Intermediation, Compensation and Tacit
Collusion in Insurance Markets
Uwe Focht
Andreas Richter
University of Hamburg
Ludwig-Maximilians-University Muinch
Jörg Schiller
WHU – Otto Beisheim School of Management
ARIA Annual Meeting
Washington 2006
Agenda
1. Introduction
2. Model Framework
3. Market without Intermediation
4. Market with Intermediation
a) Fee-for-Advice
b) Commission
5. Collusion and Intermediation
6. Concluding Remarks
Intermediation, Compensation and Tacit Collusion in Insurance Markets
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Collusive Behavior in German Commercial Insurance

In 2005, the German Federal Cartel Office imposed a 150 Million
Euro fine against 17 leading commercial insurance companies.

From 1999 to 2002 insurance companies established a cartel in order
to enforce higher premiums as a “reorganization measure”.

In particular, they agreed to
– Increase premiums and deductibles
– Waive premium reductions
– Unify terms and conditions

Enforcement measures for the cartel
– Insurers: Exclusion from pool solutions
– Brokers: Termination of cooperation
Intermediation, Compensation and Tacit Collusion in Insurance Markets
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Main focus

Why is collusive behavior in commercial insurance a common
phenomenon?

What is the specific role of an insurance broker in this context?

To what extent does the broker’s compensation affect pricing and
collusive behavior of insurance companies?
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Model Framework (I)

Insurance market with heterogeneous risk profiles and
differentiated products (Schultz, 2004).

Consumers’ risk profiles are uniformly distributed in [0,1].

Two insurers (i = 0,1) offer policies at the two extremes of the risk
profile space and compete in premiums pi.

Constant marginal costs c.
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Model Framework (II)

Willingness to pay v for consumers is sufficiently large.
→ In equilibrium the market is completely covered.

Disutility of mismatch t·, increases linearly in the distance to the
demanded product.

Two types of consumers:
– Informed consumers with fraction   (0,1] are perfectly
informed about their risk profile and the premiums pi;
– Uninformed consumers with fraction (1−) only form rational
expectations regarding their risk profile and premiums pi.
Intermediation, Compensation and Tacit Collusion in Insurance Markets
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Market without Intermediation
Sequence of play:
1. Insurers simultaneously offer contracts at premiums pi.
2. Consumers decide whether and where to purchase an insurance
policy.

In the symmetric subgame perfect Nash equilibrium prices and profits
are
t
t
*
p c
and
* 

2

Both premium level and profits decline in the fraction of informed
consumers.

One half of the uninformed consumers match with the wrong product
→ Resulting welfare loss:
1    1 t
4
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Market with Intermediation


The broker is endowed with an information technology which
perfectly reveals the risk profile of an individual consumer.
Cost per risk analysis k  0 .

Two compensation systems are considered:
- Broker is paid by the insured (fee-for-advice)
- Broker is paid by the insurance company (commission)

The broker acts completely non-strategic!
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Market with Intermediation (Fee-for-Advice)

Broker‘s fee at which uninformed consumers are indifferent
mˆ 


1
t
4
If k ≤ (1/4)t holds, the broker offers risk analyses and all uninformed
consumers purchase this service.
Thus, since  = 1, equilibrium premiums and profits are
pˆ  c  t
and
ˆ 
t
2
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Market with Intermediation (Commission)

The risk analysis service does not cause any costs for uninformed
consumers, therefore  = 1.

Broker’s commission at which insurers are indifferent
~ 1
h t
4

Insurance companies accept offer and charge the premiums
~
p i  c  t and

The resulting insurer profit is:
~ 
5
~
pu  c  t
4
t
2
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Fee-for-Advice vs. Commisson System

From a social planner‘s point of view both remuneration systems are
equivalent.

But: In a modified model there might be incentives for a broker to
match uninformed consumers with the wrong insurance company
(intentional mismatch).

In both cases, due to the increased transparency on the consumer
side, the insurers’ profits decrease.
→ Greater incentives for collusion
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Collusion (I)

Assumption: Insurance companies jointly decide upon premium offers
and the broker’s remuneration.

The coalition maximizes its joint profit subject to the broker’s
participation constraint  m  0 .

In our model, rationing is not profitable for the cartel.

A commission system is superior to a fee-for-advice system.
→ Prices can not be differentiated in a fee-for-advice system.
→ A fee reduces the maximum possible premium, since
p
max
c
1
v t m
2
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Collusion (II)

The broker is compensated by a break even commission.

The profit maximizing premium for the cartel is:
1
pc  v  t
2

In our model, collusion does not affect social welfare (no rationing)
→ There is (just) a redistribution of income.
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Concluding Remarks

In markets with uninformed consumers and heterogeneous risk
profiles, intermediation has the potential to improve social welfare.

Intermediation reduces the market power as well as profits of
insurance companies and increases collusion incentives.

In a competitive market both remuneration systems are equivalent.

Under collusion
– a fee for advice limits the insurers‘ opportunities to extract rents
from informed consumers.
– less differentiated products are offered (→ in the paper).

In our analysis we do not examine the broker’s incentive problem.
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Backup
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Product Differentiation
Without collusion:
 Insurance companies maximize profits by offering differentiated
products outside at:
 1 5
 ; 
 4 4

Product differentiation increases consumers’ disutility of mismatching
and negatively affects social welfare.
In the case of collusion:
1 3 
 Profit maximizing product characteristics are:  ; 
4 4

In order to maximize the coalition’s joint profit, insurance companies
equalize product characteristics.
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Rationing

Rationing is only profitable, if and only if
 5 
vc 
t
 4 

Collusion is profitable, if and only if
 7  
vc 
t
 4 
→
The coalition’s joint profit under collusion is strictly higher without
any rationing!
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