A Two-stage Biform Game model Study between Service Providers in Cloud Manufacturing
Zhao-yang BAI1,*, Lin-jie Song1
1. Faculty of Management and Economics, Dalian University of Technology, Dalian 116030, China
Abstract: There is not only competition but also cooperation between service providers in a new, service–oriented manufacturing
paradigm―cloud manufacturing, compared to traditional paradigm. The operation decision environment is more complicated. This paper
establishes a two-stage biform game model aiming at maximizing returns between service providers in cloud manufacturing. The first stage
is competition stage in which service providers make decisions of competitive strategy independently to meet the needs of long-term
customers and non-heavy customers; the second stage is cooperation stage in which mutual influences exist between service providers’
decisions and they are influenced by the first stage’s decisions. The point is whether to participate in manufacturing alliance to get more
profits. Further, a case is studied to discuss the effect of the variation of four factors: comprehensive service ability, potential market size,
priority of users’ needs and expectation of other service providers’ participation willingness. The result provides insights into the decisionmaking of service providers and sustainable development of cloud manufacturing alliance.
Keywords:
1. Introduction
Cloud manufacturing is a web-based, service-oriented new smart manufacturing paradigm. Manufacturing resources and manufacturing
capabilities are virtualized in a form of service cloud pool to provide service, which can be managed and operated in an intelligent and
unified way to ensure their full sharing and circulating. The business operations of cloud manufacturing are built on the market formed by
service providers, consumers and operator who serve as intelligent subjects and aims at maximizing total profit.
Some typical business application cases are emerged with the deep study of cloud manufacturing. Such as the cloud manufacturing
service platform for group service providers oriented to orbit transportation equipment mainly developed by CNR, the cloud manufacturing
service platform for group service providers oriented to complicated product in aerospace industry developed by the Second Academy of
China Aerospace, the cloud manufacturing service platform for small and medium service providers developed by DG-HUST
Manufacturing Engineering Institute and so on. The management of service providers arouses the attention of people gradually.
Compared to other cloud services, cloud manufacturing depends more on its service providers instead of operators and technology, due
to its characteristics of personality, diversity and small batches. In contrast with traditional manufacturing mode, service providers under
cloud manufacturing are not oriented to separate production activity but the product life cycle solutions collaborative activities, thus its
operations strategies are more easily influenced by cloud manufacturing alliance. Both competition and cooperation are involved in cloud
manufacturing between service providers. Service providers can achieve orders through competition and call resources through cooperation.
Therefore, how to make full use of its own resources and industrial advantage to maximize its profits is a realistic problem faced by service
providers. Exploration of the game relationship between service providers under cloud manufacturing can contribute to problem resolution
and the stability of service providers and the realization of sustainable development of cloud manufacturing alliance (Bohu Li, Lin Zhang, et
al.2012).
2. Related works
There are some literatures about game between service providers at home and abroad. Pal and Hui et al. investigate the game between
cloud service providers and operators and prove the existence of Nash equilibrium through the game of price and quality of service. They
established the balance model of customer service quality and resources with the goal of minimization of waste of resources through the
study of capacity programming and resource supply between single and multiple cloud networks with technical and economic method (Pal
R,& Hui P 2013). Allon and Gurvich study the influence of market size to the game of multiple service providers and propose a framework
that combines many-server heavy-traffic analysis with the notion of ε-Nash equilibrium and apply it to the research of equilibria in a market
with multiple large-scale service providers competing in price and response time. The proposed framework allow us to provide first-order
and second-order characterization solutions which can be used to provide insights into price and service level decisions especially into the
impact of market scale on the dependence of the two strategic decisions (Allon G & Gurvich I 2010). Afanasyev and Mendelson focus on
the impact of additional costs on the game of service providers who serve delay-sensitive customers. Delay cost is divided into generalized
delay cost which depends on the valuation of service and additive delay cost which is independent from the valuation of service. And they
study how the delay cost, the market size and the service providers’ cost affect the equilibrium of the game (Afanasyev M & Mendelson H
2010). Fan, Kumar and Whinston et al. analyze the factors that affect the game between different service modes based on software service
and construct short-term and long-term competition model between SaaS and SWS providers. User implementation costs, SaaS provider’s
operation efficiency, and quality of service are examined to show its effect on equilibrium and equilibrium price (Fan M et al. 2009).
As a new advanced manufacturing paradigm, related research and exploration about cloud manufacturing is in the initial stage. The
previous literature on service providers mostly provides insights towards competition or cooperation between traditional service providers,
but falls short of providing similar insights for cloud manufacturing in which service providers primarily play game with other service
providers. In this paper, we propose a two-stage competition and cooperation game model between service providers under cloud
manufacturing considering the comprehensive service ability, the potential market size, the will of involvement in cloud manufacturing, the
priority of customers’ needs and the anticipation of achieving the maximal profit with biform game theory. Further the effect of the variation
of different factors on decision is tested. The results provide significant insights into the decision-making of the sustainable development of
cloud manufacturing alliance.
3. Construction of Model
The first assumption is that cloud manufacturing service platform (hereinafter referred to as CMSP) runs effectively and can be used to
assess the comprehensive service ability of service providers. CMSP contributes to the timely communication of service providers and
customers and gives prerequisite for the game between service providers. Service record for every service provider is established according
to its service history and assessment from customers in the CMSP. Excellent service providers stand out of the record list and will be
recognized as evaluation criteria with scientific method in delivery, quality, cost, timeliness, production coordination ability, production
Journal of Residuals Science & Technology, Vol. 13, No. 5, 2016
© 2016 DEStech Publications, Inc.
doi:10.12783/issn.1544-8053/13/5/61
61.1
γ ∈ 0,1
γ
 
flexibility and after-sale service and so on. Let be the comprehensive service ability index of every service provider, where
and that of the top service providers equals to 1.
Pegels, C.C. and Song, Y.I. divided the market into different groups according to the interaction patterns using a strategic interaction
(action-response) matrix (Pegels, C.C.& Song, Y.I 2007). Rawal and Aditya et al. focused on the simultaneous cooperative and competitive
coevolution in a complex predator-prey domain (Rawal& Aditya et al.2010). There are two-stage decisions in the market of service
providers. In the first stage, service providers compete to get customer orders. They are unable to product thus cannot enjoy returns without
orders. Therefore, service providers are willing to participate in the second stage of cooperation. In the second stage, service providers get
and complete new orders as an alliance through cooperation. Idle resources and capabilities are virtualized into a resource pool which
enables service providers to free from the rigid constraints of limited resources. As a result, we can achieve the optimal allocation of
resources as well as the improvement of resources use efficiency. This stage is affected by many factors. The decision of the second stage is
clearer when the first stage decision is made. In other words, there is interaction between the two stages. The two-stage decision matrix of
service provider M is shown in Figure 1.
Stage 1
Stage 2
Stage 1
Stage 2
(Y,Y)
(Y,N)
(N,Y)
(N,N)
Y:joining in the game
N:not joining in the game
Figure.1 The two-stage decision matrix of service provider M.
We can see from Figure 1 that there are four decision combinations in the two-stage decision matrix of service provider M. They are (a)
(Y ,Y ) ; (b) the participation in stage 1only that is (Y ,N ) ; (c) the participation in stage 2 only that
(N ,Y ) ; (d) participation in nether of the two stages that is (N ,N ) . Above all the four decision combinations, (c) and (d) won’t be
is
the participation in two stages that is
taken by service providers in which they don’t involve in market competition. Our analysis highlights decision combinations (a) and (b).
The priority of customers’ needs has impact on the choice of service providers. In the cooperative game stage, whether a service
provider is willing to use remaining resources and how many resources it is going to use depends not only on profits obtained from
cooperative game but also on customers’ needs. Customers’ needs can be divided into design service, manufacturing service,
implementation service and maintenance service and so on according to the product life cycle. If a customer is satisfied with the prior
service, it may well continue to obtain service from the same service provider to reduce switching costs and risk and ensure consistency.
Similarly, service providers prefer to provide comprehensive service to customers as far as possible. Therefore, the stage of customers’
needs in the product life cycle will be considered as an important factor in the decisions making of service providers. Let be the priority of
customers’ needs. The effects of cultural differences on competitive and cooperative behavior have been investigated by Taylor H. C. and
Sharon A. L. et al. which is not included in this paper because it is an interesting topic for future research (Taylor H. C. & Sharon A. L. et
al.1991).
We study a two-stage game model of different service providers in cloud manufacturing to obtain profit optimization where every
service provider decides whether to join in cooperation game or serve other customers with remain resources. The decision is influenced by
the comprehensive service ability, the potential market size, the will of involvement in cloud manufacturing, the priority of customers’ needs
and the anticipation of achieving the maximal profit. The two-stage game model of different service providers in cloud manufacturing is as
follows:
In the first stage, service providers make decisions independently to meet fixed customers’ needs and then decide the extent to meet
other customers’ needs.
In the second stage, service providers make decisions of whether to join in cooperation game to form cooperative alliance.
In this section, we state a number of assumptions to simplify the problem without changing its essence. For i = 1, 2 , n
The number of service providers in the market is and they are able to provide design service, manufacturing service, implementation
service and maintenance service.
The potential market size is larger than the total production (service) capabilities of all service providers.
0
The fixed customers’ need of every service provider is denoted by D i . The set of all customers’ need all service providers’ are
0
=
{
0
, ,
0
, ,
0
}
D1 D i D n .
denoted by D
Service providers still have remaining resources after satisfying fixed customers’ needs.
In this section, we list the parameters related to all service providers involved in the two-stage biform game model.
n : the number of service providers in the market.
x, y : the strategy of service provider i in stage one and stage two.
c0 ( x) : the profit of service provider i by serving fixed customers which is a constant.
c1 ( x) : the profit of service provider i in the competitive game stage.
c2 ( y ) : the profit of service provider i in the cooperative game stage.
Di : the needs of fixed customers of service provider i in the competitive game stage.
Journal of Residuals Science & Technology, Vol. 13, No. 5, 2016
© 2016 DEStech Publications, Inc.
doi:10.12783/issn.1544-8053/13/5/61
61.2
i in the cooperative game stage.
Di − : the potential needs of service provider
β
where
j
: The probability of service provider
0 ≤ β ≤1
j
j joining in cooperative game stage is β
j
in service provider
i
’s opinion,
.
γ : the comprehensive service ability index of service provider i
ε : the priority of customers’ needs.
−
v i : the anticipation of profits from the cooperative game stage of service provider i . v i and v i − represent the upper bound and
lower bound of v i .
In the first stage: Service providers compete to obtain orders from fixed and other customers’ needs. To keep the reputation and brand
established before, a service provider is not going to input all of its manufacturing resources and capabilities to cloud manufacturing because
in which it is exploded to very large risk. The decision of whether and to what extent meeting other customers’ needs on the basis of
satisfying fixed customers has a direct impact on the cooperative game stage decision.
Let
Di
 , n}
N be a set of service providers and N = {1，
. The fixed customers’ demand of service provider
D = {D1 , Di , Dn }
and the set of all fixed customers’ demands is denoted by
strategy of service provider i in the competitive stage. We denote service provider
i
c
satisfies 1
xi ∈ X i
and
X = { X1 , X i , X n }
, where
xi is the
i with participant i in biform game. The profit of
( x1 , , xn ) ∈ R when all other participants’ strategies are ( x1 , , xn ) . Therefore the profit of the
c ( x) = c ( x* , , x* , xi* , xi*+1 , , xn* )
1
1
i −1
first stage is 1
x1* , , xi*−1, xi*+1 , , xn*
.
are
(
is characterized by
which is rigid to service providers. Besides,
whether and to what extent to satisfy other customers is the decision-making focus. Let
participant
i
)
.
xi*
denotes the strategy of participant
i
where all other participants’ strategies
c ( x)
of participant i , we need to focus on the strategies of all other participants in the second stage.
To describe the profit 1
In the second stage: the strategy is influenced by the first stage and the existence of the core and in turn it influences strategy in the first
stage. The decision-making point is whether to form an alliance to obtain more profit.
i
Participant
j
is not sure whether to join in the second stage while it has an anticipation of the probability of service provider joining
in cooperative game stage
β
j
, where
0 ≤ β ≤1
j
. The comprehensive service ability index
on its decision of joining in the second stage. Participant
γ
resources even with a low .
By forming an alliance, participant
i may choose to join in the cooperative game stage to make full use of its idle
i is able to share resources with other participants and get more orders in order to maximize their
profit allocation, thereby achieving their maximum profits. In the cooperative game stage,
S⊆N
where
where
V
S | 2 −1
|=
γ of participant i has an important influence
N and S is the big alliance and sub alliance,
|N |
and
( x1,, xn )
.
The
characteristic
function
(φ ) = 0 . We denote the cooperative game as ( N ,V
of
the
alliance
( x1,, xn )
is
denoted
by
V
( x1 ,, xn )
(S )
,
).
C1 ( x) . The strategy in the second stage is influenced not
γ
only by the decision in the first stage but also the comprehensive service ability , the priority of customers’ needs ε and the anticipation
The profit of satisfying fixed customer of all participants in the first stage is
β
j
y = f ( x, γ , ε, β ) . We denote c2 ( y )
j
,that is
of provider joining in cooperative game stage
of the biform game is to maximize the total profit. The objective function of the two stages is:
=V
( x1 ,, xn )
( S ) . The objective
max x∈X , y∈Y {c1 ( x ) + c2 ( y )}
4. Model solution
Here we use confidence index
µ(
Brandenburger A & Stuart H 2007), where
p(=
v
i
i
anticipating capturing the most and the least profit which can be written as
of the cooperative game maybe empty, we will discuss the problem in two situations:
The core is nonempty.
C  N , v ( x1,x n) 
We denote 
−( x1,x n )

= max
=
|v
Vi
v
 i


µ ∈ [0,1] . µi
−
v=
i )
and 1− µi indicate that participant
µi , p(vi = vi − ) = 1− µi . Given that the core
as the core of the cooperative game. And it follows that:

(v1,, v n ) ∈C  N , v ( x ,x ) 
1
n

Journal of Residuals Science & Technology, Vol. 13, No. 5, 2016
© 2016 DEStech Publications, Inc.
doi:10.12783/issn.1544-8053/13/5/61
61.3

( x ,x n) = min
=
|v
V i- 1

(v1,, v n ) ∈C  N , v ( x ,x ) 
v
 i

1
n

( x1,x n)
Vi
i ; V i-( x
x)
1, n
−
implies the upper bound of the profit in the second stage of participant
the second stage of participant i .
implies the lower bound of the profit in
)
(
x1, x n;V ;µ1,, µ n , if the core of the cooperative game ( N ,V ( x1,, xn ) ) exists for all
For the given biform game
( ,, x n ) ∈ X 1× × X n , the objective function of the biform game can be written as:
nonempty sets x1
(
∗
*
)
max xi∈X i, y j∈Y j c1 ( x i ) + c 2 ( y i )
=
i x ,y
F
( )
=
yi
where c 2
µ iV i (
−
y1,, y n)
+
(1 − µi )V i( −y
,,
1
y n)
.
µ
When there is only one solution in the core, the confidence index
( x1,x n) = ( x1,x n)
−
V
V
ibecause i
The core is empty.
has no difference on the computing of the profit
.
There is no stable allocation to all participants when the core is empty. We assume that the strategy of participant
sub alliance or not joining in any sub alliances. Participant
than the lower bound that is
vi ≥ v



( ).
y1, y n  i
{}
i is joining in one
i will join in the alliance at least the profit it gets from the alliance is not smaller
Next, we will use the Shapley to calculate the upper bound of the profit obtained from the cooperative stage of participant
the profit of the alliance subtracting the profit created by all other participants without participant
i , which is
i i.e. the marginal profit of participant
i .( Jiekun Song& Yu Zhang 2012)
− y ,, y 
=
V i  1 n



,, y 
v y1
n
( s ) − ∑ v y1,, y n ({i})






 
 
 
i∈s\ i
Next we will use the sub alliance
s to calculate the upper bound of the profit of participant i since the nonexistence of the big
µ
union N . Thus we can use the confidence index to solve the anticipated profit of participant i .
Participants seek the chance to cooperate with others as a sub alliance in order to get more profit than not joining in any alliances. The
sub alliance is P , where
P ⊆ N ( P ≠ φ ) . Thus, the stable allocation of the sub alliance P exists, that is the core is nonempty which
V P,( y1 ,, yn ) ( S ) = V ( y1 ,, yn ) ( S )
S⊆P
means that we can still use the core to solve the model.
( x1 ,, xn )
C ( P, V
− P ,

Vi
y1, y

= max =
v i | v
( vi )





n
1
=
min =
v i | v

. When
) ≠ φ , P is stable. Based on the assumption, we now give the upper and lower bound of the profit of participant i .

n 
P , y , y
V i-
for all

( vi )

i∈P





i∈P

∈ C  P, v  y1, y n   

∈ C  P, v  y1, y n   




i in the biform game is:
max xi∈X i, y i∈Y i c1 ( x i ) + E i ( y1, , y n )
The anticipated profit of participant
(
∗
∗
)
=
i x ,y
F
( y1,, y n ) µiV i
E i=
− P , y ,, y
In which,

s.t.



1

n 
+
P , y ,, y
(1− µi )V i−

1

n 

C  P, v  y1, y n   ≠ ∅


Price is the linear function
y / γ = D− − ∏ β j p
of market demands in the market activities, where
p stands for the market price and
D − stands for the potential market demands (Ekeland I, Djitté N 2006) . If and only if p > 0 , the core of the cooperative game exists.
c1 be the unit production cost, c0 be the fee charged by the service platform, c be the unit variable cost, ϕi be the unit residuals rate
∏ β j ( j ≠ i) be the probability of all participants except participant i joining in the cooperative game.
and
Let
According to the method identifying the upper and lower bound of profit we proposed before, the maximum profit most probably
 ( D− − y / γ )

2
v 2max = y  ∏ β j − ε c − cl − c0
=ϕ y


obtained from the cooperative game is
. And the minimum profit most probably is v min i from the
disposal of the raw materials.
The profit from the biform game of participant
i can be written as:
Journal of Residuals Science & Technology, Vol. 13, No. 5, 2016
© 2016 DEStech Publications, Inc.
doi:10.12783/issn.1544-8053/13/5/61
61.4
max Z =
2
2
+ (1 − µ i ) v min
v1 + µiv max
max Z = v + µ
 
y
i  

(D
)
1
i.e.

= v1 +  y 
 
−
(D
−
)
− y / r / ∏β
(1)

− εc  − l − 0  +
j


c c

− y / γ / ∏ β j − εc  − c l − c 0 − v i y  µ i + ϕi y


=+
v1 M µi + ϕi y
=
M
(1− µi ) ϕi y
{ y ( D − y / γ ) / ∏ β − εc − c − c − ϕ y} . When M > 0 , µ i is positively correlated to the comprehensive profit Z ,
−
j
l
0
i
which means that the higher the anticipated profit obtained from the cooperative game by participant
cooperative game.
i
, the more likely it joins in the
We can derive the manufacturing resources
used in the cooperative game stage by solving its first derivative:
*  −


=  D − εγc ∏ j − iγ ∏ j  i + iγ ∏ j  / 2 i



(2)
We can draw conclusion 1 and 2 from (2).
−
Conclusion 1 The larger the potential market demands D in the cooperative stage, the more services they can provide in the
cooperative stage when other factors stay consistent. That is to say, service providers are more easily to get orders through cooperation with
larger market size.
y
β ϕ
β µ ϕ
β
( µ)
Conclusion 2 Service providers prefer to offer services with smaller customers’ priority when other factors stay consistent. Constant
demands from the same customers are more easily to be satisfied for a service provider because in the prior service process they have
established great relationships and the communications between them become smooth.
By changing the form of (2), we can derive:
We can draw conclusion 3 from (3).
y
*
(
)
( )
=v i − εcµ i − ϕiµ i ∏ β jγ / 2µ i + D
−
(3)
(ϕ − εcµ − ϕ µ ) > 0
γ
i
i
i i
Conclusion 3 The larger the confidence index , the easier for the service provider to get orders when
.
Because customers are more sensitive to the service providers with higher confidence indexes which are on top of the service providers list
of the service platform. The larger the probability
∏βj
of other service providers joining in the cooperative game, the more service
provider i wants to join in the cooperative game.
5. Conclusion
We have investigated the competitive and cooperative game i.e. the biform game between service providers under cloud manufacturing
and propose the two-stage biform game model. Five factors that influence the willingness of service providers participating in the biform
game are analyzed, which are: the comprehensive capability index, the potential market size, the will of involvement in cloud manufacturing,
the priority of customers’ needs and the anticipation of achieving the maximal profit in the cooperative game. We have examined the impact
of the change of five different factors on the willingness of service providers participating in cloud manufacturing. The results provide
insights into the decision-making of service providers.
Acknowledgements
This research is financially supported by the National Key Technology R&D Program of China (Grant No.2013BAF02B03,
Manufacturing Information Technology Demonstration Project of Dalian City), Humanity and Social Science Youth foundation of Ministry
of Education of China (Grant No.14YJCZH001, Study on Cooperation Mechanism of Autonomous Entity for Mutual Value Creation in
Cloud Manufacturing ).
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