Download Complementary inputs

A Leverage Theory of Reputation
Building With Co-Branding
(Preliminary)
Seoul National University, August 3, 2006
Jay Pil Choi (Michigan State University)
Doh-Shin Jeon (Universitat Pompeu Fabra)
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
1
A general research question
• There are two sectors X and Y.
• Firms in sector X have already established their
reputation.
• Firms in sector Y have yet to establish their
reputation.
• Is there any mechanism to leverage the reputation
of a firm in X to a firm in Y?
 Is there any complementarity in reputation
building?
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
2
Building reputation by cobranding
• We study a mechanism to leverage
reputation from one sector to another
through co-branding: in order to establish
my brand, I attach the name of a well
known brand to my brand name.
• Under what conditions does this mechanism
work?
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
3
Lenovo and IBM alliance
• In May 2005, Lenovo, a Chinese PC
maker, acquired IBM PC division and
IBM kept a 13.4 % stake in the
combined company.
• The first major merger between an
American company and a Chinese one.
• Lenovo can use IBM’s logo for at least
five years.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
4
In an interview with Advani, the chief
marketing officer of Lenovo
• Knoweldge@wharton: what role does the IBM
image play in the Lenovo marketing?
• Advani: The IBM logo will stay on the ThinkPad
and ThinkCenter PCs for up to five years. For 18
months it remains exactly as it is now. After that,
the IBM part becomes smaller and Lenovo
becomes bigger. …In the near term, the IBM
association and brand are key bridges as we
establish Lenovo.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
5
Our approach and questions
•
1.
2.
•
•
-
-
We consider two cases:
Two new sectors: no firm in both setors has established its reputation
One mature and one new sectors: the firms in one sector have
established their reputation while the firms in the other have not.
Approach: We compare “signaling through prices in the case of two
new sectors” with “signaling through brand association in the case of
one mature and one new sectors”
More precisely, we ask:
How is the comparison affected by the technology linking the two
sectors?
How is the comparison affected by consumers’ cross-sector inference
problem?
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
6
Summary of the main results
Independent inputs
Complementary
Inputs
No
No complementarity No complementarity
inference in reputation
in reputation
problem building
building
Inference N.-A. (Notproblem Applicable)
August 3, 2006 at SNU
Complementarity in
reputation building
A Leverage Theory of Reputation
Building
7
Literature review (1/2)
• Name trade: Tadelis (AER,1999)
 signaling through name trades in an adverse
selection model
 Name trades between different generations within
one sector
• What we do:
 Name trades across sectors within one generation
 We also consider signaling through price
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
8
Literature review (2/2)
• Export subsidy (or infant industry
protection): Bagwell and Staiger
(JIntE,1989)
Signaling through prices within one sector
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
9
Roadmap
1. The Model with Complementary Inputs
2. Benchmark I: Single input product
3. Benchmark II: Complementary inputs without
cross-sector inference problem
4. Complementary inputs: two new sectors
5. Complementary inputs: one mature and one new
sectors
6. Other Application
7. Implications
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
10
Model with Complementary Inputs
• Consider a final product requiring two
complementary inputs x and y.
• There is a mass one of firms producing input x
• There is a mass one of firms producing input y
• Two-period model with common discount factor 
• Each firm can produce at most one unit of input in
each period
• Consumers are homogenous and they are more
than mass one
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
11
Model: Adverse Selection
•
•
•
•
•
The quality of an input can be good or bad
ji : type of firm i producing input j=x,y
Two possible types: H,L
I.I.D. with  (0,1) the proportion of high types.
In period one, type H (L) produces a good input with
probability qH (qL ) with 1>qH > qL 0
• Cost of production in each period: cH , cL
• The final product is composed of one unit of input x and
one unit of input y.
• Perfect complements: the final product is successful (S)
and renders service of value one if and only if both inputs
are good: otherwise, it fails (F) and renders no service.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
12
Model: information structure
• Each firm knows its type and other firms’ types
• Consumers know only the distribution of types
• Inference problem: When a final product fails, a
consumer does not know whether it is due to the
failure of input x or y (or due to both). However,
firms have no inference problem.
• Period one outcome of each final product becomes
known publicly
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
13
Model: dynamics of reputation
• Each firm’s probability of making a good quality
input in period two depends on its type and the
realized quality of its input in the previous period.
• Let qjS (qjF ) with j=x,y denote type  firm’s
success probability in period two depending on the
previous success or failure.
• 1 qjS > qjF  0,
• 1 qjHS > qjLS  0, 1 qjHF > qjLF  0
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
14
Model: two cases
• Two new sectors:
 Consumers know only the distribution of
types in both sectors
• One mature and one new sectors
 Consumers know types of firms in sector x
but know only the distribution of types of
firms in sector y
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
15
Timing in the case of two new sectors: period one
1.
2.
3.
4.
5.
Firms discover their and other firms’ types.
Assortative matching between firms in sector x and firms
in sector y
Each pair of matched firms decides whether or not to
produce a unit of final product and each firm chooses a
name to attach to the final product.
Each final product is randomly matched to a consumer.
Each pair of firms chooses a price and makes a take-it-orleave-it offer to its consumer.
At the end of period one, the outcome of each product is
realized and publicly known and each firm’s name is
associated with S or F.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
16
Timing in the case of two new sectors :
period two
1. New assortative matching among firms based on
each firm's type and past record.
2. Each pair of matched firms decides whether or
not to produce a unit of final product and each
firm either keeps the old name or chooses a new
name to attach to the final product.
3. Each final product is randomly matched to a
consumer. Each pair of firms chooses a price and
makes a take-it-or-leave-it offer to its consumer.
4. The outcome of each product is realized.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
17
Assumptions
• Incomplete contracts a la Grossman-HartMoore: Even though the outcome of each
final product becomes known to all, it is not
verifiable and hence is not contractible.
• Short-term contracts
• (qH)2 > 2cH > 2cL > (qL)2 and cH +cL >qHqL
• qxHFqyHF > 2cH > 2cL > qxLS qyLS and cH +cL
>max qxHSqyLS, qxLSqyHS}
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
18
Methodology
• Find
(1) The condition to have a separating equilibrium
with signaling through prices in the case of two
new sectors
(2) The condition to have a separating equilibrium
with signaling through brand association in the
case of one mature and one new sectors
• Complementarity in reputation building exists if
(2) is more relaxed than (1)
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
19
Roadmap
1. The model with Complementary Inputs
2. Benchmark I: Single input product
3. Benchmark II: Complementary inputs without
cross-sector inference problem
4. Complementary inputs: two new sectors
5. Complementary inputs: one mature and one new
sectors
6. Other Application
7. Implications
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
20
Benchmark I: Single input product
• Each input can be consumed as an
independent final product
No inference problem
• Consider just one sector
• q H > c H > cL > q L
• qHF> cH > cL > qLS
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
21
Singaling through price
• Consider a separating equilibrium in period one
• Then, in period two, the price that a high type charges depends on his
past record
 p* 2S = qHS, p* 2F =qHF
• The sufficient and necessary conditions for a separating equilibrium:
p1H should satisfy
(ICL-1) p1H  cL
(ICL-2) p1H - cL + [qLp* 2S + (1-qL) p* 2F - cL]  0
(ICH) p1H - cH + [qHp* 2S + (1-qH) p* 2F - cH]  0
• Intuition for the separating equilibrium: An H type charges a very low
price in period one since he can make much more money in period two
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
22
Signaling through name trades
There is a mass  of good names (i.e. firms with good
reputation) and an ininite number of bad names (i.e.
firms with bad reputation) in the economy
•
We look for a separating equilibrium in which a high
type firm buys a good brand name and no low type buys
a good brand name.
•
Timing at periond one
1. Each type of firm makes a bid to buy a good brand
name.
2. Each good brand chooses to which firm to sell its name.
•
In a separating equilibrium,
 p** 1H = qH , p** 2S = qHS, p** 2F =qHF
•
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
23
Signaling through name trades
• The maximum willingness to pay to buy a good brand:
bH= p** 1H - cH + [qHp** 2S + (1-qH) p** 2F - cH]
bL= p** 1H - cL + [qLp** 2S + (1-qL) p** 2F - cL]
• A separating equilibrium exists iff bH > bL.
• Proposition 2: The possibility to buy a name does not
affect the condition to have a separating equilibrium
 No complementarity in reputation building in the case of
single input product
• Intuition: Each type’s gain from building reputation is the
same in both cases
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
24
Benchmark II: Complementary inputs
without consumers’ inference problems
•
There is no complementarity in reputation
building: the condition for the existence
of a separating equilibium is the same
regardless of the mode of signaling
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
25
Roadmap
1. The Model with Complementary Inputs
2. Benchmark I: Single input product
3. Benchmark II: Complementary inputs without
cross-sector inference problem
4. Complementary inputs: two new sectors
5. Complementary inputs: one mature and one new
sectors
6. Other Application
7. Implications
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
26
Complementary inputs: two new sectors
<signaling through prices>
•
In period two:
(i) pC*2S = qxHSqyHS,
(ii) Assuming an assortative rematching among firms with F
records, C*
q
1
x
y
x
y
p2 F 
•
H
1  qH
qHS qHS 
1  qH
qHF qHF
The three sufficient and necessary conditions to have a
separating equilibrium:
(ICL-1) pC1H 2 cL
(ICL-2) pC1H - 2cL + [(qL)2pC*2S + (1- (qL)2)) pC*2F - 2cL]  0
(ICH) pC1H - 2cH + [(qH)2pC*2S + (1- (qH)2)) pC*2F - 2cH]  0
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
27
Roadmap
1. The Model with Complementary Inputs
2. Benchmark I: Single input product
3. Benchmark II: Complementary inputs without
cross-sector inference problem
4. Complementary inputs: two new sectors
5. Complementary inputs: one mature and one
new sectors
6. Other Application
7. Implications
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
28
Complementary inputs: one mature and one
new sectors
•
Types of firms producing input x are known to
consumers
• We look for a separating equilibrium in which a
high type in sector y is associated with a good
brand (i.e. a high type) in sector x and no low
type in sector y is assoicated with a good brand
in sector x.
• In a separating equilibrium:
qH
1
C **
x
y
x
y
C**
x
y
(i) p 2S = q HSq HS, p2 F 
qHS qHS 
qHF
qHF
1  qH
1  qH
(ii) pC**1H = qHqH
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
29
Complementary inputs: one mature and one
new sectors
• Assuming an even split of revenue in each period, the
maximum willingness to pay to be associated with a good
brand x is given by:
b**H= pC**1H/2- cH + [(qH)2 pC**2S/2+ (1- (qH)2) pC**2F/2- cH]
b**L= pC**1H/2- cL + [qHqLpC**2S/2+ (1- qHqL) pC**2F/2- cL]
• The payoff of a good brand firm in sector x when he is
associated with type H (L) firm in sector y
**(b:H)= b+ pC**1H/2- cH +
[(qH)2 pC**2S/2+ (1- (qH)2) pC**2F/2- cH]
**(b:L)= b+ pC**1H/2- cH +
[qHqLpC**2S/2+ (1- qHqL) pC**2F/2 - cH]
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
30
Complementary case with established
reputation in one sector
•
A separating equilibrium exists iff
**(b**H:H) > **L(b**L:L)
• Proposition 5: The condition for the existence of
a separating equilibrium is more relaxed in the
case of one mature and one new sectors than in
the case of two new sectors.
 There exists complementarity in reputation
building
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
31
Intuition
•
How does the mode of signaling affect the difference
between both types’ payoffs from building reputation?
•
Stand-alone reputation effect: the gain from being
recognized as an H type in the absence of inference
problem
•
Because of the inference problem,
(1) Reputation externality: my partner’s type affects my
future reputation
(2) Dilution of bad reputation: a failure record is not that
bad
•
The mode of signaling does not affect the first and the
third but the second.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
32
More on intuition: reputation
externality
•
In the absence of inference problem, the move from the
case of two new sectors to the case of one mature and
one new sectors does not affect an L-type’s incentive to
deviate
•
When we add the inference problem in the case of two
new sectors, an L-type is more willing to deviate
because of the reputation dilution
•
When we add the inference problem in the case of one
mature and one new sectors,
(1) An L-type is even more willing to deviate because of the
the reputation externality
(2) However, an H-type with established reputation is
reluctant to being matched with an L-type for the same
reasons
August 3, 2006 at SNU
A Leverage Theory of Reputation
33
Building
Other application: superstars
•
•
•
•
Empirical literature on movie stars (Albert 1998,
Chisholm 2004, Ravid 1999, Wallace et als. 1993)
They test a signaling hypothesis: “the commitment of a
star in an early stage of a project signals the quality of
the project to outside financiers.”
We provide a formalization of the signaling hypothesis
Economics of superstars (Rosen 1981, MacDonald,
Kremer, 1993): We identify a premium to superstars
from certifying other inputs.
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
34
Implications on economic development
or international trade
•
•
In a closed economy, if there is any
complementarity in reputation building, a
developed country has some advantage over a
developing one: the former can leverage
reputation from mature sectors to new sectors.
In an open economy, our theory explains the
certification function played by well-known
brands of multinational firms
August 3, 2006 at SNU
A Leverage Theory of Reputation
Building
35