Recent developments in the
economics of information:
The role of intermediaries
Maarten C.W. Janssen
University of Vienna
Middlemen (Intermediaries)
• General role of Middlemen (Spulber)
– Reduce search cost
– Reduce other transaction cost
– Certify quality (because of increasing returs to
scale technology in certification)
– Diversify and pool risks
– Mitigate adverse selection, moral hazard
Focus on Information Revelation
• One Role Middleman: check information
(quality) a party has, then (partially) reveal it.
• Examples:
– Laboratory agricultural products
– Auditors (financial rating agencies)
– Quality schools, hospitals
• Main question: how much information should
be revealed? What is optimal for the
middleman himself?
Simple Model Lizzeri (Rand ‘99)
• Seller can be of different types t, between a and b
• Monopoly intermediary sets a fee P and a
disclosure rule D (not knowing quality t)
• Knowing P,D and t seller decides whether or not
to have quality certified
• Upon testing, intermediary gets to know value of
t, and discloses according to rule D
• Buyers observe P,D and info that is disclosed and
bid (against each other) to get commodity.
Different disclosure rules
• Full disclosure: observe t, reveal t
• Interval disclosure (grading, partial pooling)):
there are a certain number of pre-determined
intervals. If t is observed to be within a certain
interval, disclose that interval
• Noisy disclosure: observe t, reveal t + ε, where ε
is a random variable
• Mixtures: For example full disclosure above a
certain level, insufficient grade below treshold
level
Pay-offs, strategies
• Seller: pay-off = market price (depending on D) –
fee; strategy “have product (not) certified
conditional upon P,D and t”
• Buyers: pay-off = expected quality (depending on
D) - market price if they buy; 0 otherwise;
strategy “bid x for product conditional upon P,D
whether or not product is tested and test result”
• Intermediary: pay-off = P times the probability
the seller decides to be certified; strategy “set P
and D”.
Analysis I
• Who has most incentives to have information revealed?
(who has least?)
– Lowest quality (type) has no incentive to have his type
revealed
• Can there be an equilibrium with full disclosure (for all
t)?
– No, lowest type seller is not prepared to pay anything for
having quality disclosed; others have. Because intermediary
is profit maximizing firm it will charge a positive price-
• Closest one can get to full disclosure is that above
treshold there is full disclosure, below sellers do not
have product certified.
– Indifferent type is x(P) such that x(P) – P = E(t given x ≤ x(P)
– Figure
Analysis II: example
• Quality uniformly distributed between 0 and 1.
– E(t given x ≤ x(P) = x(P)/2
– x(P) – P =x(P)/2 gives x(P) = 2P
• Intermediary max profits P*(1-F(x(P)) = P*(1-2P)
– Gives optimal P = ¼, expected profit 1/8
• Sellers below .5 do not have quality certified, tarde at P =
1/4
• Sellers of type t above .5 have quality perfectly certified,
trade at price t
• Without intermediary price will be ½ (what about adverse
selection here?)
• Comparison surplus, with and without intermediary
(figure)
Optimality disclosure rule?
• So far, if it perfectly discloses above a certain treshold it is optimal to
set P=1/4
• Consider different rule: “everybody who goes passes the test”
– What are sellers willing to pay (consider uniform case). If t is lowest
certified type, he gets (t+b)/2 – P if he is highest uncertified type he gets
(t+a)/2
– If P ≤ (b-a)/2 = (a+b)/2 – a everyone goes to be certified
• Surplus sellers equals a
– Without certification seller’s surplus depends on expectations (can also
be equal to a)
– Everyone goes, no disclosure!
• If a= 0 and b = 1,
– P = ½, profits equal ½ (larger than before), all surplus goes to
intermediary without revealing anything!
– This is optimal strategy for intermediary!
• In general, P = E(t) – a; D is no disclosure; all sellers go to
intermediary, sellers make minimum surplus equal to a.
Some goods better not to be traded I
• Suppose a < 0 <b.
• Inefficiencies without intermediary
– E(t) < 0, no trade in equilibrium, some trade would be
optimal
– E(t) > 0, all goods trade in equilibrium, but restricted trade
would be optimal
• With intermediary
– Charge P = E(t given t ≥ 0), disclose that quality is positive (if
it really is)
– Sellers with positive quality have goods certified
– Buyers only buy certified goods.
– Sellers do not make profits, intermediary absorbs all surplus
– Total surplus is larger than without intermediary
Some goods better not to be traded II
• Intermediary’s profits (1-F(0))*E(t given t ≥ 0)
• Is this rule optimal? (different demarcation
criterion x than 0 gives (1-F(x))*E(t given t ≥x).
• For uniform distribution:
– F(x) = (x-a)/(b-a), E(t given t ≥ x) = (x+b)/2
– Profits intermediary (b2 – x2) / (2(b-a))
– Optimal to choose x=0
– Intermediary chooses welfare optimal fee.