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 178903. E-mail :
[email protected]. I am indebted to Ashok Guha for helpful discussions, in particular about the role of competing
fairs.
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.
“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.
2
1
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
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
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
C2, while each merchant’s expected payoff would be proportional to the number of other merchants at the fair, M1. Nothing of essence would change if this were so – in fact our results would be reinforced.
4
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 Cn, n = 1 to N, with C1
denoting the lowest cost, and CN 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) > Cn
(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:
(a)
(b)
– H(N) > C1 7
β(N) – H(1) > CN
(c) There exists some n between 1 and N for which β(n) – H(N-n+1) < Cn
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.
Indeed C1 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.
6
5
Figure 1
β(n)H(N-n+1),
Cn
N-M
n
N*
N
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
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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,
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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(nt) = nt-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 + δ2εM/(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
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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 ≥ N1-(N-M)
(A2)
then the collective boycott takes the number at the rival fair beyond N1. 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
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Appendix Figure 1
β(n)H(N-n+1),
Cn
N-M
N1
N*
N2
n
N
Appendix Figure 2
β(n)H(N-n+1),
Cn
N-M
N1
N*
n
N
Champagne fair to the rival fair until there are N2 merchants at the rival fair and N-N2 at the
Champagne fair. This is a stable equilibrium. Now the LM’s no collusion condition becomes
α(M) – H(M) – Q < p[δεG + δ2ε(M-N+ N2)/(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-N2.
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≥N1-(N-M)
(A4)
then the boycott takes the number at the rival fair beyond N1. 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 + δ2ε(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) : 525-548.
Greif, Avner, Milgrom, Paul and Weingast, Barry (1994) “Coordination, Commitment and
Enforcement : The Case of the Merchant Guild.” Journal of Political Economy 102(4) : 745776.
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 : 1-23.1159222
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