix Figure 1 β(n)- H(N-n+1), Cn N-M N1 N2 N* N n

13 Appendix Figure 2 β(n)- H(N-n+1), Cn N-M N1 n N* N

14 Champagne fair to the rival fair until there are N 2 merchants at the rival fair and N-N 2 at the Champagne fair. This is a stable equilibrium. Now the LM s no collusion condition becomes α(m) H(M) Q < p[δεg + δ 2 ε(m-n+ N 2 )/(1-δ)] (A3) The second term on the RHS of (A3) reflects the fact that the number of merchants at the Champagne fairs eventually shrinks from M to N-N 2. We now see what happens when the number of intersections is odd and greater than two (we look at Appendix Figure 2, which shows us a case with 3 intersections). If the LM were to collude and be detected, and if the reporting trader s guild organized a collective boycott, then if we have G N 1 -(N-M) (A4) then the boycott takes the number at the rival fair beyond N 1. At this point, again, the payoffs to joining the rival fair are higher than those from deviating to the Champagne fair. Moreover, some other merchants outside the guild are also induced to switch from the Champagne fair to the rival fair until there are N* merchants at the rival fair and N-N* at the Champagne fair. This is a stable equilibrium. Thus the LM s no collusion condition becomes α(m) H(M) Q < p[δεg + δ 2 ε(m-n+ N*)/(1-δ)] (A5) The second term on the RHS of (A5) reflects the fact that the number of merchants at the Champagne fairs eventually shrinks from M to N-N*. Thus we see that irrespective of the exact number of intersections, we can always derive conditions which deter collusive behavior for the LM conditions definable in terms of guild size and other model parameters. References Greif, Avner (1993) Contract Enforceability and Economic Institutions in Early Trade : The Maghribi Traders Coalition. American Economic Review 83(3) : Greif, Avner, Milgrom, Paul and Weingast, Barry (1994) Coordination, Commitment and Enforcement : The Case of the Merchant Guild. Journal of Political Economy 102(4) : Milgrom, Paul, North, Douglass and Weingast, Barry (1990) The Role of Institutions in the Revival of Trade : The Law Merchants, Private Judges and the Champagne Fairs. Economics and Politics 2 :