A Model of Two-Sided Costly Communication for Building New
Product Category Demand
Yi (Michelle) Lu and Jiwoong Shin∗
August 2015
Abstract
When a rm introduces a radical innovation, consumers are unaware of the product's uses and
benets. Moreover, consumers are unsure whether they even need the product. In this context,
we model the marketing communication process as a two-sided process that involves both rms'
and consumers' costly eorts to transmit and assimilate the novel product concept. Its success
endogenously generates consumers' need recognition and thereby market demand for a novel
product. We study a rm's dierent information disclosure strategies for a radical innovation.
We nd that sharing an innovative idea, instead of extracting a higher rent by keeping the idea
secret, can be optimal. A rm may benet from the presence of competitors and their communication eorts. The innovator can share an innovation so that competitors can also prot and
thus have incentives to create and expand the market.
Keywords:
Communication, information disclosure, endogenous demand, strategic
.
complementarity, strategic substitutability, free-riding
∗
Yi (Michelle) Lu: 165 Whitney Avenue, P.O. Box 208200, New Haven, CT 06520, [email protected]; Jiwoong Shin:
165 Whitney Avenue, P.O. Box 208200, New Haven, CT 06520, [email protected]. We thank Arthur Campbell for
his many insightful comments and suggestions through numerous conversations. We would also like to thank Jaehwan
Kim, Vineet Kumar, Subrata Sen, K. Sudhir, and seminar participants at CEIBS, HKUST, McGill University, UC
Riverside, and Yale University for their helpful comments.
1
Introduction
In 2014, within four years of its IPO, Tesla Motors had already achieved a market value half that of
Ford's.
1 That same year, the company decided to share all of its patents with other car manufac2 This
turing companies, opening its vault to expand the long-range electronic car market category.
controversial move wasn't entirely unprecedented. In the semiconductor industry, for instance, it is
common practice for an innovative rm one that that has developed a new generation of processor
to license its innovation to one or more competing rms. This strategy creates multiple sources
3
of supply (Semiconductor Licensing Trends 2013 ) and can spur broader product demand for the
next generation semiconductor (Shepard 1987).
In fact, publicly releasing innovative technology has become a routine practice in high-tech
markets, with many companies following similar practices. For some products, rms pre-announce
an innovation by revealing the details and marketing plans for the product well in advance of its
release, practically inviting competitors to participate in the category.
Consider Google: In April 2012, Google announced its marketing plan for the new product,
Google Glass a radical wearable technology. Interestingly, the product was at the conceptual
stage; Google had not even developed a prototype. Rather, the Google Glass Team posted a video
about an ideal day using their (then) imagined product. The design team shared prototype ideas
online. Google marketed Glass so early that Samsung, Microsoft, Intel, and many other technology
companies quickly followed and announced they would commercialize a similar product in the mass
market. Although the project was declared a failure due to consumer concerns over privacy and
4 in January 2015, Google ocially announced its plan to withdraw the product
social awkwardness
from the market many industry experts acknowledge that Google Glass fostered a market for new
wearable technologies.
5 Nowadays, technology experts widely recognize wearable technology like the
6
Apple Watch and Samsung Gear as the next big thing for consumers : in 2014, wearable technology
7 and
has thus far generated $3 billion in revenue; and it is estimated to grow to $6 billion by 2016
$19 billion by 2018.
1
8
https://www.washingtonpost.com/opinions/charles-lane-tesla-takes-on-car-dealerships-in-a-ght-to-the-
death/2014/03/12/2956a9f2-a9-11e3-8599-ce7295b6851c_story.html.
2
3
http://online.wsj.com/articles/tesla-motors-says-it-will-allow-others-to-use-its-patents-1402594375.
Trends and Opportunities in Semiconductor Licensing:
http://www.skyworksinc.com/downloads/press_room/published_articles/Les_Nouvelles_122013.pdf.
4
5
http://www.cnn.com/2015/01/20/opinion/pease-google-glass-what-went-wrong/
4 Ways Android Wear Can Succeed Where Google Glass Has Failed,: http://time.com/79972/androidwear-
google-glass-wearables/,
Why Google Glass Failed (But Might Still Succeed),: http://www.lifehacker.com.au/2015/01/why-google-glassfailed-but-might-still-succeed/
6
7
Get Ready: Wearable Tech is About to Explode, http://www.entrepreneur.com/article/229347#.
Google Glass Woos Developers to $6 Billion Wearable Market: Tech, http://www.bloomberg.com/news/2013-
05-13/google-glass-woos-developers-to-6-billion-wearable-market-tech.html.
8
Wearable tech revenue to hit $19B by 2018, http://www.cnet.com/news/wearable-tech-revenue-to-hit-19b-by-
2018/.
1
In the examples of Tesla and Google Glass, rms released key information on a new technology
or product into the public domain.
This behavior is curious since this type of information is
usually considered a trade secret that serves as a key competitive advantages against potential
competitors. When companies market a half-baked idea or share a technological breakthrough, they
risk prematurely disclosing a potentially disruptive innovation. This may lead to greater competition
and weak appropriability in the product market competition. This is why rms sometimes opt for
great secrecy around new products: to maximize their competitive surprise (i.e. Apple's iPhone).
In this research, we focus on the introduction of revolutionary new products and rms' marketing
strategies for such products. Specically, we try to explain the puzzling dierences in information
disclosure strategies among innovating rms: how much do these rms choose to keep secret, and
how much of their innovation do they reveal? We propose an explanation for why a rm sometimes
shares an innovative idea with competitors, which might potentially undermine its dominant position
in the market, and when this choice (as opposed to keeping the innovation secret) is optimal. Our
explanation is based on the persuasion motive of rms in communication and the strategic role of
consumers.
When a rm introduces a novel product for which the market does not exist, consumers do not
understand the product's uses and benets.
product.
They are even unclear as to whether they need the
In this context, the role of marketing communication is to educate consumers and en-
courage them to deliberate their potential needs, and thus increase product acceptance. In contrast
to incremental innovations, where consumers generally know the benets from the category, and
can passively learn about the value of new features from advertising, consumers bear relatively high
costs to learn about the potential benets of revolutionary new products. Therefore, a key challenge
to marketing radical innovation is persuading consumers to expend more eort in paying attention
to the content, assimilating the new idea, and deliberating their needs by examining an unproven
product category. For example, consumers can be aware of new wearable technology products like
Google Glass from advertising alone. However, awareness of a radical product does not necessarily
translate into consumers' need recognition or product acceptance. Consumers might be unwilling
to incur further learning costs for a product that seems to aim at tech geeks and not them. The
potential promise of wearable technology can fail to emerge and expand as a category due to con-
9 Marketers therefore need to not only advertise the product and
sumers' aversion to costly eort.
its features, but also create the right marketing environment in which customers are willing to invest
in costly learning. Without consumers on board, the rm's eort alone is insucient to convey the
new idea and convince consumers that they need the product.
We model marketing communication for a radical product as two-sided costly communication,
a process that involves both rms' and consumers' eorts to transmit and assimilate information
9
Glass, Darkly for its wearable computer to be accepted, Google must convince people that the device isn't
creepy, MIT Technology Review, http://www.technologyreview.com/review/524576/glass-darkly/.
2
(Dewatripont and Tirole 2005, Wernerfelt 1996). This two-sided perspective of communication is
widely recognized in sociology and economics, but has not yet been embodied into formal modeling
in marketing literature.
Most marketing literature considers marketing communication as one-
sided costly communication; that is, only rms exert communication eort (such as advertising)
and consumers eortlessly become informed. Such one-sided communication is reasonable in many
situations where consumers know about the product and their needs (for example, existing product
categories and incremental innovations).
However, one-sided communication is not applicable to
radical innovation, in which consumers are clear neither about the uses and the benets of a product
nor their needs for it.
10 When a rm communicates the values of radical innovations to consumers,
consumers have to expend eort in learning about the product and considering whether it suits
their needs. In this paper, we recognize that the acts of both formulating and absorbing the content
of a communication are privately costly, and it takes both parties (i.e., rms and consumers) for
11 Through this two-way communication process, consumers can come
communication to succeed.
to understand product's uses and benets, and become potential buyers.
Therefore, successful
marketing communication is a critical process whereby a rm creates a market for a novel product.
In the situation where two-sided costly communication plays an important role in endogenously
creating and expanding the demand for the new product, the rm's incentive to disclose its innovation to competitors or to keep it secret is determined by the trade-o between the two eects.
On the one hand, by disclosing its innovation to competitors, rms can invite the competitors to
share costly communication eorts and thus expand the total market size through cooperation in
communication stage. Nevertheless, this demand-enhancing eect does not necessarily arise because
of the free-riding incentive of rms that is, rms may not expend costly eorts to increase the total
12 However, we show that when
demand, and may instead simply free ride on the other rm's eorts.
both rms' and consumers' communication eorts endogenously determine the market demand for
the new product, strategic consumers alleviate the potential free-riding eects of rival rms.
By
inviting the competitor, the innovator can credibly commit to providing consumers with greater
surplus, which increases the incentives for consumers to expend more costly eort in deliberating
about the new innovation. In turn, this increased consumer eort encourages rms further to put
10
We follow the notion that a radical innovation is a new product that represents substantial improvements in
technology or consumer benets (Chandy and Tellis 1998) and thus consumer preferences for such products are not
yet fully formed (Christensen 2003).
On the other hand, incremental innovation concerns an existing product or
service whose performance has been enhanced or upgraded.
Consumes already have a stable preference for such
products.
11
In reality, we can observe the necessity of two-sided eorts in a wide variety of scenarios; for example, when a
teacher tries to convey a new idea to students, if the students are not interested or do not spend time to pay attention
or think, they will not absorb and internalize the new knowledge no matter how hard or clearly the teacher tries to
elaborate. On the other hand, no matter how hard students try to learn, if the teacher does not explain things clearly
then, the idea is hardly understood and accepted by the students. Both eorts are necessary for the communication
to succeed.
12
The eects of free-riding on competitor's service eorts on retail competition (also, known as showrooming eect)
is analyzed in Shin (2007).
3
more eort into the communication stage. This complementarity in communication between rms
and consumers through consumers' strategic decision mitigates the potential free-riding problem.
Therefore, to induce greater consumer eorts, an innovator may benet from inviting competitors
by sharing an idea.
On the other hand, the rm can achieve competitive advantage and greater
market share in the product market by keeping the innovation secret. Even though the innovating
rm will bear all the costs for communication and creating the market, it can then enjoy a monopoly
situation in the product market.
These two eects are related to the fundamental issue rms often face whether to focus on
maximizing their market share (which can be achieved by keeping the innovation secret) or on increasing the total market size (which can be achieved by sharing their innovation with competitors).
Understanding these tradeos enables us to understand an important issue of coopetition (Brandenburger and Nalebu 1996): whether to cooperate with competitors to reach a higher value creation
(e.g., market expansion) or struggle to achieve a competitive advantage without cooperation.
In our model, we analyze the strategic interactions not only among rms that compete with
each other, but also between rms and consumers who jointly create market demand through
communication. The game involves three players (two rms and consumers) and each makes multiple
decisions at dierent stages; these are endogenously interlinked. By analyzing the entire game, we
identify conditions related to demand and product market competition under which an innovator
should disclose an innovation, inviting competitors into the market.
The remainder of this paper proceeds as follows. In section 2, we relate our paper to the existing
literature in marketing and economics. Section 3 presents the model, and section 4 provides our
main results and analysis. In section 5, we extend our model and Section 6 concludes.
2
Literature Review
This paper is related to several streams of research. First, it contributes to the literature on a rm's
communication strategy by highlighting the two-sided costly eorts in the communication process.
Marketing communication is typically viewed as one-sided costly communication, with rms bearing
all the costs. In those models, consumers eortlessly become informed and recognize their needs once
they are exposed to a rm's advertising. In contrast, we recognize that the success of communication
requires both a rm's persuasion eorts and consumers' learning or elaboration eorts. Wernerfelt
(1996) is the rst paper that recognizes marketing communication as teamwork between rms and
consumers, and he suggests that an ecient communication plan should induce the ecient division
of labor between the two parties. Dewatripont and Tirole (2005) formalized this perspective and
developed a formal model of communication. They argued that the acts of formulating and absorbing
the content of communication are privately costly, and the successful communication depends on
the eorts of both sender and receiver together. Furthermore, they suggested that communication
4
eorts are strategic complements; that is, one side will try harder if the other side also tries harder.
We expand Dewatripont and Tirole (2005)'s framework by incorporating the competition between
rms. Thus, the communication in our model is characterized not only by strategic complementarity
between the consumers' eort and the rms' aggregate eort, but also by strategic substitutability
between each rm's individual eorts. Our model explores several interesting tradeos between these
two key strategic eects in communication, and its implications for secrecy within an innovative
rm.
Second, a number of papers examine the impact of consumers' costs of learning and deliberation.
Shugan (1980) is among the earliest to highlight the importance of incorporating consumers' cost
of thinking, and several subsequent papers explore its implications for a rm's strategy (Guo and
Zhang 2012, Kuksov and Villas-Boas 2010, Villas-Boas 2009, Wathieu and Bertini 2007). Wathieu
and Bertini (2007) explores the rm's pricing strategy to spur deeper thinking among consumers
about the personal relevance of product benets; others (Guo and Zhang 2012, Kukosv and VillasBoas 2010, Villas-Boas 2009) explore the rm's optimal product line decisions when consumers
need to incur costly deliberation eorts to evaluate the product. We also explore the implications
of consumers' costly eorts for deliberation to evaluate a new product, but our focus is on the
consumers' essential role in marketing communication.
Third, the current work also relates to the literature on a rm's strategies of managing business
secrets and information sharing.
between patenting and secrecy.
One stream of research in this area focuses on a rm's choice
Patents protect but publicize the rm's proprietary knowledge
through the patent process thus enabling it to exploit its private information (secrets) while reducing
asymmetry between the rm and its competitor. Competitors can imitate and create dierentiated
products. Thus, rms may sometimes forgo patenting and keep secrets internally. Several papers
have examined when to disclose secrets for patent protection and when to retain trade secrets
internally (Kultti et. al. 2007, Denicolo and Franzoni 2004, Horstman et. al. 1985, and Anton and
Yao 2004).
Another stream of research in this area deals with the information sharing decision in the context
of R&D whether or not a rm discloses its interim R&D results to the public. If R&D contests
are winner-take-all, rms disclose pessimistic or no information to discourage a rival's investment
(Hendricks and Kovenock 1989 and Gill 2008).
If the appropriability of an innovation is weak,
the free-riding incentive arises and rms disclose positive information about their interim R&D
results to further encourage a rival's R&D investment (De Fraja 1993 and Jansen 2010).
While
the appropriability of an innovation is exogenously given in these papers, the appropriability in
ours is endogenously determined by the degree of information disclosure; moreover, this endogenous
appropriability aects the rival's incentive to invest in communication eorts in equilibrium.
Fourth, broadly speaking, our research deals with a rm's strategies around cooperation and
competition with competitors, an important issue of coopetition (Brandenburger and Nalebu 1996).
5
A large body of literature examines various forms of coopetition such as strategic alliances among
competing rms (Amaldoss et al. 2000, Bucklin and Sengupta 1993, Luo et al. 2007, Harbison and
Pekar 1998),
13 collaboration with a rival rm through licensing (Inkpen 1996, Steensma 1996), and
impacts of these actions on innovation (Bonaccorsi and Lipparine 1994, Hamel et al. 1989, Nieto
and Santamaria 2007, Tsai 2009). Our paper contributes to this literature by providing one new
micro-foundation for coopetition based on the rm's communication motives.
Farrell and Gallini (1988) and Shepard (1987) are the two most closely related works in this
area.
These suggest that inviting competitors might increase the total market demand because
competition can serve as a credible commitment to lower price (Farrell and Gallini 1988) or higher
quality (Shepard 1987), both of which guarantee a higher ex post consumer surplus.
Our paper
captures a similar insight, but also provides a micro model of how this increased consumer surplus
leads to greater market demand based on the communication mechanism.
Moreover, our micro
model of communication captures not only complementarity between rms and consumers (Farrell
and Gallini 1986, and Shepard 1988), but also substitutability between rms.
Finally, the current work is related to a large body of marketing literature on a rm's preannounement strategy. The common premise of literature in this area is that the rm always wants
to deter the entry of competitors and preannouncement is used to achieve this end through communication with competitors (Bayus et al. 2001, Haan 2003, and Ofek and Turut 2013) or consumers
(Farrell and Saloner 1986, Garlach 2004, and Choi et. al. 2005). Our paper primarily diers from
these in that we provide another strategic motive of preannouncement to invite the competitor to
14
enhance the potential market demand through jointly communicating with consumers.
3
Model Set-up
The market consists of two rms, rm 1 and 2, and a continuum of consumers with mass of
1
is an innovator who discovers a radical innovation and rm
2
1.
Firm
is a follower. Once rm 1 discovers
a new idea, it chooses a level of secrecy by deciding the amount of information to publicly release
about its novel product idea.
disclose, and thereby,
variable,
13
d ∈ [0, 1],
1−d
where
We denote
d
as the amount of information that rm
1
chooses to
15 The degree of disclosure is a continuous
represents the level of secrecy.
d=0
means no disclosure (i.e., complete secrecy) and
d=1
means full
Harbison and Pekar (1998) nd that more than 50% of strategic alliances are typically formed among competing
rms within the same industry.
14
In our model, the market demand is endogenously determined by the communication between rms and con-
sumers.
There are several papers that also study the issue of endogenous market demand (in particular, market
expansion by the supply side eorts); Agarwal and Bayus (2002) nd empirical evidence that the entry of rms in
the early stage of the industry can increase consumer awareness and learning, and thus expand the potential market.
Shen and Xiao (2014) nd that market demand can increase endogenously with the number of rms by facilitating consumer learning in fast food market in China. Similarly, Shen (2014) emphasizes the role of rms' collective
advertising on generating the demand for the new product category.
15
We use secrecy and disclosure interchangeably throughout the paper.
6
Stage 2:
communication subgame
Stage 3:
product market competition
The innovator, the follower
(if   1), and consumers
choose communication efforts:
(p1 ,p2 ) and compete in
Stage 1:
information disclosure subgame
The innovator discovers a new idea,
and decides the degree of disclosure
d  [0, 1]
The follower decides whether or not
to enter the new product market
  {0, 1}
time
Firms choose their prices
(e1 ,e2 , ec )
Product Launch
the product market.
Consumers make a
purchase decision
Figure 1: Sequence of the game
disclosure (i.e., no secrecy). Then, as long as
d > 0,
the follower makes a decision about whether or
not to enter the market by following the new idea and developing a similar product,
If the follower decides not to enter (χ
follower decides to enter (χ
= 1),
= 0),
χ = {0, 1}.16
the eventual product market will be a monopoly. If the
the market becomes a duopoly.
Prior to competition in the product market, consumers and rms communicate with one another
about the new product idea. We model this marketing communication process as two-sided costly
eorts, a process that involves both rms' and consumers' eorts to transmit and assimilate the
novel product concept (we will discuss the communication mechanism in greater detail later). The
communication's success endogenously generates consumers' need recognition and thereby market
demand for a novel product.
and the follower (if
χ = 1)
competition whereas if
Finally, once the product is launched in the market, the innovator
oer dierentiated products at prices
χ = 0,
{p1 , p2 },
and engage in Bertrand
rm 1 monopolizes the market and oer its product at
p1 .
The entire game involves several distinctive decisions for each rm and consumers at dierent
stages as we can see in Figure 1. At stage 1, the innovator discovers a new idea and decides the
amount of information to disclose,
d ∈ [0, 1].
Then, the follower makes a decision whether to enter
the market after observing the innovator's disclosure decision.
At stage 2, rms and consumers
decide their optimal levels of communication eorts to transfer and assimilate the idea. Finally, at
stage 3, rms compete with each other in the product market and decide on prices while consumers
make a purchase decision.
It is important to note that these decisions are interlinked. For example, when the innovator
decides the secrecy in stage 1, it fully takes into account the eects of secrecy (1) on the follower's
decision regarding whether to enter the market (at stage 1), (2) on the equilibrium outcomes of
the communication game between rms and consumers (communication subgame in stage 2), and
(3) on the equilibrium outcomes of the pricing game in the product market played by the rms
(product market subgame in stage 3). Similarly, the communication eorts by rms and consumers
endogenously determine the potential market demand, which clearly aects the equilibrium payos
16
Here, we make a simplifying assumption that the competitor can immediately understand the value of the new
innovation, and therefore, can always make a similar product once a little piece of the innovation is shared (d
7
> 0).
for the rms in the product market at the stage 3. Hence, when the rms choose their optimal eort
levels for communication, they fully internalize the future payos from the product market, in which
they compete in pricing. Furthermore, these considerations aect the follower's decision regarding
whether to enter the market at stage 1. Thus, we use the Subgame perfect Nash equilibrium as our
solution concept. We now discuss each of these decisions in detail.
Information disclosure
Managing the secrecy of the innovative idea has strategic implications for the innovator's competitive
advantage. The more innovation the innovator keeps secret (or equivalently, the less the innovator
discloses), the more the technological leadership it can possess, and thus the innovator can have
greater competitive advantage over the competitor when the product idea is fully developed and
launched in the product market. We model the decision of the innovator's information disclosure as
a continuous variable,
d ∈ [0, 1].17
An innovator can disclose a piece of proprietary information to its
competitor through licensing contracts which can directly aect the relative competitive advantage
of the innovator (for example, Tesla and semiconductor companies). Here, we impose a truth-telling
assumption such that revealed information is truthful. In this licensing case,
the amount of innovation disclosed (no innovation disclosure as
as
d = 1).
d=0
d can be interpreted as
and full innovation disclosure
Alternatively, an innovator can release information about its upcoming product well
18 By making preannouncement,
in advance of actual market availability through preannoucement.
rms can deliver information on a product while it is still being developed. In this preannouncement
case,
d
can be interpreted as the length of time prior to actual launch of the product or the actual
maturity of an innovative idea upon market announcement; for example, keeping the innovation
completely secret and announcing the product on the same time as the product release (d
= 0)
or
disclosing its premature idea so early that the follower can fully catch up with the innovator on the
time when the actual product is launched (d
= 1).
We capture the inuence of information disclosure on the innovator's competitive advantage
through a cost function.
19 We assume that the innovator can retain its cost advantage stemming
from its technical breakthrough if the rm keeps it secret. For example, when Procter & Gamble
rst introduced disposable diapers in 1969, the company used a synthetic ber technology that
17
We assume that there is a xed cost of
associated with the information disclosure this
cost is a tie-breaker
for the innovator; when it is indierent between disclosing information and no disclosure, it chooses not to disclose
because of this small xed costs.
18
The credibility of the announcement is an important issue, and preannouncement can be a pure cheap talk (Bayus
et al. 2001, Choi et al. 2005, and Ofek and Turut 2013). However, this cheap-talk analysis is beyond the scope of this
paper, and we treat the preannouncement as truthful information sharing. By doing so, we can focus on the eects
of information disclosure on market competition, and analyze the strategic motives for a rm to convey its private
information on a new innovation in order to change other parties' behavior in a way that is benecial to the rm.
19
Alternatively, one can model the competitive advantage through demand side advantage (consumers may have
higher willingness to pay for the innovator's product, and the sharing of innovation reduces this advantage). We also
explored this specication, but the qualitative results remain the same.
8
helped them to create the diapers at a cheaper, more protable price over competition (Morrison
et al.
2000).
We can capture the extent of competitive advantage through secrecy; we x the
innovator's marginal production cost as
is a decreasing function in
and
m2 (d = 0) = m > 0.
m1 = 0,
and the follower's marginal production cost
d, m2 (d) = m · (1 − d)
Thus, when
d = 1,
without loss of generality. Hence,
m2 (d = 1) = 0,
the technical innovation is shared with the competitor
perfectly, and the innovator has no relative cost advantage (m1
competitive advantage is maximized when
m2 (d)
= m2 (d = 1) = 0)
while the
d = 0 (m2 (d = 0) = m̄ > 0 = m1 ).
Communication technology
We consider a communication technology where both the rms and consumers simultaneously exert
elaboration and learning eorts to transfer and assimilate the idea (Dewatripont and Tirole 2005).
20
The probability that the idea is properly communicated to and accepted by consumers is
,
σ(ef , ec ) = ekf · e1−k
c
where
ef ∈ [0, 1]
is the aggregate eort of the rms to transmit the innovative idea and persuade
consumers to accept it, and
message. Moreover,
ec ∈ [0, 1] is consumer's eorts to pay attention, deliberate and assess this
k ∈ [0, 1] captures the relative importance of two side eorts in communication.
In a monopoly situation (χ
(χ
(1)
= 1), ef = e1 + e2
= 0),
the total eort of the rms is
ef = e1 ;
in a duopoly situation
21
.
When radical new product categories such as HDTV and recordable DVD format are rst introduced in the market, the realization of the market demand is uncertain and, prior to launch,
rms need to expend eorts to stimulate greater demand by showing advertisements that mainly
promote the benets and advantages of these new product concepts without touting brand-specic
features (Bass et al. 2005). Such advertisements are particularly common in the introduction of
new product categories: when satellite radio was rst introduced, both Sirius and XM allocated
signicant portions of their advertising budgets for generic advertising to inform and educate consumers about the product's uses and benets to enhance product acceptance (Beardi 2001).
can think of these advertising activities as a rm's communication eorts
of learning and deliberation to evaluate these new product idea as
ec ,
ef ,
22 One
and consumers' costs
which is time consuming and
leads to depletion of cognitive resources (Shugan 1980, Guo and Zhang 2012). Thus, communication
eorts involve private costs
C(e) for the rms and consumers.
We assume these costs are increasing,
20
This is a generalized version of Dewatripont and Tirole (2005), and their model can be considered as a special
k = 12 .
21
To guarantee the probability σ ≤ 1, we assume v ≤ 1. The assumption is only for expositional purpose. We will
v
see later that the results rely on the relative ratio of vertical dierentiation to horizontal dierentiation (i.e., t ) not
case where both parties' eorts are equally important:
on a specic value of
22
v.
XM's ads will be about continuing to 'grow the whole category pie,' rather than competing with Sirius (Boston
and Halliday 2003).
9
convex such that
C(e) =
e2
2.
There are several important properties in this communication technology that we employ. First,
σ(ef , ec ) = 0
ef = 0
when
or
ec = 0 .
This captures the key characteristic that communication
requires two-sided eorts, and the communication can never succeed without both sides exerting
eort.
Second, this communication technology assumes complementarity between the eorts of
consumers and the aggregate eort of the rms:
σf c =
∂ 2 σ(ef ,ec )
∂ef ∂ec
≥ 0.
That is, each side is willing
to exert more eort if the other side also exerts more eorts, and the return from expending eort
increases when the other party explains better or listens better (Dewatripont and Tirole 2005, p.
1224).
23 Furthermore, in the duopoly case, we assume that both rms are symmetric in terms
of their eects on the eectiveness of communication; that is,
σ2
24
.
σ1 =
∂σ(e1 +e2 ,ec )
∂e1
=
∂σ(e1 +e2 ,ec )
∂e2
Thus, the eorts between each rm and consumers are strategic complements.
=
Finally,
another key characteristic of our communication technology is that the eorts of the two rms
are strategic substitutes:
σ12 =
∂ 2 σ (ef ,ec )
∂e1 ∂e2
≤ 0.
Because communication involves private costs,
rms have incentives to reduce their eorts and free ride on the other side's communication eorts.
Hence, the communication stage can be characterized by the strategic complementarity between the
consumers' eort and the rms' aggregate eort, and the strategic substitutability between each
rm's individual eorts, which are the crux of the current paper's premise.
Once the idea is successfully communicated (with probability
σ ), consumers can understand the
potential benets of the new product idea. If the idea fails to be communicated (with probability
1 − σ ),
consumers cannot be aware of the potential benets for this new product, and they may
think the new innovative idea (such as Google Glass) is only for geeks and not for them. Thus, they
will not even consider purchasing the new product.
Consumers consider purchasing the product
only if the idea is successfully communicated with probability
σ.
Those who become educated about
the radical innovation are the potential buyers when the product becomes available in the market.
Here, the role of marketing communication is to generate the consumers' need recognition and
product acceptance. Thus, marketing communication eorts endogenously creates and expands the
total demand for the new product; the total number of potential buyers is
σ T = σ(ef , ec ).
Competition in product market
The product market competition is modeled as a traditional Hoteling model. The innovator and
the follower are located at the two extremes of a Hoteling line,
in prices by charging
23
0
and
1,
p1 , p2 , respectively when the market is a duopoly.
Note that this strategic complementarity arises because
σ
respectively. They compete
If the market is a monopoly,
is endogenous and strategic choices of both rms and
consumers. On the other hand, as Dewatripont and Tirole (2005) explained, if
σ
is xed and exogeneously given, one
side can expend less eort as the other side has expended more eort.
24
The rms may have asymmetric inuences in persuading consumers. We can capture the asymmetry by setting the
total rm-side eort as
eF = βe1 + e2 .
The parameter
β
aects the exact equilibrium eort levels, but the underlying
mechanism that drives the equilibrium outcomes does not change due to the additive form of the specication. Hence,
our main results do not change qualitatively.
10
only the innovator chooses the monopoly price
p1 .
When communication between rms and consumers succeeds (with probability
become a potential buyer.
Potential buyers therefore receives a base utility
if they purchase a product. Besides the base utility
v,
v
σ ),
consumers
from consumption
consumers receive an idiosyncratic match
once the idea is developed into a product. Consumers' preferences (zj ) are uniformly distributed
along the Hoteling line,
zj ∼ U [0, 1].
Their utility is
uj = v − t · zj − pi ,
where
i = 1, 2,
and
t
is
the consumer's travel (mismatch) cost from the ideal point in Hoteling line. After observing their
preferences
zj
and the price(s), potential buyers make their purchase decisions and the rms receive
their payos. And we assume that
t is small enough (t <
v
3 ) that in equilibrium, all potential buyers
purchase from one of two rms in duopoly case.
4
Analysis
The game consists of three subgames: innovation disclosure, communication, and product market
competition.
We use the Subgame Perfect Nash Equilibrium as our solution concept.
We begin
our analysis using backward induction to solve the game and all the proofs are presented in the
Appendix.
4.1
Stage 3: Product market competition
We rst solve the nal stage of the game of product market competition. We denote rm 1's disclosure level as
d
and the rms' aggregate communication eorts and consumers' eorts as
{ef , ec }.
These will be endogenously determined in equilibrium, but for now we take them as given. There
are two dierent cases we need to consider depending on whether the follower, rm 2, decides to
enter the market or not (which again will be endogenously determined in equilibrium).
Duopoly (χ = 1)
As we can see later, there always exists for rm 1 a disclosure level
2 chooses to follow rm
a xed
d ≥
1's
idea (χ
=
d∗ and communication eorts
ef = e1 + e2
buyers are uniformly distributed along the Hoteling line
1
and utility
or rm
2.
Consumer
j
u2j = v − t(1 − zj ) − p2
such that for all
and
ec ,
rm
obtains utility
the total number of consumers
σ T = σ(ef , ec ).
zj ∼ U [0, 1],
u1j = v − tzj − p1
if purchasing from rm
2,
We impose a simplifying assumption of tie-breaker such that when
Those potential
and purchase a product either
if purchasing from rm
1
where the consumer's travel cost
t
captures the extent of product dierentiation between two products. Consumer
25
d ≥ d∗
1), and thus the market is a duopoly at Stage 3.25 Given
who are convinced about the need for the new product is xed as
from rm
d∗
d = d∗ ,
j
purchases from
rm 2 chooses to enter the market
even though it makes exactly zero prot in the product market. This is purely for expositional easiness and it does
not aect the results.
11
rm
1
rm
2's
1
2
−
if
1
2
u1j ≥ u2j ⇒ zj ≤
demand
p1 −p2 and
2t
p1 −p2
T 1 − p1 −p2 and
2t . Thus, rm 1's demand is D1 (p1 , p2 ) = σ
2
2t
−p2 T denes the total category demand while
σ T 12 + p12t
. Here, σ
−
D2 (p1 , p2 ) =
p1 −p2 1
dene
2 + 2t
two rms compete on prices
(p1 , p2 )
the selective demand for each rm within the category.
that maximize the retail their own prots
1
T
pD
= arg maxp1 R1 (p1 ; pD
2 ) = σ (p1 − m1 )( 2 −
1
1
T
pD
= arg maxp2 R2 (p2 ; pD
1 ) = σ (p2 − m2 )( 2 +
2
1's
where rm
marginal cost
decreasing function of
m1 = 0
and rm
2's
2's
R1 , R2 :
p1 −pD
2
2t )
D
p1 −p2
2t )
(2)
m2 = m · (1 − d),
which is a
d.
Then, we have the equilibrium duopoly prices
the rm
marginal cost
The
m
2m
D
pD
1 = t + (1 − d) 3 , p2 = t + (1 − d) 3 .
Because
marginal production cost should be low enough to enable it to make positive prot in
the product market
pD
2 ≥ m2 ,
we obtain that
d ≥ d∗ = 1 −
3t 26
m.
Also, the equilibrium duopoly retail prots are
R2D =
where
π1D =
(3t+(1−d)m)2
18t
,
π2D =
(3t+(1−d)m)2
18t
(3t−(1−d)m)2
T
σ
18t
R1D = σ T
(3t−(1−d)m)2
18t
= σ T · π1D ,
(3)
= σ T · π2D ,
are average prot that rm 1 and 2 make in the
duopoly product market per customer, respectively. It is important to know that this average prot
πi
is independent of the total market size, and only captures the marginal benet to the rm from
the increase in the total category demand
σT .
This will play an important role in the subsequent
analysis.
Therefore, as long as rm
1
discloses sucient information (d
≥ d∗ = 1 −
3t
m ), rm
2
makes
non-negative prot by entering the market. Also, note that rm 1's prot decreases as it discloses
more information (i.e.,
retail market if rm
1
d
increases) whereas rm 2's prot increases in
becomes the monopolist (i.e.,
d<
d.
Next, we analyze the
d∗ ).
Monopoly (χ = 0)
As long as rm
1
keeps a sucient degree of secrecy (d
by entering the market. Therefore, rm
2
< d∗ ),
rm
2
cannot make a positive prot
chooses not to work on a similar idea (χ
= 0),
and rm
1 becomes the monopolist in the product market at stage 3. Similar to the duopoly case, potential
buyers make purchase decisions once they observe the price and their preferences
Consumer
j 's
utility is
v − tzj − p1
if they decides to buy.
26
Consumer
j
zj ∼ U [0, 1].
purchases the product
∗
3t
We assume that m > 3t for the non-emptiness of d = 1 − m . Also, v > 3t ensures that even the marginal
∗
1
1 m·(1−d)
consumer (zi = 2 + 2t
) who is indierent between purchasing from rm 1 and rm 2, receives a positive
3
∗
1
1 m·(1−d)
utility in equilibrium: u = v − t 2 + 2t
− t − (1 − d) m
> 0.
3
3
12
v − tzj − p1 ≥ 0 ⇒ zj ≤
1
D1 (v, p1 ) = σ T · max v−p
,
1
. Under
t
if the utility
M
equilibrium price is p1
= v − t,
v−p1
t .
Thus, the market demand for rm 1's product is
the market coverage condition in duopoly (v
and the market demand is
D1 =
σ T .27 Firm
1's
> 3t),
the
monopoly retail
prot is
R1M = σ T · (v − t) = σ T · π1M
π1M = (v − t)
where
(4)
is the average prot that rm 1 makes in the monopoly product market per
customer.
4.2
Stage 2: Communication game
The market size
σ T = σ(ef , ec )
is the outcome of a two-sided marketing communication, a process
in which rms and consumers both exert costly eort. There are three players involved in marketing
communication (rm 1 and 2, and consumers), and they are all strategic and forward looking. For
a given
d of rm 1's choice in the rst stage, each player decides on their own communication eorts
anticipating the equilibrium product market outcomes at stage 3. Firm
communication eorts
e1 , e2 ,
and consumers also decide on their eorts
1
and rm
ec .
2
decide on the
Since consumers have
not observed the idiosyncratic preferences (zj ) yet, they form expectation on the consumption utility
taking into account the equilibrium prices oered by both rms in the product market competition
at the stage 3:

ũM
Eu = ũ =
ũD
=
=
´
´
z
max{v − tz − pM
1 , 0}dz
- Monopoly case
D
D
z max{v − tz − p1 , v − t(1 − z) − p2 }dz
(5)
- Duopoly case
When we compare the expected utility of consumers between the monopoly case and duopoly
case, it is immediately clear that the competition of duopoly provides a higher expected consumer
utility.
Thus, competition can serve as a credible commitment to guarantee a higher consumer
surplus.
Lemma 1.
The consumer's expected utility from purchasing the product is higher under duopoly
than monopoly market:
ũD > ũM .
Strategic complementarity and substitutability
When
d < d∗ ,
the follower (rm 2) chooses to not follow the innovator's idea (χ
= 0)
and the
innovator (rm 1) engages in marketing communication by itself. The single-rm communication
subgame simply displays a strategic complementarity between a rm and consumers.
However,
v−p1
27
T
The optimal price from FOC is p1 = arg maxp1 σ · p1 ·
= v2 . However, even the consumer at zi = 1 nds
t
v
the positive utility under this price: u = v − t − 2 > 0 because v > 3t. Hence, the equilibrium price is determined by
T
u(zi = 1) = v − t − p1 = 0⇒ pM
1 = v − t, and the market demand is D1 = σ .
13
when
d ≥ d∗ ,
both rms engage in collective marketing communication, and each rm has an
incentive to free ride on the other's costly eorts. Hence, the communication also displays a strategic
substitutability between the two rms, which complicates the analysis.
Let us start from the case of monopoly market (χ
marketing communication by itself. Therefore, rm
cation eorts
e1 , ec
1
= 0)
when
d < d∗ .
The innovator engages in
and consumers choose the optimal communi-
that maximize their total expected payos:
M
ek1 · e1−k
π1 −
c
M
k
1−k
e1 · ec
ũ −
EΠ1 =
EU
=
e21
2,
e2c
2.
(6)
Here, the single-rm communication simply displays a strategic complementarity between a rm's
and consumers' eorts:
∂ 2 EΠ1
∂e1 ∂ec
−k M
= k (1 − k) ek−1
1 ec π1 ≥ 0,
and
∂ 2 EU
∂e1 ∂ec
−k M ≥ 0.
= k (1 − k) ek−1
1 ec ũ
Due to this strategic complementarity eect, increasing eort from one side leads to higher
response from the other side. Thus, the equilibrium eorts under monopoly are determined by the
following best response functions
Both equilibrium eorts
eM
1
=
eM
c
=
kπ1M e1−k
c
1
2−k
,
1
(1 − k) ũM ek1 1+k ,
(7)
M
eM
1 (ec ) and ec (e1 ) are increasing in the other side's eort ec
and
e1 , and its
M
M
own expected average payos from the product market π1 and expected utility ũ , respectively.
∗
Next, we consider the case of duopoly market (χ = 1) when d ≥ d . In duopoly, both rms
engage in collective marketing communication.
optimal communication eorts
(e1 , e2 , ec )
where
i = 1, 2,
and
ef = e1 + e2
ekf · ec1−k πiD −
=
ekf · e1−k
ũD −
c
= 0),
= k (1 −
and consumers choose the
e2i
2,
e2c
2,
(8)
there exist a strategic complementarity eect
between consumers's eorts and rms' aggregate eorts:
−k D
k) ek−1
f ec ũ
2
is the rm side total eort.
Same as in the monopoly market case (χ
∂ 2 EU
∂ei ∂ec
rm
that maximize the following payo functions:
EΠi =
EU
1,
Thus, rm
≥ 0,
for all
∂ 2 EΠi
∂ei ∂ec
−k D
= k (1 − k) ek−1
f ec πi ≥ 0,
and
i = 1, 2.
In addition to strategic complementarity, the communication game also shows the strategic
substitutability between each rm's individual eort:
for all
i = 1, 2.
∂ 2 EΠi
∂ei ∂e−i
= −k (1 − k) (e1 + e2 )k−2 e1−k
πiD ≤ 0,
c
This strategic substitutability eect between each rm's individual eort creates a
free-riding problem in communication such that each rm has an incentive to lower its own eort
in response to the other rm's eort.
To measure this free-riding problem more directly, we rst examine the equilibrium eorts under
14
duopoly case for rm
i ∈ {1, 2}
and consumers, which are implicitly given by
k−1
1−k D
D
kπiD eD
e
+
e
,
c
i
j
1
D k k+1
=
(1 − k) ũD eD
i + ej
eD
=
i
eD
c
Similar to the monopoly case (equation 7), the optimal eort of rm
side's eort
eD
c ,
and its own expected average prot
πiD .28
This is the direct eect of the rival rm
−1
e2−k
eck−1
f
1+
−i's
i (eD
i ) is increasing in consumer
However, dierent from the monopoly
0
case, the rm i s eort is now aected by the other rival rm
∂ei
=
∂e−i
(9)
−i's
eort:
≤ 0.
(10)
(1−k)kπiD
eort on its own eort arising from strategic substi-
tutability. The success of communication benets both rms, but eorts are costly. Therefore, each
individual rm has an incentive to free ride on the other rm's costly eort and lower its own eort
in response to increase in the other rm's eort.
Because of the countervailing eects of strategic complementarity and strategic substitutability,
the total eect of an increase in the rival rm's eort is ambiguous. More precisely, there are two
(direct and indirect) eects of the rival rm's eort on the focal rm's own eorts. Firm
i's
best
response to the increase of the other rm's eort is to decrease its own because of its incentive
to free ride on the other rm's costly eort (equation 10).
complementarity eect between
∂ec
(
∂e−i
≥ 0).
∂e
eorts ( i
∂ec
ec
and
ei ,
consumers' eorts
Nevertheless, due to the strategic
ec
increases with rm
−i's
eorts
More importantly, this increased eort in consumers (ec ) in turn increases rm
≥ 0).
This is the indirect eect of rm
may nd it protable to raise the eort with rm
−i's
−i's
eort on the rm
i's
i's
eort. Hence, rm
i
eort through this indirect eect that arises
from complementarity through consumer eort. In other words, complementarity may reduce the
rms' free-riding incentives, which may result in higher total eorts. We explore this interaction
between these countervailing eects next.
Communication incentives and optimal eorts
We rst note that the incentives for all players (rms and consumers) to exert eort increases in
the expected payos that they can receive from the product market at stage 3 in both monopoly
and duopoly cases. Also, because of strategic substitutability, one rm has incentives to free ride
o the other rm's eorts in a duopoly. Such a case, we can see that the ratio of eorts
two rival rms is equal to the ratio of their expected average prots
28
π1D
π2D
e1
e2 between
.
D
Also, the optimal level of eort for consumers ec is again increasing in the other side's eorts (the rm side's
D
eD
)
and
its
own
expected
utility
in
the
product
market ũ .
f
total eort
15
Proposition 1.
Equilibrium communication eorts can be characterized as follows:
1. Each player's equilibrium eort in communication increases in its own expected surplus from
∂eM
the product market: ∂π1
1
≥ 0,
2. Moreover, in duopoly case (χ
∂eD
i
∂πiD
= 1),
≥0
(for
i = 1, 2),
∂e
and ∂ ũc
≥ 0.
the ratio of eorts between two rival rms in duopoly (
is equal to the ratio of their expected average prots from the product market:
eD
1
eD
2
=
π1D
.
π2D
eD
1
)
eD
2
In a duopoly case, the relative eorts between the two rms is only determined by the split of
the total product market prots regardless of levels of consumers eorts. Hence, the innovator may
nd it optimal to sacrice market prot by sharing its innovation with competitors. Increasing the
competitor's average prot can induce the competitor to shoulder more communication costs and
expand the total market size through cooperation in this stage.
D
disclosure), the expected average prots are identical (π1
D
levels of eorts are identical (e1
=
In particular, when
= π2D ),
d = 1
(full
and therefore, the equilibrium
eD
2 ). However, the exact level of rms' eorts is inuenced by
consumer eorts for communication, which are aected by consumers' expected payos from the
product market.
From Lemma 1, we already know that the consumer's expected utility is higher under a duopoly
D
than under a monopoly market (ũ
> ũM ).
This proposition implies that consumers always have
more incentives to incur costly learning eorts under duopoly than under monopoly (since
∂ec
∂ ũ
≥ 0).
This is summarized in the following corollary.
Corollary 1.
eD
c
>
Consumers exert more eorts under a duopoly than a monopoly market for all
k < 1:
eM
c .
This result suggests another important incentive for the company to share its innovation with a
competitor. The presence of a competitor serves as a commitment mechanism to assure consumers
that they will receive higher utility in the product market, which increases the incentives for consumers to expend more costly eort in deliberating about the new innovation. More importantly,
this increased consumer eort further encourages rms to put more eorts in the communication
stage through complementarity between rms and consumers (equation 9). Sharing the innovation
is a way to invite the competitor to the market, which triggers higher consumer eorts and ensuing
rms' eorts all together. Thus, an innovator may benet from attracting a competitor.
Next, we compare the equilibrium market size. Under both monopoly and duopoly cases, the
total market sizes are given by
σ T = (1 − k)1−k k k (ũ)1−k (πf )k ,
where
πf
πfM = π1M ;
denotes the rm side aggregate average retail prots.
if the market is a duopoly,
πfD = π1D + π2D .
16
(11)
If the market is a monopoly,
The direct comparison of the total market size
σT
under duopoly and monopoly (equation 11
above) allows us to identify the exact condition under which the market expands under duopoly.
Proposition 2.
For any given
such that for all
k ≤ k (d),
d ∈ [0, 1],
there always exists a threshold
1
k̄(d) ≡
1+ln
M
π1
D +π D
π1
2
/ ln
ũD
ũM
the total market size is greater under duopoly than under monopoly:
σ T D (d) ≥ σ T M .
This result nds that whether or not the market expands under duopoly simply depends on the
consumers' expected utility
ũ
and the rms' aggregate average retail prots
πf .
More importantly,
as consumers play an even more important role or the complementarity eect of consumers becomes
larger (k
≤ k̄ ),
the market tends to expand under duopoly, and thus, the innovator is more likely
to disclose its innovation to invite competitor in the market.
When the competitor's communication eort increases (which can be induced by sharing more
information and thus guaranteeing a sucient amount of prot in the product market), the innovator has incentives to lower its eorts because of substitutability or free-riding eect (equation
10). At the same time inviting the competitor allows the innovator to commit to provide greater
surplus to consumers, which increases the incentives for consumers to expend more costly eort in
deliberating about the new innovation. Moreover, as the complementarity eect of consumers becomes larger (k
∂ei
≥ 0).
≤ k̄ ), this increased eort in consumers (ec ) in turn increases rm's eorts ( ∂e
c
This complementarity in communication between rms and consumers through consumers' strategic
decision is the key to mitigating the potential free-riding incentives of rms.
The next subsection highlights this insight by investigating a benchmark case where consumers
do not play a role in communication (i.e.,
k = 1).
4.2.1 One-sided Communication
In order to highlight the importance of the role of consumers, we study a benchmark where marketing
communication is purely one-sided; that is, only rms' eorts matter.
This is a situation where
consumers can passively learn about the potential benet of the product through rms' eorts (such
as advertising). We study this situation by looking at the extreme case of
k = 1. In communication,
only rms eorts aect the success of communication and the size of the potential market. Consumer
eort
ec
has no eect on the outcome of communication.
First, when
own. Firm
1
d < d∗ ,
rm
1
is the monopolist and engages in marketing communication on its
chooses an eort level that maximizes
EΠ1 = (e1 ) π1M −
e21
2 , which is
M
eM
1 = π1 = v − t.
Then, rm
1's
expected payo as a monopolist is
EΠM
1 =
17
(12)
1
2
· π1M
2
=
1
2
· (v − t)2 .
When
d ≥ d∗ ,
rm
2
follows the idea and the market becomes duopoly. Both rms decide on
the optimal communication eorts. Since consumers do not play a strategic role in the marketing
communication, there only exists the free-riding eect between the two rms. Firm
D
e1 and e2 maximize EΠD
1 = (e1 + e2 ) π1
D
D
optimal eorts are ei = πi , i = 1, 2.
−
e21
2,
EΠD
2
e2 ) π2D
= (e1 +
−
1 and 2's eorts
e22
2 , respectively. Then, their
And the total rm-side eort is
D
D
eD
f = π1 + π2 =
((1 − d)m)2
t+
9t
!
.
(13)
2
EΠD =
1
2
Then, their expected payos under duopoly are
where
π1D =
(3t+(1−d)m)2
18t
,
π2D =
(3t−(1−d)m)
18t
(π1D )
2
+ π1D · π2D , EΠD
2 =
(π2D )
2
2
+ π1D · π2D ,
.
Comparing the equations (12) and (13), we nd that whether the market can expand under
duopoly is determined by the two rms' total retail prots.
Proposition 3.
When marketing communication is one-sided (i.e.,
k = 1),
M
eort is always greater under monopoly and so is the total market size: ef
the rm side aggregate
> eD
f
and
σT M > σT D .
When consumers do not play a strategic role in marketing communication, the market never
expands in duopoly, and a duopoly market always leads to a smaller market size (σ
TM
≤ σ T D ).
This is a stark contrast to the case of two-sided costly communication case, where the aggregate
rm-side eort as well as the total market size can be greater under duopoly.
Moreover, we can show that when the communication is only one-sided such that the market
does not expand under duopoly, the innovator has no incentive to disclose innovation and invites
competition.
Proposition 4.
When marketing communication is one-sided, the innovator never shares the in-
novation and prefers to become the monopolist in the product market.
Without a complementarity eect between consumers and rms, the market never expands
under duopoly compared to the monopoly market case. Also, without the market expansion eect,
the communication sharing eect itself does not compensate for the loss in prot from the retail
market. Hence, the innovator prefers to become the monopolist in the product market and it is never
protable for an innovating rm to invite competition. This suggests that sharing communication
costs is not a key driver for the innovator's information disclosure decision in stage 1.
4.3
Stage 1: Innovation Disclosure
In the rst stage, the innovator (rm
1)
decides on the degree of innovation disclosure,
taking into full consideration the eects of disclosure on (1) the follower's entry decision (χ
18
d ∈ [0, 1],
∈ {1, 0}),
(2) equilibrium outcomes of the communication game between rms and consumers (e1 , e2 , ec ), and
(3) the equilibrium prot from the product competition (π1 (d), π2 (d)).
Upon observing
d,
rm
2
decides to follow the idea and enter the market (χ
and does not enter the market (χ
= 0)
if
d < d∗ .
= 1)
if
d ≥ d∗ ,
They both correctly anticipate the equilibrium
outcomes in the proceeding communication and product market competition stages given the actions
(d, χ)
they play.
First, we analyze rm
cation mode, rm
1
1's
optimal disclosure level when
prefers a certain level of disclosure
d
EΠ1 (d) = σ T D (d)π1D (d) −
Hence, rm
1's
preferred
∂EΠ1
=
∂d
d
∂EΠ1
∂σ
|
d ≥ d∗ .
that maximizes its expected payo:
1 D 2
e (d)
2 1
solves the following optimality condition:
∂σ T D ∂eD
∂σ T D ∂eD
c (d)
2 (d)
+
∂ec
∂d
∂e2
∂d
{z
}
increasing eorts from consumers and rm
To understand the underlying forces that aects
∂EΠ1
∂d
= π1D
=
=
If under a collective communi-
d,
+
∂EΠ1 ∂π1D (d)
∂π
∂d
| 1 {z
}
(14)
retail prot loss
2
we transform the above equation as follows:
∂σ T D ∂eD
∂σ T D ∂eD
∂σ T D ∂eD
∂σ T D ∂eD
∂π D
c
2
1
1
+ π1D
+ π1D
− π1D
+ σT D 1
∂ec ∂d
∂e2 ∂d
∂e1 ∂d
∂e1 ∂d
∂d
D
T
D
D
T
D
D
D
D
T
D
∂ec
∂σ
∂e2
∂σ
∂e1
∂e1
∂π
∂σ
+
+
) − C 0 (eD
+ σT D 1
π1D (
1 )
∂ec ∂d
∂e2 ∂d
∂e1 ∂d
∂d
∂d
D
∂EΠ1 ∂σ T D
∂EΠ1 ∂C(eD
∂EΠ
)
∂π
1
1
−
+
·
·
· 1
∂π
∂d
| ∂σ {z ∂d }
| ∂C {z ∂d }
| 1 {z
}
potential market expansion
reducing comm. cost
where the second equality follows from the rst-order condition:
∂σ T D D
∂e1 π1
(15)
retail prot loss
= C 0 (eD
1 )
at
e1 = eD
1 .
The equation (15) clearly suggests that there are three main eects of disclosure in play: (1)
∂σ T D
∂d ), (2) a cost-saving eect
D
∂EΠ1 ∂C(e1 )
on communication through the sharing of communication with competitors (−
∂C ·
∂d ), and
D
∂EΠ1 ∂π1
(3) an eect on the retail prot (
∂π1 · ∂d ). Clearly, as the innovator discloses more information
D
∂EΠ1 ∂π1
about its innovation, its own prot decreases due to the increased competition (
∂π1 · ∂d ≤ 0),
D
∂EΠ1 ∂C(e1 )
and the cost saving from communication stage can be greater (−
≥ 0). However, as we
∂C ·
∂d
the eect on the market expansion through communication (
∂EΠ1
∂σ
·
have seen from the one-sided communication case, the cost saving from the communication can't
fully compensate for the prot loss in the competitive product market (Proposition 4). Hence, the
key for rm 1 in deciding whether to share its innovation with the competitor depends on the eect
on the market expansion. Only if the market expansion can be suciently large such that it can
outweigh the loss in the product market (i.e., net prot loss including the cost saving eect), then
will the innovator l disclose information.
19
Proposition 5.
1. When
e
(Equilibrium) There exists a threshold k
k > ke ,
ln
=
ln
πM
ũD (d∗ )
−ln D1 ∗
ũM
π1 (d )
M
π1
ũD (d∗ )
D (d∗ ) +ln ũM
π1
such that
the optimal strategy for the innovator is not to disclose any information
and the market becomes a monopoly.
k ≤ ke
de ∈ d∗ = 1 −
2. Otherwise (i.e.,
de = 0,
29
), the optimal strategy for the innovator is to disclose sucient infor-
3t
mation
m , 1 , such that the follower decides to enter the market (χ
3t
∗
e
the market becomes duopoly (i.e., d = 1 − m ≤ d ).
= 1)
and
Proof. See the Appendix.
The market expansion eect (
become more important (i.e.,
k
∂EΠ1
∂σ
·
∂σ T D
∂d ) increases as consumers' roles in communication
decreases). Otherwise, inviting competition does not increase the
market demand due to the free-riding eect between two rival rms. Only when
k
is suciently
low (or consumers' roles are suciently important), can the market expansion eect more than
compensate for the net loss in the product market and a rm be better o inviting its competitor by
sharing its innovation. By disclosing sucient information to the competitor, a rm can convince
a sucient surplus of the competitor in the product market, and therefore it may benet from
joint eorts to create a new category demand with its competitor.
Otherwise (i.e.,
k ≥ k e ),
the
innovator will prefer to maintain its competitive advantage by keeping its innovation secret, avoiding
competition, and extracting monopoly surplus in the product market.
Figure 2 demonstrates the tradeos in the rm's disclosure decision under two dierent cases
(k
= 0.1
vs.
k = 0.9).
When the importance of consumers in communication is low (k
= 0.9),
the
innovator's expected payo is greater under a monopoly than a duopoly. Thus, the rm is better
o avoiding competition by keeping its innovation secret and being a monopolist.
hand, when the importance of consumers is high (k
= 0.1),
On the other
the innovator's expected payo under
a duopoly can be greater than under a monopoly due to the market expansion eect. Hence, the
rm can benet from inviting the competition by disclosing sucient innovation to the competitor
e
(d
≥ d∗ ).
d∗ = 1 −
3t
m is the minimum level of information disclosure which can induce the
∗
follower to enter the market. Also, we already know that at d the threshold level of k for the
Note that
29
Technically, without any disclosure cost, any amount of information disclosure
de ∈ [0, d∗ ) can be optimal because
the overall equilibrium payos for both rms and consumers are independent of the amount of information disclosure
e
∗
3t
de as long as de < d∗ = 1 − m̄
. This is so because the follower does not enter the market χ = 0 when d < d ,
and thus, the market is monopoly. As long the market is a monopoly, the amount of the information disclosure does
not change consumers' expected utility, and thus, the optimal communication eort will be the same irrespective of
de ∈ [0, d∗ ). However, this indierence result is an artifact from the model assumption of zero cost for information
disclosure. As long as we allow some small costs associated with information disclosure, the innovator is no longer
e
indierent to the amount of information disclosure, and the optimal strategy is not to disclose any information d = 0.
This no-information disclosure is uniquely optimal under
cost of information disclosure.
20
E
k =0.9
k = 0.9 :
k = 0.1 :
k =0.1
k =0.1
k =0.9
d
d*
Monopoly
Figure 2: Firm
1's
Duopoly
expected payo under
k = 0.1
and
k = 0.9
duopoly market to be greater than that the monopoly market (from proposition 2) is
1
k (d∗ ) =
1 + ln
D ∗)
π1M
/ ln ũ ũ(d
D
M
π1 (d∗ )
πM
ln πD 1(d∗ )
1
⇒
ln
We can further understand the threshold
D
k
e
=
∗)
ln ũ ũ(d
M
ke
ln πD 1(d∗ ) + ln
1
1
ũD (d∗ )
ũM
=
1
− 1.
k (d∗ )
(16)
in Proposition 5 in terms of further
πM
− ln πD 1(d∗ )
πM
ũD (d∗ )
ũM
πM
=
D
∗)
D
∗)
1 − ln πD 1(d∗ ) / ln ũ ũ(d
M
1
πM
1 + ln πD 1(d∗ ) / ln ũ ũ(d
M
1
k (d∗ )
as follows:
1
k(d∗ )
1
k(d∗ )
2−
=
∗
= 2k (d ) − 1,
where
k e = 2k (d∗ ) − 1 ≤ k (d∗ )
This relationship (k
e
(17)
always holds for
≤ k (d∗ ))
k (d∗ ) ∈ [0, 1].
implies that larger market size under the duopoly than the
monopoly is a necessary condition for information sharing. The market expansion eect from the
increased role of consumers in communication (i.e., low
oset the retail prot loss from sharing its innovation.
k)
should be much greater such that it can
For example, when
market size can be larger under a duopoly than under a monopoly.
nds it optimal not to disclose any innovation. Only when
k<
k e ≤ k ≤ k (d∗ ),
the
However, the innovator still
k e , does rm
1
nd it optimal to
disclose innovation.
Interestingly, the innovator sometimes nds it optimal to share its innovation more than the
∗
minimum level of information disclosure (d ) if the role of consumers becomes even greater.
21
Proposition 6.
information
When
de > d∗ ,
k
becomes even smaller (i.e.
t>
2v−7t
3t−2v ), the innovator discloses
so that the follower makes positive prot from the product market competition,
and therefore exerts positive communication eort
only when
k ≤ k =
eD
2 > 0.
Moreover, the threshold
k > 0
exists
2v
7 .
As consumer eorts become more important for the success of marketing communication, the
innovator can be better o by disclosing more information than necessary for inviting competition
e
(d
> d∗ ).
In particular, when the horizontal dierentiation becomes suciently large (t
and consumers' roles in marketing communication are increasingly signicant (k
< k ),
>
2v
7 ),
creating
a market environment where consumers have sucient incentives to exert more learning eorts is
crucial. As
t increases, consumers have lower expected utility from consuming a product and thereby
less incentives to incur upfront learning costs.
In this case, rm
1
has to convince consumers to
exert more upfront communication eorts by committing to even more intense competition and
lower prices. Disclosing more information to the competitor can serve as a commitment mechanism
for higher consumer utility in this case.
2v
7 ), even if rm
e
∗
keeps the maximal secrecy d = d (since
On the other hand, when horizontal dierentiation is not large enough (t
1
prefers to invite the competitor to the market, rm
there does not exist
k > 0).
1
≤
In this case, rm 2 does not exert any communication eort (since
d∗
is the level of information disclosure that makes rm 2 zero prot by entering the market). Given
the low
t,
the expected utility of consumers is already suciently high such that the existence of
competition itself is sucient to convince consumers to expend learning eorts in communication.
The purpose of information disclosure is not to use competitors for expanding the market together;
rather competition serves as a commitment to not hold up consumers in the product market.
In summary, there are two key mechanisms through which a rm may benet from revealing
information to its competitor in equilibrium: First, a direct eect on the competitor's entry decision and communication eorts. More information disclosure increases the follower's prot, which
facilitates the competitor's entry and makes a rival engage in more communication eorts. Second,
there is another indirect eect of information disclosure on consumer eorts: the existence of competition (triggered by the information disclosure) can serve as commitment mechanism for higher
consumer surplus, which accelerates consumer eorts in communication. This increased consumer
eort can contribute to market expansion through the complementarity of consumers and rms in
communication.
5
Extension: sequential two-sided communication
In our main model, we consider a case where rms and consumers simultaneously decide their
communication eorts without observing the other's decisions.
In our rst extension, we relax
this assumption and study a realistic case where communication decisions are sequential such that
22
consumers adjust their learning eorts after observing rms' marketing eorts. We nd that the
eect of complementarity is amplied in the sequential communication, which results in a higher
level of equilibrium communication eorts and disclosure compared to simultaneous communication.
The last stage of retail competition remains the same as the simultaneous communication case.
However, at the communication stage, the sequentiality would aect the equilibrium results. Under
this sequential communication case, consumers adjust their eorts
ef .
in reaction to the rm's choice
EU = ek1 · e1−k
ũ −
c
of eorts. Consumers maximize their expected utility,
given eort
ec
e2c
2 , after observing a
Hence, the best reply function for consumers is still the same as the simultaneous
case and given by
1
k+1
.
ec = (1 − k) ũef k
However, the rm is now a Stackelberg leader.
(18)
Anticipating the consumers' best response
(Equation 18), the rm solves the following maximization problem:
max EΠi = σ (ef , ec ) · πiD −
ei
where
,
σ (ef , ec ) = ekf · e1−k
c
and
ef = e1 + e2
when
χ = 1,
The rst order condition for the optimal eorts for rm
e2i
,
2
and
(19)
ef = e1
when
χ = 0.
i (i = 1 under monopoly while i ∈ {1, 2}
under duopoly) is given by
∂σ ∂ec
∂σ
+
·
∂ei ∂ec ∂ei
πiD = ei
(20)
Compared to a simultaneous communication case, there is an additional incentive (
0
because of complementarity
∂ec
∂ei
> 0)
for rm
i
∂σ ∂ec
D
∂ec · ∂ei ·πi
to exert an eort. Consequently, rm
i
>
expends
more eorts in a sequential communication case, which in turn leads to greater eort for consumers
in a sequential communication than simultaneous case.
At the last stage, rm
1
chooses the optimal disclosure level
de ∈ [0, 1].
Similarly, we can nd
that the amount of disclosure increases under sequential communication compared to the simultaneous communication case. Under sequential communication, both rms and consumers incur more
communication eorts and thereby the market expansion eect through communication is amplied,
which increases the rm 1's incentive to disclose more information.
Proposition 7.
The threshold
ke
at which rm
1
is indierent between inviting competition and
becoming a monopolist does not change. Nevertheless, in the case in which rm
competitor (i.e.,
k≤
k e ), the optimal disclosure level
case than in the simultaneous communication case.
23
1 intends to invite the
de is higher in the sequential communication
6
Conclusion
In this research, we study the strategy for introducing revolutionary products and try to explain
the rationale for dierent information disclosure strategies among innovating rms: whether rms
disclose innovation to competitors or keep it secret.
Our explanation is based on the persuasion
motive of rms in communication and the strategic role of consumers.
Specically, we model
marketing communication as two-sided costly eorts and the key determinant for market demand
of a novel product. Not only does a rm exert costly eort during the communication process, but
consumers also have to expend eort in assimilating the idea and deliberating their needs. Hence,
a key challenge for rm is how to persuade consumers to expend more communication eorts in
assimilating the new idea, and clarifying their needs by examining an unproven product category.
Our analysis suggests that there are interesting tradeos facing the innovating rms in choosing
their level of secrecy.
Disclosing innovation can increase the follower's expected prot from the
product market, which encourages entry of competition and makes a rival engage in more communication eorts. Thus, the innovating rm can benet from disclosing innovation, which serves as an
invitation for competitors, because the presence of the competitor can help to expand the market
through cooperation in communication stage.
This communication stage is characterized by strategic complementarity between consumers'
eorts and the rms' aggregate eort, and strategic substitutability between each rm's individual eorts. Our analysis further reveals that without consumers playing a complementary role in
marketing communication, free-riding problem arising from strategic substitutes between each individual rm's eorts causes the market size to shrink under a duopoly. Only when communication
shows a strong strategic complementarity between consumers and rms, can an innovating rm
benet from sharing innovation; strategic consumers alleviate the potential free-riding eects of
rival rms.
More precisely, the presence of competition induced by sharing the innovation, can serve as a
commitment to guarantee greater surplus for consumers, which helps rms to convince consumers to
expend more communication eorts. Consequently, the increased consumer eort can result in market expansion through the complementarity of consumers and rms in communication. Therefore,
to induce greater consumer eorts, an innovator may benet from inviting competitors by sharing
an idea.
Of course, inviting competitors to jointly expand the market by sharing its innovation involves
signicant costs. In particular, we nd that the relative prot of the product market determines
the division of eorts between the two rms. The follower has an incentive to exert more eort only
when it would get sucient prot in the product market.
To incentivize the follower to expand
the market, the innovator has to pay costs of giving part of market share to the follower. But the
innovating rm can achieve competitive advantage and greater market share in the product market
24
by keeping the innovation secret.
Even though the innovating rm should bear all the costs for
communication and creating the market, it can still enjoy the monopoly situation in the product
market. It is thus not obvious that it will be protable to share innovation and invite competitors
into the market. Nevertheless, we nd conditions that lead a rm to reveal information to increase
its protability in the product market despite the additional competition.
Essentially, the issue that any innovator faces is trade-os in coopetition whether to increase
market size with competitors or capture market share. In this sense, we believe our research can shed
light on understanding this important issue of coopetition by providing one micro-mechanism about
when to cooperate with competitors to reach a higher value creation (such as market expansion) or
struggle to achieve a competitive advantage without cooperation.
Finally, our results critically depend on the key features of communication: strategic complementarity between consumers' eorts and the rms' aggregate eort, and strategic substitutability
between each rm's eorts. Although we believe that imposing those characteristics in marketing
communication is reasonable in many situations, we would not wish to claim that marketing communication always takes on strategic complementarity between rms and consumers.
In certain
situations, it is possible that communication takes on strategic substitutability between rms and
consumers. For example, many inbound marketing rms encourage consumers to search product information on their own instead of bearing all communication costs if this can be more eciently done
by consumers (see a seminal paper by Wernerfelt 1994 for the conceptual argument for eciency
30 Nonetheless,
criterion on who should bear communication costs between rm and consumers).
communication between rms and consumers can be better captured through strategic complementarity in many situations like radical innovation, in which consumers are unsure of both the uses and
the benets of a product and their needs. In these situations, rms' eorts cannot totally substitute
for consumers' eorts, because consumers have to incur private costs in learning about the product
and clarifying their needs. In this research, we recognize that the acts of formulating and absorbing
the content of a communication are privately costly, and we provide a new perspective on marketing
communication (as two-sided costly eorts) and its implications.
30
Also, Mayzlin and Shin (2011) formalize this perspective by considering rms' and consumers' eorts in commu-
nication as substitutes. They show that inducing consumers' eorts in the communication is sometimes more ecient
for rms.
25
Appendix A
Proof of Lemma 1.
Proof. Under monopoly, rm 1 oers its monopoly price
pM
1 = v−t such that all consumers purchase
ˆ
the product, thus we have
M
ũ
(v − t · z − v + t) dz =
=
z
t
2
Under duopoly,
ˆ
D
ũ
D
max v − tz − pD
1 , v − t (1 − z) − p2 dz
=
z
ˆ
pD −pD
1
− 1 2t 2
2
=
ˆ
v − tz −
pD
1 dz
+
0
1
v − t (1 − z) − pD
2 dz
pD −pD
1
− 1 2t 2
2
1
1
5
((1 − d) m) 2 − (1 − d) m + v − t
36t
2
4
p
1
⇔ d ≤ d = 1− m
9t + 6 t (4t − v) or d ≥ d = 1 −
=
Hence,
ũD ≥ ũM
Note that the market is duopoly (χ
d∗ >d
because
v > 3t.
= 1)
only when
d ≥ d∗ = 1 −
Hence, when the market is duopoly (i.e.,
d≥
1
m
9t − 6
p
t (4t − v) .
3t
m . Also, it is immediate that
d∗ ), ũD > ũM .
Proof of Proposition 1.
Proof. The rst part of the proposition can be easily checked by examining the equilibrium efk
k
forts.
Consumers' equilibrium eort is
tal rm prot, i.e.,
∂ec
∂ ũ
=
k
1−
2
πf =
π1M if monopoly or
− k2
((1 − k) ũ)
(kπf )
k
2
≥ 0.
M
case, rm 1's equilibrium eort is e1
1+k
2
k−1
M
πf =
π1D
+
where
πf
π2D if duopoly.
For all
Next, we check the rms' eorts.
= (1 −
k) ũM
1−k
2
kπ1M
1+k
2
∂eM
1
. So
∂π1M
denotes the to-
k ∈ [0, 1],
In the monopoly
= (1 − k) ũM
1−k
2
·
k ∈ [0, 1]. In the duopoly case, the equilibrium eort of rm
1−k
1−k
1+k πiD
∂eD
i
2
. So
= (1 − k) ũD 2 ·
i, i ∈
= (1 − k) ũD 2 k π1D + π2D
π1D +π2D
∂πiD
!
D
k−1
1+k
D
π
π
j
1+k
i
2
2
+ k π1D + π2D
k π1D + π2D
≥ 0 holds for all k ∈ [0, 1].
D D 2
2
π D +π D
kπ1
2
≥ 0
ec = ((1 − k) ũ)1− 2 (kπf ) 2 ,
holds for all
{1, 2}, is eD
i
1
π1 +π2
2
The second part of the proposition is straightforward by comparing the rst-order conditions. For
rm
i, i ∈ {1, 2},
its equilibrium eort
eD
i
solves the following rst-order condition:
D
D
σi eD
=
eD
i + ej , ec πi
i ⇒
k−1
D
k eD
ec1−k πiD = eD
i + ej
i
Hence,
eD
1
eD
2
=
k−1 1−k D
ec π1
k−1 1−k D
D
D
e1 +e2
ec π2
D
k(eD
1 +e2 )
k(
)
=
π1D
.
π2D
26
Proof of Corollary 1.
k = 1,
Proof. If consumers do not play a role in the communication, i.e.,
no eect.
Hence, in the proceeding analysis, we consider the case when
equilibrium eort is
ec = ((1 − k) ũ)
1− k2
(kπf )
k
2
, where
πf
consumers' eort has
k ∈ [0, 1).
Consumers'
denotes the total rm prot, i.e.,
πf = π1M
πf = π1D + π2D if duopoly. So consumers exert more eort in the duopoly situation
D 1− k D D k
2
2
π1 +π2
= ũũM
> 1. Taking logarithm of both sides, we have the equivalent
π1M
D +π D
D
π
π1M
k
ũD
ũD
ũ
k
k
1
2
as 1 −
>
0
⇒
ln
+
ln
ln
+
ln
−
ln
> 0. We will show
M
D
D
M
M
M
2
2
2
ũ
ũ
ũ
π
π +π
if monopoly or
when
eD
c
eM
c
condition
1
1
next that the aforementioned condition always holds for all
1,
ũD
ln ũM > 0.
Second, we nd that for all
v > 3t
π1D + π2D = t +
So
and
d ∈ [d∗ , 1].
and
First, by Lemma
d ∈ [d∗ , 1],
(1 − d)2 m2
< v − t = π1M
9t
(21)
πM
1
ln πD +π
D > 0.
1
2
v > 3t
Moreover, for all
d ∈ [d∗ , 1],
and
ln
ũD
ũM
because
=
π1M
ũD (d)
>
ln
>0
ũM
π1D (d) + π2D (d)
1
((1−d)m)2 − 21 (1−d)m+v− 54 t
36t
t
2
>
v−t
=
(1−d)2 m2
t+
9t
ln ũũM −
1
2
ũD
ũM
1
2
D
−
πM
1
ln ũũM + ln πD +π
D
π1M
π1D +π2D
D
1
ln
ũD
ũM
+ ln
> 0
.
Lastly, for all
2
(22)
π1M
.
π1D (d)+π2D (d)
D
ln ũũM −
Hence, we know the following inequality should hold:
ln
2
v > 3t
1
2
D
ln ũũM =
πM
D
ln ũM > 1 ln D 1 D ⇒
ũ D 2 π1M+π2
π1
>
− k2 ln ũũM + ln πD +π
D
D
k ∈ [0, 1), ln ũũM
1
2
1
2
> 0.
Proof of Proposition 2.
Proof. According to equation (11), the relative market size
1−k D
ũ
ũM
ũD
ũM
k ln
1−k π1D +π2D
π1M
D k
π1D +π2
π1M
π1D +π2D
π1M
and
and
M
π1
D +π D
π1
2
ũD
ũM
and
π1D + π2D
(1−k)1−k kk (ũD )
(π1D +π2D )k
1−k
1−k
k
M
(1−k)
k (ũ )
(π1M )k
=
σ T D ≥ σ T M if and only if
D 1−k D D k
D
π1 +π2
ũ
≥ 1 to (1 − k) ln ũũM +
ũM
πM
are functions of
We can reduce the condition
1
M
π1
D +π D
π1
2
belongs to
d ∈ [d∗ , 1]
d ∈ [d∗ , 1]
/ ln
ũD
1−k
=
d.
Hence,
1
k (d)
1
1+ln
≥ 1.
1+ln
v > 3t
v > 3t
k
≥0⇔k≤
Next, we show
all
, where
σT D
σT M
.
∈ (0, 1)
So
.
/ ln
ũD
ũM
(0, 1).
So
ũD
ln
≡ k (d).
From equation (21), we know that
π1M
π1D +π2D
ln ũM > 0.
> 0.
Hence,
ln
.
27
π1M > π1D + π2D ,
And Lemma 1 shows that
π1M
π1D +π2D
ũD
/ ln ũM
ũD > ũM ,
is also positive.
for
for all
Then we know
Proof of Proposition 3.
Proof. The inequality (21) in the proof of Corollary 1 has shown that
and
d ∈ [d∗ , 1].
It follows immediately that
D
eM
1 > ef .
M
only determined by the rm-side eort. Therefore, ef
π1D + π2D < π1M
for all
v > 3t
In the benchmark case, the market size is
= σ T M > σ T D = eD
f .
Proof of Proposition 4 .
M 1 M
1's expected prot is: EΠM
1 = π1 · 2 π1 ; whereas in the duopoly
1 D
D
D
D
becomes EΠ1 = π1 ·
2 π1 + π2 . The inequality (21) in the proof of
Proof. In the monopoly case, rm
case, its expected payo
M 1 M
EΠM
1 = π1 · 2 π1 >
Corollary 1 implies that the following inequality should hold as well. That is,
1
2
D 2
π1D + π2
=
1
2
D 2
π1
+ π1D π2D +
1
2
D 2
π1
= EΠD
1 +
1
2
D 2
π1
> EΠD
2 .
Proof of Proposition 5.
Proof. We rst suppose
∗
∗
EΠD
1 (d) monotonically decreases in the range [d , 1] so that d is the optimal
disclosure level in the duopoly case. With that supposition, we nd the condition on
k
under which
D
∗
EΠM
1 > EΠ1 (d ). Then, we verify the supposition is indeed true under that condition of k .
∗
D
∗
At d , rm 1 does not leave any surplus to rm 2, i.e., π2 (d ) = 0. Firm 1's expected payo
becomes:
∗
EΠD
1 (d ) =
1−k D ∗ 1+k
k
(1 − k)1−k k k ũD (d∗ )
π1 (d )
1−
2
In comparison, as a monopolist, its expected payo is:
EΠM
1
Firm
1
1−k M 1+k
k
π1
(1 − k)1−k k k ũM
= 1−
2
nds a monopoly market more protable if:
EΠM
1
>
EΠD
1
EΠM
1
(d ) ⇔
=
∗
EΠD
1 (d )
∗
ũM
ũD (d∗ )
1−k π1M
π1D (d∗ )
1+k
>1
Take the logarithm of the both sides, we have
ũM
π1M
+
(1
+
k)
ln
> 0
ũD (d∗ )
π1D (d∗ )
π1M
ũM
ũD (d∗ )
π1M
⇔ k ln D ∗ − ln D ∗
> ln
−
ln
ũ (d )
ũM
π1 (d )
π1D (d∗ )
(1 − k) ln
Since the inequality (22) suggests that
πM
M
1
ln
π1M
D
π1 (d∗ )
πM
D
∗)
ln πD 1(d∗ ) −ln ũDũ(d∗ ) = ln πD 1(d∗ ) +ln ũ ũ(d
M
1
ln
>0
hold, we can reduce the inequality (23 ) to the condition
k>
ln
28
(23)
D
∗
)
> 0 and ln ũ ũ(d
−
M
πM
ũD (d∗ )
−ln D1 ∗
ũM
π1 (d )
M
π1
ũD (d∗ )
D (d∗ ) +ln ũM
π1
≡ ke
and
k e ∈ (0, 1).
Therefore, under the condition
EΠD
1 (d)
We proceed to verify that
k>
k e . Firm
[d∗ , 1]
is indeed monotonically decreasing in the range
when
expected duopoly payo is:
1−k
EΠD
1
The sign of
1's
D
∗
k > k e , EΠM
1 > EΠ1 (d ).
(d) = (1 − k)
k
k
1−k D
k D
π1D (d)
k
D
ũ (d)
π1 (d) + π2 (d) π1 1 −
2 π1D (d) + π2D (d)
D
∂EΠ1
∂d is equivalent to that of its log-transformation, which is
∂ π1D + π2D
1 ∂ ũD
1
= (1 − k) D
+k D
ũ | ∂d
∂d
π1 + π2D |
{z }
{z
}
∂ log EΠD
1
∂d
+
(24)
>0
<0
1
1
+
D
π1D
π1 | ∂d
{z } 1 − k2 πD +π
D
k ∂
π1D
− D
2 ∂d
π1 + π2D
|
{z
}
∂π1D
1
<0
2
>0
We further reduce the above formula to a quadratic function of
k.
Denote that function as
G (k),
which is
2
G (k) = k 2 9t (m̃ − 3t)2 m̃2 − 9t2 + 2m̃ (3t − 2v) − 8 m̃2 + 9t2
m̃2 − 12m̃t + 18t(v − 2t)
+k (m̃ + 3t) 2m̃5 + 15m̃4 t + 36m̃3 t(4t − 3v) − 216m̃2 t3 + 162m̃t3 (t − 6v) − 43t4 (25t − 8v)
where
m̃ = (1 − d) m.
For all
v > 3t
d ∈ [d∗ , 1], EΠD
1 (d)
and
monotonically decreases as long as
is a convex function and there exists a point, e.g.,
two roots
k1
d ∈ [d∗ , 1],
and
k2
such that
G (k) < 0
all we need to show is that
First, when
v > 27 t, k1 < 0
(0, 1) ⊆ (k1 , 1)
and
is so becausemin k
e
for all
G (k) < 0.
≥ k1
when
d ∈ [d∗ , 1].
always holds for
such that
k ∈ (k1 , k2 ).
k ∈ (k e , 1)
Next, when
k = 1,
G (k) < 0
Notice that
is a subset of
(k1 , 1)
v > 72 t
Thus, when
G (k) < 0
and
for all
v > 3t
and
v > 3t
and
d ∈ [d∗ , 1].
d ∈ [d∗ , 1], k ∈ (k e , 1) ⊂
7
e
2 t, we only need to verify that k ≥
[d∗ , 1]. Therefore, when v ≤ 27 t and d
v ≤
d ∈
G (k)
, we are able to nd
k2 > 1
for all
. Since
k1 .
This
∈ [d∗ , 1],
k ∈ (k e , 1) ⊂ (k1 , 1).
Proof of Proposition 6.
Proof. As we have already shown in the above proof, when
maxd k1 ,
we can nd the condition on
monotonically decreases in
v≤
d,
k
and thus,
such that
k > k1 , G (k) < 0.
G (k) ≥ 0
maxd k1 = k1
(d∗ )
=
hold for some
2v−7t
3t−2v
≡ k. k
d.
As long as
k ≤
Notice that
k1 (d)
[0, 1)
when
exists in
7
2 t.
For any given
speaking,
k ≤ k , we can nd a unique disclosure amount de such that G (k; de ) = 0.
k = k1
(de ).
e
Next, we need to verify d indeed maximizes rm
29
1's
Equivalently
expected payo.
0
0
d < de . Since k1 (d) decreases in d, a lower d < de corresponds
0 0
0
0
to a higher
such that G k1 d
; d = 0. Then G k; d > 0 when k < k1 d .
00 00
00
e
Similarly, consider a higher disclosure amount d > d . That d corresponds to a lower k1 d
00 such that G k1 d
, d,, equals zero. G k; d” < 0 when k > k1 d” . Therefore, G (k; d) > 0
Consider a lower disclosure amount
0
k1 d > k1 (de )
D
(EΠ1
And
(d)
increases) when
de > d∗
d ∈ [d∗ , de );
whereas
G (k; d) < 0 (EΠD
1 (d)
d ∈ (de , 1].
decreases) when
is the optimal disclosure amount.
Proof of Proposition 7.
Proof. Following equation (20), rm i's optimal eort
ei
in the duopoly case is:
1−k
−k
k−1
D k k+1
k
D k k+1
kef
(1 − k) ũ ef
+ (1 − k) ef (1 − k) ũ ef
The total rm-side eort
ef = e1 + e2
1
k
D k k+1
(1 − k) ũ ef
ef (k + 1)
πiD = ei
is determined by adding up the rst-order conditions of the
two rms:
1−k
−k
k+1
k+1
(1 − k) ũD ekf
kek−1
+ (1 − k) ekf (1 − k) ũD ekf
f
1−k
k+1
k (1 − k) ũD
1 k
k+1
(1 − k) ũD ekf
π1D + π2D
ef (k + 1)
!
1−k
−k2
k
k(1−k)
k (1 − k)
+k−1
D k+1 k+ k+1 −1+ k+1
k+1
ef
(1 − k) ũ
ef
π1D + π2D
+
(k + 1)
1−k k−1
k (1 − k) D
k+1
k+
π1 + π2D
ef k+1 (1 − k) ũD
(k + 1)
k+1 1−k k+1
2
2
2
2
(1 − k) ũD
k π1D + π2D
k+1
=
ef ⇒
=
ef ⇒
=
ef ⇒
=
ef
Therefore, we have the equilibrium eorts:
eD
1
+
eD
2
=
2
k+1
{z
|
k+1
2
× k π1D + π2D
|
}
multiplier eect in sequential comm.
Firm i's equilibrium eort is simply
eD
i =
πiD
D
π1 +π2D
1+k
2
(1 − k) ũD
1−k
2
{z
}
eqm. eort in simultaneous comm.
D
· eD
1 + e2 , i = 1, 2.
And consumers' equilibrium
eort is:
eD
=
c
=
1
D k k+1
(1 − k) ũD eD
1 + e2
k
2
2
k+1
| {z }
(1 − k) ũD
×
|
multiplier eect in sequential comm.
30
1− k2
{z
k π1D + π2D
k2
}
eqm. eort in simultaneous comm.
Then, we can compute rm
1's
expected payo in the duopoly market:
D 1 D 2
D D
= σ eD
e
EΠD
1
1 + e2 , ec π1 −
2 1
k
2
k
π1D
1−k k
D 1−k
D
D k D
=
(1 − k)
k ũ
π1 + π2 π1 1 −
1+k
1 + k π1D + π2D
Similarly, we will get equilibrium eorts in the monopoly case as follows:
eM
1
=
2
k+1
k+1
2
and
eM
c
1's
Firm
EΠM
1
=
2
k+1
k
2
(1 − k) ũM
1−k
2
kπ1M
k+1
2
(1 − k) ũM
1− k2
kπ1M
k2
expected payo in the monopoly market is
M
eM
1 , ec
=σ
π1M
1 M 2
−
e
=
2 1
2
1+k
k
(1 − k)
1−k
k
k
We follow the reasoning in the proof of Proposition 5 and 7.
at which rm
1
M 1−k
ũ
1+k
π1M
1−
(
2
( 1+k
)
ke
First, we nd that the cuto
is indierent between becoming a monopolist and inviting competition remains
unchanged in the sequential setting. Because the relative ratio in the sequential setting
k
k
1+k
k
2
(1−k)1−k kk
1+k
)
(1−k)1−k kk (ũD (d∗ ))
1−k
1−k
ũM
(
)
(
1+k
π1M
)
(π1D (d∗ )+π2D (d∗ ))
k D
π1
1− k
1+k
(
)
D (d∗ )
π1
k
1− 1+k
D (d∗ )+π D (d∗ )
π1
2
=
ũM
ũD (d∗ )
1−k same as that in the simultaneous setting and we will get the same cuto point
π1M
π1D (d∗ )
ke
EΠM
1
∗
EΠD
1 (d )
1+k
=
is the
by applying the
same reasoning in the proof of Proposition 5.
Again, we will check
∗
EΠD
1 (d)indeed monotonically decreases in [d , 1].
to a quadratic function of
k.
Denote that function as
G̃ (k),
Similarly, we reduce
∂ log EΠD
1
∂d
which is
2
G̃ (k) = k 2 9t(m̃ − 3t)2 (m̃ + 3t) m̃2 + 6m̃t − 4m̃v − 9t2 − 4 m̃2 + 9t2
m̃2 − 12m̃t + 18t(v − 2t)
!
2m̃6 − 51m̃5 t − 9m̃4 t(11t − 12v) − 108m̃3 t2 (7t − v)
−k
−810m̃2 t3 (t − 2v) + 243m̃t4 (13t − 4v) + 2187t6
where
m̃ = (1 − d) m.
For all
∗
v > 3t and d ∈ [d∗ , 1], EΠD
1 (d) monotonically decreases in [d , 1] as long as G̃ (k) < 0.
G̃ (k)
We have already shown that
concave function and
G̃ (k) = 0.
subset of
Observing
(k2 , 1)
ke >
G (k) < 0
k>
2v−7t
3t−2v in the proof of Proposition 6. For all
d∈
k1 < 0
for all
when
for all
v > 3t
and
G̃ (k) = 0
k < k1
v > 3t
or
and
d ∈ (d∗ , 1].
at
k > k2 ,
d∈
k=
2v−7t
3t−2v
When
is a downward-sloping function and
where
k1
and
k2
d∗ ,
2v−7t
3t−2v , G̃ (k) < 0.
(d∗ , 1], G̃ (k) is a
are the two roots at which
(d∗ , 1], then we are left to show
This is so because
31
= k.
At
k e > k > k2
k ∈ (k e , 1)
always holds.
is a
The fact that
when
k ≤ k.
k2
increases in
The cuto
k
d
and the relation
k > k2
also indicate that
G̃ (k) ≥ 0
for some
in the sequential setting remains unchanged compared to that in the
simultaneous setting.
When
k ≤ k,
the optimal disclosure
de
solves the following equation:
∂ π1D + π2D
1
1 ∂π1D
1
∂
∂ log EΠ1
1 ∂ ũD
π1D
+k D
+ D
+
=0
= (1 − k) D
− D
D
π1
∂d
ũ | ∂d
∂d
∂d
π1 + π2D |
π1 + π2D
− πD +π
{z }
{z
} π1 | ∂d
{z } 1+k
D |
{z
}
k
1
2
>0
<0
In comparison with equation (24), for
<0
>0
k ∈ [0, 1),
∂ π1D + π2D
1 ∂ ũD
1
1 ∂π1D
1
∂
π1D
(1 − k) D
+k D
+
+
−
D
π1D
ũ | ∂d
∂d
∂d
π1 + π2D |
π1D + π2D
{z }
{z
} π1 | ∂d
{z } 1+k
k − π1D +π2D |
{z
}
>0
<0
D
> (1 − k)
d
∂
1
1 ∂ ũ
+k D
D
ũD | ∂d
π
+
π
1
2 |
{z }
>0
Hence, the optimal disclosure
de
<0
π1D
D
>0
∂π1D
+ π2
1
1
+ D
+
π1D
2
∂d
∂d
π
1 | {z }
{z
}
k − π D +π D
<0
<0
1
is higher in the sequential setting.
32
2
∂
πD
− D 1 D
∂d
π1 + π2
{z
}
|
>0
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