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Network Externality, Dynamic Competition and Social Welfare in the
Banking Industry- A Real Options Approach
T.S. Johnson Cheng†, I-Ming Jiang∗, Shih-Cheng Lee‡ and Banghan Chiu§
Abstract
By using the Real Options Approach, this paper concludes that banking industries
have to maintain the flexibility of decision-making when facing uncertain market demand. In addition, when the network externality exists, although there are sufficient incentives to attract banking industries to invest in electronic commerce platform, the increasing uncertainty of network externality will have the optimal investment timing deferred, implying leaders must have investment strategies adjusted for the first-mover advantage in response to potential threats from opponents entering the market. Finally, our sensitivity analysis indicates that competition does not necessarily improve social welfare due to market uncertainty and network externality.
Keywords：Real Options Approach, Network Externality, Banking Industry, Strategic
Investment, Social Welfare
† Associate Professor, Department of international Business, Soochow University, No. 56, Kueiyang Street, Section 1, Taipei, Taiwan. Email: [email protected] ∗ Assistant Professor, Department of Finance, Yuan Ze University, No. 135, Far-East Rd., Chung-Li, Taoyuan, Taiwan. Email: [email protected] ‡ Associate Professor, Department of Finance, Yuan Ze University, No. 135, Far-East Rd., Chung-Li, Taoyuan, Taiwan. Email: [email protected] § Associate Professor, Department of Finance, Yuan Ze University, No. 135, Far-East Rd., Chung-Li, Taoyuan, Taiwan. Email: [email protected]
1. Introduction
Shy (2001) indicates that the network industry includes telecommunications, radio
broadcasting and television, information and communications technology (ICT),
aviation industry, and banking industry. According to the OECD 2008 report, among all
above industries, the banking industry contributes 6%~7% value-added shares relative
to the total economy in G7 countries. Thus, compared to other network industries only
contributing 1%~3%, the banking industry deserves more attention.
The network economics is used to mainly discuss pricing strategies, compatible
standards and market competition; however, the issue of network externality4 has drawn
great interests nowadays. For example, in the banking industry, the establishment of
Automatic Teller Machine (ATM) has become an un-neglected job because of its great
possibility of network externality, although it requires lots of capital input. According to
the estimation of Kivel and Rubin (1996), the server of online bank costs US$10,000
and the network assess costs around US$200,000~US$4 billion, depending on the scale
4 Rohlfs (1974) pointed out that the network externality in the telecommunications industry is with
higher telecommunication value when there are more linking points, that is, the necessity of
telecommunication is reinforced. In other words, people prefer to majority communications due to a
herding psychology; therefore, a greater network, the more importance of joining the network. Katz and
Shapiro (1985) defined it in the sense of industrial economy as: “the utility to the consumers is with
higher value along with the increase of network users in number.” Varian and Shapiro (1999) defined it as:
“if the price that an individual is willing to pay for the network system is relevant to the number of
network users or targets, the network externality is in existence”.
1
of operation. Besides, Forrester Research Center estimates the construction and
maintenance of a trade network costs around US$5 million~US$23 million (Bank
Network News, June 23, 1998).
Apparently, the scale of business and network externality do affect the performance
of banks. The information technology system of ATM and Internet Bank has high
development cost and high customer service expense; also, the feature of scale
economies, that is, the more users the lower marginal cost of transmission service.
Therefore, the profits of banks rely on the number of users or the market share. The
effort of developing and maintaining customers is important to banks; therefore,
network externality plays an important role in this industry.
The impact of network externality on the profits of banks is mostly on the ATM,
branch setup, and the Internet use of credit cards. Saloner and Shepard (1995)
concluded that banks would adopt ATM sooner along with the increase of branches and
customers in number. Osterberg and Thomson (1998) pointed out that the
network-dependent value would be generated and the profits of banks would be
improved if the credit card business and the number of merchants accepting the credit
card business increase. Under the circumstance, credit card market is with significant
network externality effect5. Ishii (2005) argued that the incompatibility of ATM caused
5 The Electronic Payment Systems (EPS) of PC banks faces the situation stated by Osterberg and
Thomson (1998), and Stavins (1997) confirmed the existence of network effect, that is, the more Internet
2
surcharge and with a significant impact on the deposit business of banks6.
The empirical research of Nickerson and Sullivan (2006) indicated that the profits
distribution of banks was affected by expected profits and variation. The scale of banks
(market share) affects the expected profits. When the variation is given, large banks will
become Internet Banks first. According to the empirical research of Berger and Dick
(2007), domestic banks that had entered the market earlier did occupy 15% more market
share. The First Mover Advantage (FMA) is resulted from the network effect among
branches7.
The establishment of information system takes a great deal of sunk cost, and the
future demand of customers cannot be expected precisely; therefore, the Net Present
Value (NPV) method for evaluating a capital investment cannot have the investment
timing and flexibility assessed, and may have the opportunity cost of investment plan
underestimated. According to the Real Options Approach, an investment plan has three
features: uncertain return, irreversible cost and flexible investment timing (McDonald
and Siegel, 1986; Dixit and Pindyck, 1994). By considering these three factors, the Real
Options Approach is able to have the disadvantages of NPV amended. Therefore, banks
users, the higher benefit for each participant.
6 There is usually no surcharge for using the ATM of the same bank; however, service charge for
inter-bank withdrawal and account transfer is inevitable.
7 The empirical study of Grzelonska (2005) shows the positive relationship between the network benefit
of the branch (adjacency) and the deposits amount of banks.
3
must maintain flexible decision-making while facing uncertain electronic commerce and
marketing development in order to have the management strategies amended and the
optimal investment opportunities controlled.
Miranda (2001) used the Real Options Approach to consider the optimal investment
decisions for equipment expansion of monopoly banks under the network externality.
The result shows that when there is a positive network effect, the increase of users in
number will cause the options value to go up. Therefore, firms own the growth options
for operation expansion once future demand increases. Mason and Weeds (2000)
discussed the best timing for duopoly firms to introduce new technology if the
technology was with network externality and preemption. The most Real Options
Approach literature believes that network externality effect must be positive and
constant whereas Prasad and Harker (2000) argued that network externality effect could
be a positive or a negative8, and could be a random variable that was in conformity with
Geometric Brownian Motion (GBM).
This study is utilizing the Real Options Approach to analyze the investment
strategies of Internet Banks under the random network effect by taking into account the
following factors: (1) irreversible construction cost, (2) future growth, (3) uncertain
network effect, and (4) the intensity of network effect. Besides, we also compute the
8 Kennickell and Kwast (1997) stated that in terms of Internet bank; only 33% users based their decision
on friends and the relevant information. Thus, network is not necessarily with a positive effect resulted.
4
social welfare under different parameter specifications. This paper is organized as
follows. Section 2 defines the Cournot-Nash equilibrium output and investment profits
under the existence of network externality. Section 3 discusses the optimal investment
timing under the banks’ strategic interaction. The demand threshold and equilibrium
entry strategy is described in Section 4. Calculation of social welfare and the sensitivity
analysis are shown in Section 5, and Section 6 concludes this study.
2. Equilibrium Output, Network Effect, and Bank’s Value
Assume there are two banks in the market, and the inverse market demand of
banking service is a linear function:
( , )p q qθ θ= − （1）
where stands for the total market demand (Total output q 1 2q q q= + , and
indicates the quantity provided by Bank 1 and Bank 2),
1q 2q
θ stands for the stochastic
demand shift parameter. As suggested by Prasad and Harker (2000), network externality
could be a random variable in conformity with Geometric Brownian Motion (GBM),
thus:
d dt dzθ α σθ
= + （2）
In Equation (2), α is the instantaneous average change per time unit of θ. σ is
the standard deviation of the instantaneous change per time unit. dz is the increase of
5
Wiener process, and the initial time is 0θ .
If the demand is with network externality, we follow Lin and Kulatilaka (2006)9
model to have the inverse demand curve of Internet banking service rewritten as
follows:
( , , ) ( )e ep q q v q qθ θ= + − （3）
where is the network scale expected by the network users. stands for the
value that network users are willing to pay for the additional network service provided,
and it increases with the network scale. According to Metcalfe’s law, the total value of
network service is a constant ratio of the square of network users.
eq ( )ev q
2( )eq v q qζ⋅ = （4）
Therefore, for each consumer, Internet banking service value could be expressed as
follows:
( )ev q qζ= （5）
Lin and Kulatilaka (2006) defined ζ as the intension of network effect and its
value falls in [0,1)10. For simplification, our model assumes that banks are without
variable costs; therefore, the profits flow of banks (i 1,2i = ) in stage 2 at time t is:
9 Lin and Kulatilaka (2006) assumed that the exogenous expectation and the network effect of consumers
to be homogeneous.
10 If 0ζ = , demand function returns to Equation (1). In order to maintain the negative slope of the
demand curve, 1ζ < is defined.
6
[ ]( ) ( )i i i iq pq q qπ θ= = − + qζ （6）
The Gross Project Value ( ) of the investment and the of Bank i in stage
2 is defined as：
iV iNPV
i iNPV V I= − （7）
and I is the initial investment in stage 2.
Since we assume there are two banks 1 and 2, under the Cournot-Nash competition,
the reaction function of Bank 1 and Bank 2, and the optimal competitive equilibrium
output are as follows:
( ) ( )2
1 2(1 )
2 1qR q θ ζ
ζ− −
=− （8a）
and
( ) ( )1
2 1(1 )
2 1qR q θ ζ
ζ− −
=− （8b）
and the Cournot-Nash competitive equilibrium solution is:
( )1 2 3 1
c cq q θζ
∗ ∗= =−
（8c）
Therefore, under the duopoly, the profits flow icπ of Bank (i 1,2i = ) equals to:
( )2
9 1icθπζ
=− （9）
From Equation (9), we notice that the greater intensity of network effect ζ , the
greater profits flow of duopoly banks. Under the Cournot-Nash competitive equilibrium,
7
the project value of Bank i (icV 1,2i = ) equals to11:
(2θ
)9 1icVδ
=−ζ （10）
In Equation (10); 02 >σ2 −−= λδ α λ is the constant equilibrium risk-adjusted
discount rate after risk adjustment12;On the other hand, under a monopoly, the project
value of Bank i equals to: imV
( )2
4 1θ
imVδ
=−ζ （11）
Comparing Equation (10) and Equation (11), it shows that the result is clearly
similar to the traditional Cournot-Nash competitive equilibrium solution in literature
except for the inclusion of the intensity of network effect. We also can know that the
project value will be higher if the intensity of network effect (ζ ↑) and the parameter
of the uncertainty of network externality are higher (2σ ↑ or δ ↓ ).
In this section, we have shown that greater the intensity of network effect and
greater the uncertainty of network externality will help banks acquire greater profits
comparing to the non-Internet bank marketing. Therefore, banks should invest to
11 In general case, the gross project value ( ) of the investment and the of Bank i in stage 2 could be derived as follows:
iV iNPV
( )2=E (i i )
)t
n 1 (1iV d ππ θδ ς
=−∫ + ⋅ ⋅
,
where is the number of banks, which is determined by the market competition structure. For example, when firm is monopoly: ; when firm is duopoly: and equation (10) and (11) can be obtained.
n=1n =2n
12 According to the Capital Asset Pricing Model (CAPM), μ should reflect the asset’s systematic
(non-diversifiable) risk, that is, xmrμ φρ σ= + , where xmρ is the correlation coefficient of portfolio x
with market portfolio, and φ is the market price of risk.
8
construct Internet bank service platform and promote Internet bank marketing before
competitors in order to improve industrial profitability significantly.
3. Bank’s Entry Strategy
In this section, we try to understand how the leading banks (the existing banks)
respond to the investment strategies of competitors attempting to invest and construct
network marketing platform for competition. We consider bank’s entry strategy in
accordance with the two-stage model of Joaquin and Butler (2000) here.
The first mover in stage 1 initially obtains the monopoly profits. Competitors will
have incentives to enter the market due to the excessive profits in stage 1. In stage 2, the
first mover has to share the monopoly profits with the competitors and with lower
profits expected; therefore, it is necessary to have the strategy adjusted in response to
the market entry of competitors. Followers (potential competitors) entering market to
share the monopoly profits of the existing banks in stage 2 will be discussed first in
Section 3.1.
3.1 Follower’s Decision-Making
Assume before the investment, the value of the investment plan of the following
Bank 2 is 0 ( )FV θ ; besides, the instantaneous equilibrium return of the following banks
9
before entering the market is:
0 ( ) [ ( )]FrV dt E dV0Fθ θ= （12）
where r is the risk-free interest rate.
The economic implication of Equation (12) is that the total expected return of an
investment project equals to the expected return of capital valuation at any time interval.
According to Ito’s Lemma, the expected capital gain [ ( ( ))]E dF V θ can be rewritten as
follows:
2 2 '' '0 0
1[ ( ( ))] ( ) ( )2
F FE dF V V dt V dtθ σ θ θ α θ θ= + ⋅ （13）
We then can derive Bellman equation by applying Equation (13) to Equation (12):
( )2
2 2 '' '0 0 0
1 ( ) ( ) ( )2 9 1
F FV V rVθ Fσ θ θ αθ θζ
+ + =−
θ （14）
where the beginning investment value must fulfill the boundary conditions: 0FV
( )00
lim 0FVθ
θ+→
= （15）
Equation (14) illustrates that follower’s investment after entering the market must
satisfy the differentials equation in accordance with the potential investment uncertainty,
the network effect intensity and network eternality. Equation (15) indicates that there is
no opportunity for arbitrage; in other words, the derived options value of an investment
with zero value is zero.
If we consider the solution of Equation (14) of the following bank’s investment is
polynomial and is specified as follows:
10
1 2
2
0 1 2( )9 (1 )
FV B Bβ β θθ θ θδ ζ
⎡ ⎤= ⋅ + ⋅ + ⎢ ⎥−⎣ ⎦
（16）
in which, 1B and 2B are constants and determined endogenously. 1β and 2β are
the solutions to the quadratic equations:
21 ( 1)2
rσ β β αβ− + − = 0 （17）
that is,
122
1 2 2 2
1 1 2 12 2
rα αβσ σ σ
⎧ ⎫⎪⎡ ⎤= − + − + >⎨⎢ ⎥⎣ ⎦⎪ ⎪⎩ ⎭
⎪⎬ （18a）
and
122
2 2 2 2
1 1 2 02 2
rα αβσ σ σ
⎧ ⎫⎪⎡ ⎤= − − − + <⎨⎢ ⎥⎣ ⎦⎪ ⎪⎩ ⎭
⎪⎬ （18b）
The duopoly banks will maintain the same output level if there is further entry
difficulty for other following banks. Therefore, Equation (16) explains the value of
Bank 2 with an assumption that Bank 1 has investment made already. In other words,
for Bank 2, ; therefore, under duopoly, the fundamental value of the
following bank’s investment is:
1 2 0B B= =
2
0 ( )9 (1 )
FV θθδ ζ
=−
（19）
If we assume that the following bank implements the investment plan and the fixed
costs equals I. The net present value of the investment plan can be obtained as follows:
0( ) ( )FFNPV V Iθ θ= − （20）
If the following bank decides to have the investment plan executed at the time
11
when θ is greater than the demand threshold Fθ∗ ( *
Fθ θ≥ ), the value of waiting
equals to the net present value of the investment plan enforced by the following banks
when *Fθ θ≥ 13.
{ }* *0( ; ) ( )F
F F FNPV E V I eθθ θ θ −⎡= −⎣rT ⎤⎦ （21）
where Eθ is the risk-neutral expectation operator of the initial demand θ .
Therefore, when the demand threshold is *Fθ θ≥
)
, the options value of investment
for the following bank today is *( ;F FNPV θ θ . By substituting Equation (19) in
Equation (21), we then derive the net present value:
1* 2*
*( ; )9 (1 )
FF F
F
NPV Iβ
θ θθ θδ ζ θ
⎛ ⎞⎡ ⎤= − ⎜ ⎟⎢ ⎥−⎣ ⎦ ⎝ ⎠
（22）
Thus, when the investment is uncertain, the cost is irreversible, and it is able to
await ( *Fθ θ≥ ), we are able to derive the optimal entry threshold for the following bank
with maximized waiting value from the First order condition of Equation (22):
( ) ( )( )1 12 2
21 1
1 1
3 1 3 2 12 2F I Iβ βθ δ ζ λ α σ
β β∗ ⎧ ⎫ ⎧
ζ⎫⎡ ⎤= − = − − −⎨ ⎬ ⎨ ⎬⎣ ⎦− −⎩ ⎭ ⎩ ⎭
（23a）
13 We defined τ as the first passage time of θ exceeding the demand threshold iθ
∗
( ) when
the initial demand is
,i F L=
0θ at time 0. It also can be expressed mathematically as:
( )* *( ; ) f 0 :tini t iτ τ θ θ θ≡ = ≥ ≥θ， ,i F L= . Besides, it is necessary to have the
rE e τθ ⎡⎣
− ⎤⎦ calculated
for solving the deferral value of an investment; and we can obtain it from Dixit and Pindyck (1994, pp.
315-316):
1
0*F
rE eβ
τθ
θθ
⎡ ⎤ =⎣ ⎦− ⎛ ⎞
⎜ ⎟⎝ ⎠ .
12
and the following bank’s value:
1* 2
***
*2
9 (1 )( ; ) if
9 (1 )
F
FFF F
F
INPV
I
βθ θ
θ θδ ζ θθ θθ θθ
δ ζ
⎧ ⎛ ⎞⎡ ⎤⎪ − ⎜ ⎟⎢ ⎥ <−⎪⎣ ⎦ ⎝ ⎠= ⎨
≥⎪ −⎪ −⎩
（23b）
Equation (23a) shows that the optimal entry threshold ( *Fθ ) has a reverse relation with
the intensity of network effect ζ ; while it has a positive relation with the uncertainty
of network externality 2σ (or δ ↓ ). Equation (23b) indicates that banks should invest
when demand exceeds the investment threshold *Fθ θ≥ ; otherwise, they should wait for
a better time to invest. Theorem 1 therefore could be derived here.
Theorem 1: If the network externality is considered, the best investment threshold of a
following bank is:
( ) ( )( )1 12 2
21 1
1 1
3 1 3 2 12 2F I Iβ βθ δ ζ λ α σ
β β∗ ⎧ ⎫ ⎧
ζ⎫⎡ ⎤= − = − − −⎨ ⎬ ⎨ ⎬⎣ ⎦− −⎩ ⎭ ⎩ ⎭
From Theorem 1, we further can understand the investment factors of a following
bank by the comparative static analysis. We concluded the results in Proposition 1.
Proposition1：If there is consumer’s network effect in existence, the following bank’s
optimal entry threshold will increase by the following factors: (1) higher fixed cost, I ;
(2) higher demand uncertainty, ; (3) lower average demand growth, 2σ α ; (4) higher
risk-free interest rate, r ; and (5) lower network effect intensity, ζ .
13
3.2 Leader’s Decision-Making
3.2.1 Decision-making in Stage 2
If there are no competitors in the market, Bank 1 enters the market and becomes
the market leader with monopoly profits generated. However, other banks will be drawn
to enter the market to compete when the profits are exceptionally high (demand
threshold is *Fθ θ≥ ).
When the leader is a monopolist, this leading bank’s value ( )LV θ must satisfy the
following quadratic differential equation:
( )2
2 21 ( ) ( ) ( ) 02 4L L LV V rV θσ θ θ αθ θ θ
ζ′′ ′+ − +
−1= （24）
In Equation (24), the first three items stand for the options value of the leaders that
are waiting for the right time to enter the market; the last item of the equation stands for
the fundamental value while the leading Bank 1 does not withdraw from the market and
the following Bank 2 does not enter the market.
The solution to the leading bank’s investment value function in Equation (24) is
similar to the solution to the following bank’s investment value function in Equation
(14):
1 2
2
1 2( )4 (1 )LV A Aβ β θθ θ θδ ζ
⎡ ⎤= ⋅ + ⋅ + ⎢ ⎥−⎣ ⎦
（25）
When the demand falls, competitors will choose not to enter the market; thus,
14
2 0A = . Equation (25) can be simplified as follows:
1
2
1( )4 (1 )LV A β θθ θδ ζ
⎡ ⎤= ⋅ + ⎢ −⎣ ⎦
⎥
*
（26）
If the demand goes up, competitors will be drawn to enter the market; therefore, a
monopoly leading bank becomes a duopoly bank. Moreover, the leading bank’s value
equals to the value function under Cournot-Nash competition. Therefore, the following
value-matching condition must be substantiated:
*0( ) ( )F
L F FV Vθ θ= （27）
We can solve by applying Equation (27) and Equation (19) to Equation (25): 1A
1*2
15
36 (1 )FA
βθδ ζ
−−=
− （28）
Therefore, leading bank’s investment value function equals to:
11
*2 25( )36 (1 ) 4 (1 )
FLV
ββθ θθ θ
δ ζ δ
− ⎡ ⎤−= + ⎢− −⎣ ⎦ζ ⎥ （29）
Equation (29) indicates that under the monopoly market, the leading bank’s
investment profit originally was 2
4 (1 )θ
δ ζ−. However, it has to be shared with the
potential competitors if the following banks eventually enter the market, and the profit
loss is 25
36 (1 )θ
δ ζ−14.
We next analyze the adjustment of investment threshold for the leading banks at
14 Because the investment timing of the following bank is at *
Fθ θ≥ , the following bank will have its
investment postponed when *Fθ θ< ; therefore, *
Fθ θ= in Equation (29).
15
stage 1 when facing potential competitors (the following banks).
3.2.2 Decision-making in Stage 1
When banks have decided to have investment plan executed at the time in which the
demand threshold is *L Mθ θ≥ ( Mθ is the demand threshold under monopoly), the
deferral options value of investment is15
1
1
2
1( ; )4 (1 )
LL L L
L
NPV A Iβ
β θ θθ θ θδ ζ θ
⎡ ⎤ ⎛ ⎞⎡ ⎤= + −⎢ ⎥ ⎜ ⎟⎢ ⎥−⎣ ⎦ ⎝ ⎠⎣ ⎦
11
1
*2 2536 (1 ) 4 (1 )
F LL
L
Iββ
βθ θθδ ζ δ ζ θ
−⎧ ⎫⎛ ⎞⎡ ⎤−⎪= + −⎨ ⎜ ⎟⎢ ⎥− −⎪ ⎪⎣ ⎦ ⎝ ⎠⎩ ⎭
θ⎪⎬ （30）
Two economic implications are in Equation (30). First, 2
4 (1 )Lθ
δ ζ− represents the
monopoly profits of the leader if there is not any threat from the potential competitors.
Second, 1
1
*2536 (1 )
FL
ββθ θ
δ ζ
−
− represents the leader’s profits that have to be shared with the
following banks in market.
When *Fθ θ= , the leading bank’s investment value function ( )L FV θ ∗ in Equation
(29) equals to * 2
9 (I
1 )Fθ
δ ζ−
−. In addition, if the following banks choose to wait for the
right timing ( *Fθ θ< ), and the leading banks have investment made *
Lθ θ= , Equation
(23b) shows:
15 It is similar to the computation of the following bank’s deferral value for an investment at the demand
threshold in the future; therefore, the calculation will not be processed here again.
16
1
*
* 2 * 2
*9 (1 ) 9 (1 )F
F F
F
I Iβ
θ θ
θ θθδ ζ θ δ ζ
=
⎛ ⎞⎡ ⎤− = −⎜ ⎟⎢ ⎥− −⎣ ⎦ ⎝ ⎠
that is, when *Fθ θ= , the leading bank’s value equals to the following bank’s value.
From Equation (30), the optimal demand investment threshold Lθ∗ of the leading
bank if considering the deferral value of an investment maximized is:
( ) ( )( )1
221
1
12
* 1
1
2 2 12
2 1 2L II β
λ α σ ζβ
βθ δ ζβ
= − − −−
⎧ ⎫ ⎧ ⎫⎡ ⎤⎡ ⎤= −⎨ ⎬ ⎨⎣ ⎦ ⎣ ⎦− ⎩ ⎭⎩ ⎭⎬ （31）
Apparently, Equation (31) shows that the optimal entry threshold ( *Lθ ) will increase:
(1) when the intensity of network effect (ζ ) decreases; (2) when the uncertainty of
network externality 2σ increase (or δ ↓ ). Thus, we can derive the Theorem 2 here.
Theorem 2: If the network externality is considered, the best investment threshold of a
leading bank is:
( ) ( )( )12
21
1
12
* 1
1
2 2 12
2 1 2L II β
λ α σ ζβ
βθ δ ζβ
= − − −−
⎧ ⎫ ⎧ ⎫⎡ ⎤⎡ ⎤= −⎨ ⎬ ⎨⎣ ⎦ ⎣ ⎦− ⎩ ⎭⎩ ⎭⎬
Similarly, we also can observe the investment factors of a leading bank by the
comparative static analysis. The results are concluded in Proposition 2.
Proposition2. If there is consumer’s network effect in existence, the leading bank’s
optimal entry threshold is same as the one in Theorem 1. However, the leading bank’s
investment threshold is lower than the threshold of the following bank.
3.2.3 Economic Implications
17
Under the market without preemption and cost difference, and banks are with the
features of demand uncertainty and network externality, banks have incentives to
become a leading bank. While the entry threshold reaches Fθ∗ , following banks are
encouraged to enter the market; therefore, the business performance is expected to go
down. The role of leading bank and following bank is assumed to be exogenously given
in this study; however, the influential factors to bank’s investment network platform are
concluded in Theorem 1 and Theorem 2.
4. Demand Threshold and Bank’s Entry Equilibrium Strategy
In the duopoly competition model above, there are two possible entry strategies: (1)
sequential entry, and (2) simultaneous entry. The initial demand condition will affect the
type of entry; thus, the first mover advantage could be described a phenomenon of path
dependence16. According to Theorem (1) and (2), the intensity of network effect will
influence the bank’s entry timing, thus the optimal investment timing strategy will be
affected by the initial threshold value. That is, banks are with various equilibrium
strategies. We then illustrate the bank’s equilibrium strategies in Figure 1.
16 According to conventional literatures, first mover advantage (FMA) origins from (1) economies of
scale and learning effect, (2) programmed and converted cost, (3) network externality, and (4) quality
uncertainty of consumer goods. However, empirical studies show that FMA could be different even in the
same industry. Thus, Muller (1997) argued that the path dependence was the main factor of FMA.
18
4.1 Sequential Entry Strategy
Once the bank’s investment game starts, if *Fθ θ≤ , the competitive banks will have
a symmetric sub-game perfect equilibrium strategy17. If the competitors have not yet
entered the market, when *Lθ θ≤ , one should enter the market immediately for
preemption. However, if the competitors are in market, a sequential entry strategy is the
optimal strategy. In other words, when *Fθ θ≤ , a second bank will enter the market and
become a following bank once the waiting entry threshold reaches *Fθ .
Under the above strategy, the oligopoly market equilibrium strategy is the leading
bank will enter market immediately once the waiting timing is *Lθ θ≤ . As for the
following bank at *Lθ , the deferral investment profit is no difference from the
investment profit due to * *0( ) ( )F
L L LV Vθ θ= .
4.2 Simultaneous Entry Strategy
When the demand exceeds threshold value *Fθ θ≥ , competitors will enter the
market simultaneously and with Cournot-Nash competition equilibrium reached.
Therefore, we have Theorem 3 stated here.
Theorem 3:
17 We considered only pure strategy for simplicity. Mixed strategy is to be studied in the future.
19
(1) When *Lθ θ< , both leading bank and following bank are waiting for the right
time to invest; (2) When * *L Fθ θ θ≤ < , leading bank is in market while the
following bank is still waiting for the right time to invest; therefore, it is a
sequential entry equilibrium strategy; (3) When *Fθ θ> , both leading bank and
following bank are in market; therefore, it is a simultaneous entry equilibrium
strategy.
5. Analysis of Social Welfare
According to the traditional economic theory, a monopoly market is with maximum
deadweight loss, and the loss in an oligopoly market could be decreased by introducing
market competition. However, under the Real Options Approach framework,
irreversible investment is a sunk cost; therefore, waiting for an investment is with time
value. Besides, banks with network externality have the economies of scale, resulting in
a decrease of average cost. Added to it the uncertainty and network intensity, the claim
of conventional theory about improving social welfare with competition should be
further studied. In this section, the social welfare derived from different demand
thresholds and parameters is used to validate the conclusion of generating higher social
welfare from competition.
20
5.1 Social Welfare under Different Demand Thresholds
(1) When *Lθ θ< , both leading bank and following bank are waiting for the right time
to invest. The deferral value for an investment is equal to:
( ) ( ), ,L L F LNPV NPVθ θ θ∗ ∗⎡ ⎤+⎣ ⎦θ
where ( )1*2
*, ( ; )9 (1 )
LL L F L
L
NPV NPV Iβ
θ θθ θ θ θδ ζ θ
∗∗
⎛ ⎞⎧ ⎫= = −⎨ ⎬⎜ ⎟−⎩ ⎭⎝ ⎠
.
Therefore, the social welfare equals to18
( )1*2
29 (1 )
LL
L
I Prβ
θ θ θ θδ ζ θ
∗∗
⎛ ⎞⎧ ⎫− <⎨ ⎬⎜ ⎟−⎩ ⎭⎝ ⎠
.
(2) When *L
*Fθ θ θ≤ < , the leading bank is in market to invest while the following bank
is still waiting for the right time to invest; therefore, it is a sequential entry
equilibrium strategy. Under this equilibrium, the leading bank’s producer surplus
(industry’s monopoly profits) equals to ( )
2
4 1imV θδ ζ
=−
; moreover, the following
bank’s waiting investment value is 1* 2
**( ; )
9 (1 )F
F FF
NPV Iβ
θ θθ θδ ζ θ
⎛ ⎞⎡ ⎤= − ⎜ ⎟⎢ ⎥−⎣ ⎦ ⎝ ⎠
; also,
18 Social welfare includes the deferral investment value and of firms and consumer; therefore,
the probability of first passage time,
NPV
( )*Pr Lθ θ< , must be considered. According to Harrison (1985):
defining [ ]0,
lnT tt TM Max θ
∈= , then
( ) ( ) ( ) 20 0
0
2ln ln, Pr ln
i i
ii T i
T TPr T M N N
T T
θ θμθ θθ σ
θ
μ μθ θ τ θ
σ σ
⎛ ⎞ ⎛− −≤ > = ≤ = −⎜ ⎟ ⎜⎜ ⎟ ⎜
⎝ ⎠ ⎝
⎞−⎟⎟⎠
, where
212μ α σ= − .
21
consumer surplus equals to ( )
2
8 1mCS θδ ζ
=−
. Thus, the social welfare at the time
equals to:
( )*( ; ) Prm im F F L FCS V NPV θ θ θ θ θ∗ ∗⎡ ⎤+ + ≤ ≤⎣ ⎦
( ) ( )1* 22
*
3 Pr8 1 9 (1 )
FL F
F
Iβ
θθ θ θ θ θδ ζ δ ζ θ
∗ ∗⎡ ⎤⎛ ⎞⎡ ⎤⎢ ⎥= + − ≤⎜ ⎟⎢ ⎥− −⎢ ⎥⎣ ⎦ ⎝ ⎠⎣ ⎦
≤
( ) ( ) (1* 22
*
3 Pr Pr8 1 9 (1 )
FF L
F
Iβ
θθ θ θ θ θ θδ ζ δ ζ θ
∗ ∗⎡ ⎤⎛ ⎞⎡ ⎤ )⎡ ⎤⎢ ⎥= + − ≤ − ≤⎜ ⎟⎢ ⎥ ⎣ ⎦− −⎢ ⎥⎣ ⎦ ⎝ ⎠⎣ ⎦
.
(3) When *Fθ θ≥ , both leading bank and following bank are in the market to invest;
therefore, it is a simultaneous entry strategy. Under this equilibrium, the bank’s
producer surplus (industry’s profits) in the oligopoly market equals to
( )2
9 1θ
cVδ ζ
⎛ ⎞= ⎟⎟⎝ ⎠⎜⎜ −
. Also, consumer surplus equals to ( )
229 1cCS θδ ζ
=−
. Thus, the
social welfare equals to:
[ ] ( ) ( ) ( )2
Pr 1 Pr3 1c c F FCS V θθ θ θ θδ ζ
∗ ∗⎡ ⎤⎡ ⎤+ ≥ = − ≤⎢ ⎥ ⎣ ⎦−⎣ ⎦
The results are illustrated in Table 1. However, the magnitude of welfare effect in
different stages cannot be identified in general. We therefore identify the change of
social welfare effect based on different parameter specifications in the next section.
5.2 Sensitivity Analysis
We assume that the demand of consumers’ banking service is with 1% annual
22
growth rate ( 0.01α = ) and use the volatility ( 0.2σ = ) to indicate the uncertainty of
demand. Moreover, we assume risk-free interest rate (annum) is 12% ( ) and the
necessary return rate (
0.12r =
λ ) equals to 14%. Also, the project due date is for 2-year,
sunk cost is
T
1I = , the intensity of network externality is 0.3ς = , and initial demand is
0 0.75θ = . Table 2 shows the results of the sensitivity analysis depending on different
parameter specifications.
5.2.1 Increase in demand uncertainty ( 2σ )
When 2σ is increased from 0.02 to 0.04 and 0.06, the waiting value of investment
for banks goes up from 0.02 to 0.54 and 1.73, respectively. It implies that waiting for an
investment is valuable. The social welfare is reduced from 2.24 to 2.11 first but
increased to 2.49 later. The conclusion is in conformity with the conventional Real
Options Approach, that is, competition does not necessarily help increase social welfare.
5.2.2 Increase in network externality intensity (ς )
If ς is up from 0.3 to 0.4 and 0.5, the social welfare is increased from 2.11 to
3.15 and 4.94, respectively. On the other hand, social welfare is the highest when the
network externality helps banks to be a monopolist. Therefore, greater network
externality helps to reinforce the incentives for bank’s entry for advantages of
23
preemption. Furthermore, a monopoly bank is able to provide the market with all
service demand without the help of following banks in order to avoid inefficiency of
over-investment.
5.2.3 Increase in initial demand ( 0θ )
When 0θ goes up from 0.65 to 0.75 and 0.85, social welfare is increased from 0.99
to 2.10 and 4.01, respectively. Social welfare under monopoly will also go up along
with the increase of initial demand. The result concluded that competition does not
necessarily help generate social welfare under the uncertainty and network externality.
6. Conclusion
It is demonstrated in the literature that network externality is a crucial factor to the
bank’s profits and market share. Greater intensity of network effect and greater
uncertainty of network externality help banks acquire greater profits than the marketing
of non-Internet banks. Therefore, to improve profitability, banks must invest in network
service platforms and aggressively promote network marketing before competitors enter
the market.
However, it takes a great deal of sunk cost and faces severe demand uncertainty for
banks to have network transaction platforms constructed. Therefore, even with the
24
25
consumer’s network effect, the Real Options Approach suggests banks to await or to
suspend investment temporarily and keep management flexible in order to increase
bank’s value when: (1) sunk cost increases; (2) uncertainty of demand increases; (3)
average growth rate of demand declines; and (4) risk-free interest rate goes up. In
addition, the demand threshold determines bank’s equilibrium entry strategy, thus, it is
important for banks to control the demand uncertainty with various marketing
strategies.
We also have different social welfare formulas calculated under different demand
thresholds. By the sensitivity analysis, we concluded that competition does not
necessarily help generate higher social welfare if: (1) demand uncertainty increases, (2)
intensity of network externality increases, and (3) initial demand is higher. The result is
different from the conclusion made under the conventional model in which competition
helps improve social welfare. This is because the waiting value of an investment is
emphasized under the Real Options Approach to avoid inefficiency of over-investment.
In this study, we do not take into account the role of the government. When the
market is with externality and deadweight loss, the government is suggested to
implement policies to correct the inefficiency. Therefore, how and to what extent
government intervention can improve social welfare under the Real Options Approach
framework is the topic for future research.
Figure 1: The investment value of leading and following banks at different demand thresholds
26
Table 1: Social Welfare under Different Investment Thresholds
*Lθ θ< * *
L Fθ θ θ≤ < *Fθ θ≥
Value of Standby
Investment
1*2
9 (1 )L
L
Iβ
θ θδ ζ θ ∗
⎛ ⎞⎧ ⎫−⎨ ⎬⎜ ⎟−⎩ ⎭⎝ ⎠
1* 2
*9 (1 )F
F
Iβ
θ θδ ζ θ
⎛ ⎞⎡ ⎤− ⎜ ⎟⎢ ⎥−⎣ ⎦ ⎝ ⎠
0
Producer’s Surplus 0 ( )2
4 1imV θδ ζ
=−
( )
2
9 1cV θδ ζ
⎛ ⎞= ⎜ ⎟⎜ ⎟−⎝ ⎠
Consumer’s Surplus 0 ( )2
8 1mCS θδ ζ
=−
( )
229 1cCS θδ ζ
=−
Social Welfare ( )
1*2
29 (1 )
LL
L
I Prβ
θ θ θ θδ ζ θ
∗∗
⎛ ⎞⎧ ⎫− <⎨ ⎬⎜ ⎟−⎩ ⎭⎝ ⎠
( ) ( )
1* 22
*
3 Pr8 1 9 (1 )
FL F
F
Iβ
θθ θ θ θ θδ ζ δ ζ θ
∗ ∗⎡ ⎤⎛ ⎞⎡ ⎤⎢ ⎥+ − ≤ ≤⎜ ⎟⎢ ⎥− −⎢ ⎥⎣ ⎦ ⎝ ⎠⎣ ⎦ ( ) ( )
2
1 Pr3 1 F
θ θ θδ ζ
∗⎡ ⎤⎡ ⎤− ≤⎢ ⎥ ⎣ ⎦−⎣ ⎦
27
Table 2: Results of Sensitivity Analysis
*Lθ θ< * *
L Fθ θ θ≤ < *Fθ θ≥ Social Welfare
2 0.02σ = 0.024663 2.180638 0.03974 2.245041
2 0.04σ = 0.54335 1.500783 0.061833 2.105966
2 0.06σ = 1.72548 0.732803 0.030011 2.488293
0.3ς = 0.54335 1.500783 0.061833 2.105966
0.4ς = 0.490633 2.515062 0.145923 3.151618
0.5ς = 0.300926 4.27239 0.370097 4.943413
0 0.65θ = 0.495298 0.485809 0.010508 0.991615
0 0.75θ = 0.54335 1.500783 0.061833 2.105966
0 0.85θ = 0.411173 3.362309 0.241137 4.014619
28
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