J. Service Science & Management, 2010, 3, 241-249
doi:10.4236/jssm.2010.32029 Published Online June 2010 (http://www.SciRP.org/journal/jssm)
Principal-Agent Theory Based Risk Allocation
Model for Virtual Enterprise
Min Huang1, Guike Chen1*, Wai-Ki Ching2, Tak Kuen Siu3
1College of Information Science and Engineering, Northeastern University, Key Laboratory of Integrated Automation of Process Industry
(Northeastern University), Ministry of Education, Shenyang, China; 2Department of Mathematics, The University of Hong Kong,
Hong Kong, China; 3Department of Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, Australia.
Received February 3rd, 2010; revised March 19th, 2010; accepted April 29th, 2010.
ABSTRACT
In this paper, we consider a risk analysis model for Virtual Enterprise (VE) by exploring the state of the art of the prin-
cipal-agent theory. In particular, we deal with the problem of allocating the cost of risk between two parties in a VE,
namely, the owner and the partner(s). We first consider the case of a single partner of VE with symmetric information
or asymmetric information and then the case of multiple partners. We also build a model for the optimal contract of the
risk allocation based on the principal-agent theory and analyze it through specific example. At last we consider the case
of multiple principal with potentially many partners based on common agency.
Keywords: Virtual Enterprise, Risk Allocation, Principal-Agent Theory, Risk Aversion, Common Agency
1. Introduction
Virtual Enterprise (VE) is a dynamic alliance composed
of independent individual enterprises which locate in
different area. It’s designed to adapt to rapidly changing
market opportunities, so as to achieve the sharing of
skills, core competencies and resources [1,2]. Based on
this concept, on one hand, member enterprises in a VE,
which are geographically distributed, keep their inde-
pendence and autonomy. On the other hand, they provide
their own core competencies in different areas such as
marketing, engineering and manufacturing to the VE.
When new market requirements arise and individual en-
terprises do not have all necessary skills and competen-
cies to undertake these requirements independently, by
combining specific expertise of other enterprises, it is
possible to create a VE which is capable of responding to
the new requirements. In a certain sense, the essence of
VE has its basis in an early and fundamental concept of
economics, namely, the division of labor, which has its
origin in the classics, namely, the wealth of nations, by
Adam Smith first published in 1776.
In spite of substantial advantages of VE, there are lots
of risks associated with it, these risks include investment
risk [3], operation risk [4], moral hazard [5,6] and market
risk, and so on. These incomplete nesses arises from
member enterprises not having sufficient background
information about the other member enterprises or about
market environment in which the VE has to operate. The
investigation of the structure, operations and economic
implications of a VE has received much interest among
researchers in the field. Much attention has been paid on
some aspects of VE, such as partner selection [7,8], op-
eration management [9], information exchanges [10] and
their scales. However, an important issue, the risk man-
agement of VE, has not been well-explored and ad-
dressed until recently. Since virtual enterprises (VEs) are
profit driven, it is one of the key issues to the successful
running of VEs whether they could construct reasonable
and efficient risk allocation mechanism in the operation
process to prevent some members from gaining profit by
harming others. The establishment of a VE can not re-
duce or eliminate the risk due to the uncertainty of mar-
ket opportunities and production capacities. The risk of
the whole enterprise is re-distributed among different
members in the VE. There are some ways to mitigate the
risk in the cooperation process, such as partner selection
[11,12], cooperation contract design [12], and coordina-
tion mechanism design [13]. After reviewing the related
literature, we found out that researchers have carried out
certain publications on VE’s risk.
Based on the research of risk in supply chain [14], it
produces partnerships [6] and joint ventures [15]. We
consider a risk allocation model for VE by exploring the
state of the art of the principal-agent theory. In particular,
we deal with the problem of allocating the cost of risk

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise
242
between two parties in a VE, namely, the owner and the
partners. Our analysis invokes some basic and important
concepts for the risk analysis, including utility function,
risk-aversion level, principal-agent theory [16] and com-
mon agency [17,18]. Here we first deal with the case of a
single partner of VE with symmetric information or
asymmetric information. Then, the model is extended to
deal with the case of multiple partners. We also build a
model for the optimal contract of the risk allocation
based on the principal-agent theory. At last we extend the
principal-agent framework with risk-neutral principals to
situations in which several principals simultaneously and
independently attempt to influence a common agent. The
remainder of this paper is organized as follows. In Sec-
tion 2, we give a brief discussion on some basic concepts
of risk analysis and related assumptions. In Section 3, we
present our risk allocation models. In Section 4, a spe-
cific example is given to demonstrate our models in sec-
tion 3. In Section 5, we discuss the incentive mechanism
on the basis of common agency [18,19] when the rela-
tionships between the principals is competition. Finally
concluding remarks are given in Section 6.
2. Basic Concepts and Assumptions
In this section, we provide a brief discussion on some
basic concepts of risk analysis, namely, the utility func-
tion, the risk aversion and the principal-agent theory, in
the context of VE which involving an owner and
risk-averse member enterprises (partners). These con-
cepts also play fundamental and important role in finan-
cial economics and corporate finance. Then summarize
the major notations to be used in this paper and give the
assumptions.
n
First of all, utility can be considered as goods or ser-
vices that meet the needs of consumer’s ability or desire.
The utility function is defined as a mapping function
which maps goods or services to consumer preferences.
Let
x
denote the receipts or earnings of a member enter-
prise. Then, the utility function is given by ()
x

, which
is interpreted as goods or services that meet the member
enterprise’s preference. It is a representation of the mem-
ber attitude towards risk.
The degree of risk aversion is an important characteri-
zation of a utility function. To measure the degree of risk
aversion, Arrow (1970) and Pratt (1964) introduce the
celebrated Arrow-Pratt ratio of risk aversion level given
as follows.
''
'
()
() ()






Principal-agent theory tries to model the following
types of questions. One participant (principal) wants to
participate in another person (agent) in accordance with
the interests of his choice of action, but the principal can
not observe directly the agent’s actions. What can only
be observed are some other variables? These variables
are decided by the agent’s action and other random fac-
tors. The principal’s problem is how to incentives the
agents in accordance with the information observed to
encourage their agents to choose the most favorable ac-
tions. The principal-agent model is built to analyze the
optimal contract with asymmetric information. To solve
the problem conveniently, we consider the optimal con-
tract with symmetric information. The central issue of
principal-agent relationship is the alternating between
insurance and incentive.
To facilitate our discussion, we define the following
notations and impose the following assumptions:
a, partner’s manpower contributing to the project (the
productive effort of the partner);
1
r
ii
i
t





, the random variables that not be con-
trolled by the alliance, where 1, 2,..., r


are independ-
ent risk factors;
2

, the variance of

;
(), ()gG

 , the probability density function and the
distribution function of

, respectively;
(, )a

 , the monetary income (outputs) of the alli-
ance;
(,)fa

, the probability density function of

;
()
s
x, the incentive contract (a way to repay partner);
(),()vxux , the owner’s and partner’s utility function
respectively;
u, the reservations utility (the greatest utility that part-
ners do not accept the contract);
P

, the owner’s risk aversion level;
A

, the partner’s risk aversion level;
()Ca , cost function of the effort . a
In this paper, we consider an owner and several mem-
ber enterprises (partners) in a VE. Each partner chooses a
level of productive effort and a level of risk aver-
sion
0a

. Both productive effort and risk aversion
level
a

are individually costly to partners and we as-
sume that the two actions are stochastically independent
and the cost of actions can be expressed in monetary
units.
3. The Risk Allocation Models
In this section, we present the risk allocation model un-
der the assumptions in section 2 based on principal-agent
theory which involving an owner and one or risk-
averse partners. We first deal with the case of a single
partner of VE with symmetric information and asymmet-
ric information (hidden action) respectively. Then, the
n

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise243
model is extended to deal with the case of multiple part-
ners.
3.1 The Optimal Contract of Risk Allocation
with Symmetric Information to a Single
Partner
In this subsection, we consider the case that the owner
can observe the partner’s action (the productive effort)
involving an owner and a risk-averse partner in a VE. As
the partner’s action can be observed, the owner can force
the partner to choose the ideal productive effort, so the
incentive is surplus.
The risk allocation model is given as follows: Give a
, the output is a simple random variable; the owner’s
objective is to maximize the utility of its own profit by
allocating the total revenue from the VE project includ-
ing choosing
a
()s

:
  

()
max( )( )(, )
sEv sv sfad 

 



(1)


 

 

..( ),
s
tIR usfadCa
EusCa u




 (2)
Equation (2) is the partner’s individual rationality con-
straint (IR). We then construct the Lagrange function as
below:
 


()() (,)
()(,)()
Lsvsf ad
usfadCau


 




(3)
The partial derivative of the function with respect to
()s

is given by




''
0vs us  

 
(4)
Therefore, we have





'
'
vs
us






 (5)
The Lagrange multiplier is a strictly positive constant
in (5) (because (2) strictly satisfied).The corresponding
optimal condition shows that the ratio of marginal utility
of income of the owner and partner is a constant, no rela-
tion with the output and uncertain variables

.
The optimal condition of (5) implicitly defined the op-
timal contract

s

, from implicit function theorem, the
partial derivative with respect to

is:
'' ''
10
ds ds
vu
dd




 

 (6)
Combining the above equations, we get
p
Ap
ds
d





 (7)
where
''
'
P
v
v


 and
''
'
A
u
u



Let

P
AP
ds
d






 (8)
Then we have
 
0
s
tdt



 (9)
In particular, if
P

and A

are constants (no rela-
tion among their level of income), then the optimal con-
tract is linear, i.e.


s


 (10)
We define RC

to be the risk cost of the alliance
project. Now, the improved risk programming model is
given as follows:
22
1
min 2A RC









Such that






 



, usfadCa
EusCa u





 RC R





arg max()Ev s   
3.2 The Optimal Contract of Risk Allocation
with Asymmetric Information to a Single
Partner
In this subsection, we consider the case that the owner
can’t observe the partner’s action (the productive effort)
involving an owner and a risk-averse partner in a VE. As
the partner’s action is hidden, the owner has to incentive
the partner to choose the ideal productive effort, i.e., the
partner chooses action to maximize the utility of its
own profit, where the owner cannot observe the value of
. We seek for maximizing the partner’s expected util-
ity:
a
a


  


max ,
ausfadCa
 
 (11)
Equation (12) is the incentive compatibility constraints
(IC).The partial derivative with respect to is: a






'
,0
a
usfadCa  
 (12)
i.e., IC constraint can be replaced by the first-order ap-
proach of (13). We then consider maximizing the utility
of the owner’s profit:


 


()
max( )( )( , )
sEv sv sfad 

 


(13)

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise
244
Such that
   
 



, usfadCa
EusCa u







(14)
and (15)
   
'
,
a
usfadC a  

Now, we construct the Lagrange function:
 


   

'
()() (,)
()(,)()
,
a
Lsvsf ad
us fadCau
usfadC a









 (16)
where

and

are the Lagrange multipliers of par-
ticipation constraint and the incentive constraint, respec-
tively. The optimal condition is given as follows:





'
'
,
(,)
a
vs
f
a
f
a
us
 
 



 (17)
By comparing with (5), it shows that, if the owner
cannot observe , the Pareto efficiency risk allocation is
impossible. As
a
0

(Holmstrom proved in 1979), in
order to motivate the partner to work hard, it has to bare
more risks.
3.3 The Optimal Contract of Risk Allocation
with Symmetric Information to Multiple
Partners
In this subsection, we discuss the case of symmetric in-
formation with multiple partners that the owner can ob-
serve the partner’s action (the productive effort) involv-
ing an owner and risk-averse partners in a VE. We
first define the following notations and assumptions.
n
i, partner ; i(1, 2,...,)in
[0, )
i
a, the productive effort of partner ; i

ii
Ca, the cost function of partner ; strictly in-
creasing convex differentiable function, and
i


00
i
C

;

12
,,..., n aaaa

, the vector of all partners’ produc-
tive efforts;
()
x
a, the common output decided by a, strictly in-
creasing concave differentiable function and(0) 0x

;
(, )a

 , monetary income (outputs);

12
,,,..., n

f
aa a  , the probability density function of

;
i
A

, the partner i’s risk aversion level;

i
s

, the revenue sharing factor of the partner.
As the owner can observe the partners’ actions, the
owner doesn’t need to incentive the partners, its objective
is to maximize the utility of its own profit by allocating
the total revenue from the VE project including choosing


i
s

(1, 2,...,)in

. Similar to subsection 1, the model
is presented as below:
 



12
, ,...,1
12
1
max
,, ,...,
n
n
i
ss si
n
in
i
Ev s
vsfaaa
 

d






 

 

 










(18)
Such that




12
,,,...,
(1, 2,...,)
iini ii
usfaaad Cau
in
  

 (19)
Again, we construct the Lagrangian function as fol-
lows:








 
  

12
12
1
12
1
, ,...,
, ,,...,
,,,...,
n
n
in
i
n
iiinii i
i
Ls ss
vsfaaad
usfaaa dCau
 
 
 










(20)
i

(1, 2,...,)in

are the Lagrange multipliers and are
strictly positive constants in (21). We then consider the
first-order condition as follow:
 




''
1
'
'
1
' '
'' ''
0(1, 2,...,)
(1, 2,...,)
10(1, 2,...,)
n
iiii
i
i
n
i
i
i
i ii
ii
ii
Lvs usi
s
vsvin
u us
ds ds
vuin
dd









 











 





n
(21)
Combining the above equations, we have
, (1,2,...,)
i
iP
AP
ds i
d

 


n (22)
Such that
''
'
P
v
v


 and
''
'
i
i
A
i
u
u
  ,( (23) 1, 2,...,)in
We assume that

i
iP
i
AP
ds
d



 


, (24) (1, 2,...,)in
Then
 
0
iii
s
tdt

 

, (25) (1,2,...,)in

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise245
We note if
P

and i
A

(1,2,...,)in

are constants
(no relation with their levels of income), the optimal
contract is linear, i.e.

ii
si


 (26)
Now, the improved risk programming model is given
as follows:
12
2
, ,...,1
1
min 2
n
n
ii
i
RC
 
2










(27)
Such that
  
12
, ,,...,
(1,2,...,)
iini ii
usfaaa dCau
in
  

 (28)
  
'
12
, ,,...,
(1,2,...,)
i
iiani i
usfaaa dCa
in
  



i



 



(29)
, (1,2,...,)
ii
RC Rin  (30)
1
n
i
i
RC R


 (31)


12
1
,,...,argmax
n
n
i
Ev s  



 

 





 (32)
3.4 The Optimal Contract of Risk Allocation
with Asymmetric Information to Multiple
Partners
We then discuss the case of risk allocation with asym-
metric information involving an owner and n risk-averse
partners in a VE. As the partners’ action can’t be ob-
served, the owner has to incentive to prevent the partners
from free riding. So the incentive constraints are neces-
sary. The owner’s objective is to maximize the utility of
its own profit by allocating the total revenue from the VE
project including choosing

i
s

and incentive the
partners . The model is given as follows: (1, 2,...,)in

d
 

12
, ,...,1
max
n
n
i
ss si
Ev s
 










 



 
12
1
,, ,...,
n
in
i
vsfaaa











(33)
Such that



12
, ,,...,
(1, 2,...,)
iiniii
usfaaa dCau
in
  

 (34)



'
12
, ,,...,
(1,2,...,)
i
iiani i
usfaaa dCa
in
  



(35)
We then construct the Lagrangian function:






 












12
12
1
12
1
12
1
'
, ,...,
, ,,...,
,,,...,
,,,...,
i
n
n
in
i
n
iiin
i
ii i
n
iiian
i
ii
Ls ss
vsfaaad
usfaaa d
Ca u
usfaaa d
Ca
 

 

 


















(36)
where i

and i

(1,2,...,)in

are the Lagrangian mul-
tipliers of participation constraints and the incentive con-
straints respectively. The optimal conditions are given as
below:





'
12
1
'
12
, ,,...,
, ,,...,
i
n
i
an
i
ii
n
ii
vs
f
aa a
f
aa a us
 
 








(37)
Compared with (21), it shows that, if the owner cannot
observe a, the Pareto efficiency risk allocation is impos-
sible. The partners have to bare more risks.
4. A Specific Example
In this section, in order to have a better understanding of
our models in section 3, we process example analyses to
make further investigation. To simplify the analysis, we
employ Linear sharing rules, Exponential utility, and
normally distributed random variables in this paper, i.e.,
adopt agency model developed by Holmstrom and Mil-
grom [20] which has been proved to be much more trac-
table in addressing multi-action and multi-period models.
This assumption does not affect the core issue, and the
total output of the VE is assumed to be a linear function
of the partners’ productive efforts, which is extended
from the simple model Holmstrom and Milgrom (1987)
proposed. The total output of the VE is:
1
n
i
i
a





, and

subjects to normal distribution
2
(0, )N

.
Therefore

1
n
i
i
Ea 



,

2
Var

 
Then


ii
si

  , (1,2,...,)in
And
 
11
nn
ii
iii
ss
1
n
i



 



The owner’s expected utility is given by

11
1
nn
ii
ii
Ev s
1
n
i
i





 


 
 
 






Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise
246
It is assumed that the marginal cost is increasing in the
level of effort and the cost function takes the quadratic
form [21], to simplify the analysis, we assume that the
cost function is continuously differentiable and strictly
convex and take the form:

2
1
2
ii ii
Ca ba
And is the coefficient (marginal cost). Partner i’s
actual revenue is
i
b


2
1
1
2
n
iiiiiiiii
i
s
Caa ba 


 



As the owner and every partner have constant absolute
risk aversion, which implies its utility function is of the
negative exponential form. Then, we make the usual
transformation of expected utility into mean-variance
terms as follows [22]:

22
22 2
1
1
2
11
22
iii
n
ii iiii
i
E
ab

 


 
i
a
(38)
And 22
1
2ii

 is partner’s risk cost. If ia

can be observed, the owner can decide
. The model is given as follows:

12
,,..., n aa a

,,
iii
a 




,, 11
max 1
iii
nn
ii
aii
Ev

 









Such that
22 2
1
11
22
(1, 2,...,)
n
ii iiiii
i
ab
in
i
a






 




i

is the reservation utility. The maximization problem
can be formulated as:

22 2
,111
11
max 22
ii
nnn
iiii i
aiii
fa ba


 


 



The optimality conditions are
20, 10
(1,2,...,)
ii ii
ii
ff
ba
a
in



 


(39)
i.e., 1
i
i
ab
, and 0
i

1
2
ii
i
b

 (40)
The Pareto efficiency risk allocation requires the part-
ners to bear no risk . If can-
not be observed, the owner can decide
(0
i

)



12
,,...,n aaa a

,
ii

 .The part-
ners choose the action a to maximize their expected util-
ity:








12
12
, ,...,
max,,,...,
n
iii i
aaa usf aaa

n
a dC  
The partial derivative with respect to

is








12
, ,,...,
(1,2,...,)
i
ii ani
usfaa aa
in


' i
d C  
Since ii ba
i


, i
i
i
ab

 the problem
can be transformed into the following form
(1, 2,i..., )n
11
ii


,
max 1
ii
nn
ii
fa












Such that
22
1
(1, 2,...,)
(1,2,...,)
n
ii iiii
i
i
i
i
a
in
ai
b
2
11
22
ii
ab
n
 











 
The problem can then be further transformed to the
following problem:
2
22
111
2
11
max 22
10 (1,2,...,)
i
nnnn
ii
ii i
iiii
ii
i
ii
ii i
fbb
fin
bb


1

 








 





 


Here we note that
2
10
1
i
ii
b



, (1,2,...,)in
This also means that the partners must bear certain risk.
While we can see i

is a deceasing function in i

,
and
i
b
2

. In other words, the risks the partners bear are
negatively correlated to their risk aversion levels and the
output variances. Now partner i’s risk costs is given by

2
22
2
2
10
221
(1,2,...,)
i
iii
ii
RC
b
in

 





5. Multi-principal Models
In this section, we extend the principal-agent framework
with risk-neutral principals to situations in which several
principals simultaneously and independently attempt to
influence a common agent that is considering the case of

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise247
n
multi principal agency relationships of the members in
VE which involving risk-neutral principals and a
risk-aversion agent. We analyze the moral hazard and
give optimal contract. To facilitate our discussion, we
define the following notations and impose the following
assumptions.
n
{1,2,...,}N, the set of principals;
i
a, the productive effort of the agent to the principal ; i
M
, the upper bound productive effort of the agent to
the principals;

, the uncertain variance the agent can’t control, and
it subjects to normal distribution2
(0, )N

;
(,)
iii
a

 
i
a
, the monetary income (outputs) of the
effort ;
()
iii
ss

, the incentive contract (a way to repay the
agent with respect to );
i
a
()
i
Ca , the cost function of efforts ;
i
a
()(())
iii
vxvs i

  , the principal ’s utility function i
1
()( ()())
n
ii ii
i
uxu sCa 


, the agent’s utility function
respectively;
i

, the actual profit from principal ; i
0
i

, the opportunities income (reservation income)
of that the principal guarantees;
i
In the multi-principal model, we assume that the total
productive effort of the agent has a limited
M
, which
means the resources are limited and guarantees the
boundedness of the solution. Because there are multiple
principals, the model becomes more complex. As the
relationship between the principals may affect the results
of the model, we consider the competition relationships
(non-cooperative). The model is given as follows: Every
principal give a ()
ii
s

non-cooperatively, the agent’s
objective is to maximize the utility of its own total profit
by allocating the total revenue from the VE project in-
cluding choosing every ,
i
a(1, 2,...,)in

:




max(()
i
iii
sEv s


. .()((()))()
(1,2,...,)
iiii i
stIR uEusC a
in
i

 


1
()max
n
i
i
I
Cu

u
1
n
i
i
aM



In order to have a better understanding of the multi-
principal models in this section, we process example
analyses to make further investigation. To simplify the
analysis, we employ Linear sharing rules, Exponential
utility, i.e., adopt agency model developed by Holmstrom
and Milgrom [20] which has been proved to be much
more tractable in addressing multi-action and multi-pe-
riod models, and consider the case of two principals. This
assumption does not affect the core issue. We add the
following assumptions:
0
i
k, the agent to principal i’s effort level to the im-
pact factor of the marginal output;
(,)
iiiii
aka

 


i
, the output of the agent to
principal ;
i

, the fixed remuneration of member enterprise ; i
0
i


i
, the revenue sharing factor of member enter-
prise ;

, the agent’s risk aversion level;
2
1
() 2
i
Ca bai
i
, the cost of ;
i
a
()
ii
s



, linear sharing rules;
2
1
2
iiii
ba   i .
For principal 1,




1, 1
111111 11
222
11111111
12
12
max(())(1)
11
..( )22
()max
vEv ska
stIR ukaba
ICuuu
aa M


 

 


1
For principal 2,




2,2
222222 22
222
22222 222
12
12
max(())(1)
11
..( )22
()max
vEvska
stIR uk aba
ICuuu
aa M

 
 

 


2
To solve the above models, we construct the Lagran-
gian function as follows:
12 12
222
1111 11
22
2222 22
12
()
11
22
11
22
()
Lu ua aM
ka ba
ka ba
aaM

 
2
 


 
 



is the Lagrange multiplier. We then consider the
first-order condition as follow:

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise
248
111
1
222
2
12
0
0
0
Lkba
a
Lkba
a
LaaM










 


So the optimal productive effort is
112 2
1
22 11
2
22
22
kk
M
ab
kk
M
ab













Substituting , into the principal 1’s object
function, the optimal problem is:
1
a
2
a
1
222
111 111
2
112 2112 2
1
22
11
11
max 22
1
()(
22 222
1
2
vka ba
kk kk
MM
kb
b

 
 
 

 





)
b




The first-order condition on the 1

:
1
1
0
v




Then the optimal solution is
2
11 122
122
1
222
1111 11
2
4
11
22
kkbMkk
kb
ka ba


1









 



Similarly, we can solve the optimal solution to the
principal 2:
2
22 121
222
2
222
222222
2
4
11
22
kkbMkk
kb
ka ba


2









 



From the above , ,
1
a
2
a
1


and 2

, we can analy-
sis their mutual relationships and conclude that. The de-
cision-making influences each other, when the other
conditions had been given; the efforts of the agent de-
pend on the strength of incentives of all principals. And
the intensity of incentives weakens each other. These
hypothesizes are also supported by many realistic cases.
6. Conclusions
Virtual enterprise is the main form of cooperation be-
tween enterprises today. Researching on the risk alloca-
tion in VE has both theoretical and practical importance.
On the basis of the introduction of the concepts of risk
analysis, this paper mainly describes the risk allocation
of VE based on the principal-agent theory and draws the
following conclusions: if the owner cannot observe the
partners’ efforts level, the Pareto efficiency risk alloca-
tion is impossible to achieve. In other words, the partners
must bear certain risks, and the risks the partners bearing
are negatively correlated to his risk aversion level and the
output variance. For the perfection of the problem, we
consider the case of multiple principal based on common
agency in Section 5. To simplify the analysis and explore
the implications of the risk allocation mechanism, we
have made some restrictions to the example in section 4,
such as linear/quadratic forms, independence, normal
distribution, etc. In the future research, we will relax
these restrictions to investigate the allocation mechanism
under much more general environment, and consider the
incentive mechanism when the relationship between the
principals is cooperative.
7. Acknowledgements
The authors wish to thank the support of the National
Natural Science Foundation of China under Grant No.
70671020, No. 70721001, No. 70931001 and No. 60673159,
Specialized Research Fund for the Doctoral Program of
Higher Education under Grant No. 20070145017, the
Fundamental Research Funds for the Central Universities
under Grant No. N090504006 and No. N090504003,
Science and Technology Research Fund of Bureau of
Education of Liaoning Province, and the RGC Grant
7017/07P, HKU CRCG Grants, Hung Hing Ying Physi-
cal Sciences Research Fund and HKU Strategic Research
Theme Fund on Computational Sciences.
REFERENCES
[1] M. T. Martinez, P. Fouletier, K. H. Park and J. Favrel,
“Virtual Enterprise-Organization, Evolution and Control,”
International Journal of Production Economics, Vol. 74,
No. 3, 2001, pp. 225-238.
[2] A. Mowshowitz, “Virtual Organization,” Communication
of the ACM, Vol. 40, No. 9, 1997, pp. 30-37.
[3] M. Ojala and J. Hallikas, “Investment Decision-Making
in Supplier Networks: Management of Risk,” Interna-
tional Journal of Production Economics, Vol. 104, No. 1,
2006, pp. 201-213.
[4] Q. L. Gao and G. P. Cheng, “Virtual Enterprise’s Ope-
ration Risk,” Value Engineering, Vol. 104, No. 9, 2006,
pp. 104-105.
[5] M. Thomas and E. Norman, “Moral Hazards on the Road
to the ‘Virtual’ Corporation,” Business Ethics Quarterly,
Vol. 8, No. 2, 1998, pp. 273-292.
[6] M. Gaynor and P. Gertle, “Moral Hazard and Risk
Spreading in Partnerships,” Journal of Economics, Vol.
26, No. 4, 1995, pp. 591-613.

Principal-Agent Theory Based Risk Allocation Model for Virtual Enterprise
249
[7] F. Ye and Y. N. Li, “Group Multi-Attribute Decision
Model to Partner Selection in the Formation of Virtual
Enterprise under Incomplete Information,” Expert Systems
with Applications, Vol. 36, No. 5, 2009, pp. 9350-9357.
[8] A. H. Yannis and C. G. Andreas, “A Goal Programming
Model for Partner Selection Decisions in International
Joint Ventures,” Journal of Operations Management, Vol.
138, No. 3, 2002, pp. 649-662.
[9] H. M. Gou, B. H. Huang, W. H. Liu and X. Li, “A
Framework for Virtual Enterprise Operation Manage-
ment,” Computers in Industry, Vol. 50, No. 3, 2003, pp.
333-352.
[10] A. F. Cutting-Decelle, R. I. M. Young and B. P. Das,
“Information Exchanges in a Cross Disciplinary Supply
Chain: Formal Strategy and Application,” INCOM’06
Conference, Saint-Etienne, 2006.
[11] W. Ip, M. Huang, K. Yung and D. Wang, “Genetic
Algorithm Solution for a Risk-Based Partner Selection
Problem in a Virtual Enterprise,” Computers and Opera
tions Research, Vol. 30, No. 2, 2003, pp. 213-231.
[12] H. Lars, “Managing Cooperative Research and Deve-
lopment: Partner Selection and Contract Design,” R & D
Management, Vol. 23, No. 4, 2007, pp. 273-285.
[13] L. M. Camarinha-Matos and C. Lima, “Cooperation
Coordination in Virtual Enterprises,” Journal of Intelli-
gent Manufacturing, Vol. 12, No. 2, 2001, pp. 133-150.
[14] R. Narasimhan and T. P. Srinivas, “Perspectives on Risk
Management in Supply Chains,” Journal of Operations
Management, Vol. 27, No. 21, 2009, pp. 114-118.
[15] L. H. Sung, H. P. Yeng, M. R. Yan and J. R. Lee,
“On-Line Multi-Criterion Risk Assessment Model for
Construction Joint Ventures in China,” Automation in
Construction, Vol. 16, No. 5, 2007, pp. 607-619.
[16] B. Holmstrom, “Moral Hazard and Observability,” Bell
journal of Economics, Vol. 10, No. 1, 1979, pp. 74-91.
[17] G. Esther, “Multi Principal Agency Relationships as
Implied by Product Market Competition,” Journal of
Economic & Management Strategy, Vol. 6, No. 1, 2004,
pp. 235-256.
[18] B. D. Bernheim and M. D. Whinston, “Common Agency,”
Econometrica, Vol. 54, No. 4, 1986, pp. 923-942.
[19] A. Attar, E. Campioni, G. Piaser and U. Rajan, “On
Multiple-Principal Multiple-Agent Models of Moral Ha-
zard,” Games and Economic Behavior, Vol. 68, No. 1,
2010, pp. 376-380.
[20] L. M. Camarinha-Matos and C. Lima, “Aggregation and
Linearity in the Provision of Intertemporal Incentives,”
Econometrica, Vol. 55, No. 5, 1987, pp. 303-328.
[21] G. Feltham and J. Xie, “Performance Measure Congruity
and Diversity in Multi-Task Principal-Agent Relations,”
The Accounting Review, Vol. 69, No. 3, 1994, pp. 429-453.
[22] R. A. Lambert, “Contracting Theory and Accounting,”
Journal of Accounting and Economics, Vol. 32, No. 1-3,
2001, pp. 3-87.