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2013 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE)

A Critical Analysis of Outsourcers’ Behaviorization of Moral Hazards

Fuyuan Zhang, Bin Geng, Zhanling Liu Shijiazhuang New Technology Application Institute

Shijiazhuang, China generzhang@sina.com

Jinna Jia Department of Information Technology

Hebei Institute of Communication Heibei, China

Abstract—This paper firstly presents analysis of outsourcers’ critical behaviors of moral hazards in the principal-agent contract of Stage I, and then analysis of outsourcers’ behaviorization of moral hazards in long-term cooperation. Finally, corresponding measures to inhibit outsourcers’ behaviorization of moral hazards as for potentiality of outsourcers’ behaviorization of moral hazards are provided.

Keywords-outsourcers; moral hazards; critical behaviors

I. INTRODUCTION

With further development of social division of labor, outsourcing has been widely accepted in the society and become an effective means for various organizations and institutions to improve self-efficiency and capacity. However, in view of asymmetric information between the principal and the agent, the principal is always encountered with outsourcers’ behaviors of moral hazards in outsourcing. The outsourcers’ behaviors of moral hazards have been the bottleneck to prevent and restrict principal’s outsourcing benefit from increasing. It is difficult for the principal to be conscious of outsourcers’ behaviors of moral hazards; therefore, scientific prevention for such problem is particularly necessary [1]. Through an analysis of critical conditions for outsourcers’ behaviorization of moral hazards, the present paper is to specify relevant factors that affect outsourcers’ behaviors of moral hazards and to furnish references and guidance for effective control of outsourcers’ behaviors of moral hazards.

II. CRITICAL ANALYSIS OF OUTSOURCERS’ BEHAVIORS OF

MORAL HAZARDS

Assumed that outsourcers’ utility function is as follows:

1 2( , )U f u u (1)

where U indicates outsourcers’ utility level, 1u indicates self-interest utility to specify the gain after the outsourcer concludes a contract with the principal, and 2u indicates altruism utility

to specify the principal’s gain thereof. Herein, 1

0

U

u

indicates that outsourcers’ utility is an increasing function of

self-interest utility; 2

0

U

u indicates that outsourcers’ utility

is a decreasing function of altruism utility.

Similarly, assumed that the principal’s utility function is as follows:

1 2( , )V g u u (2)

where V indicates the principal’s utility level, 1u indicates

payoff from the principal to the outsourcers, thus, 1

0

V

u

indicates that the principal’s utility is a decreasing function of such payoff; 2u indicates the gains obtained by the principal

through outsourcing contract, thus, 2

0

V

u indicates that the

principal’s utility is an increasing function of interest brought by outsourcers to the principal.

Considering asymmetric information between the principal and the outsourcer, and the motivation to seek for maximum utility respectively, both parties get involved in opportunism. The aforesaid assumption shows that: outsourcers’ utility U is an increasing function of relevant gain 1u while the principal’s

utility V is an increasing function of relevant gain 2u . To simplify the analysis, we replace principal’s utility with gain

2u and replace outsourcers’ utility with gain 1u . These will not affect our analysis results [2].

In the event that the gain under outsourcers’ behaviorization of moral hazards is 1 u r but unknown by the principal; the principal sets up incentive contract

1 1 S u u where indicates reward coefficient to encourage the outsourcers to make great efforts in work; after outsourcers’ behaviorization of moral hazards is realized by the principal, the principal will give a punishment to outsourcers so that outsourcers’ gain becomes 1 1u u ; the principal’s

supervision cost is ( )C p , and ' ( ) 0C p , '' ( ) 0C p , p indicates the principal’s information degree (The probability for the principal to realize outsourcers’ behaviorization of moral hazards).

In the game between the principal and the outsourcers, the principal’s strategies comprise supervision or non-supervision and the outsourcers’ strategies include behaviorization of moral hazards or not, therefore, the principal’s gain and the outsourcers’ gain shall be as follows respectively:

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(1) For the principal’s supervision and outsourcers’ behaviorization of moral hazards, the principal’s gain will be:

2 1 1( ) (1 )( ) u C p p u p u r and outsourcers’

gain will be: 1 1 1(1 )( ) u p r u p u ;

(2) For the principal’s supervision in case of no outsourcers’ behaviorization of moral hazards, the principal’s gain will be: 2 1( ) u C p u , and outsourcers’ gain will be: 1 1u u ;

(3) For outsourcers’ behaviorization of moral hazards without the principal’s supervision, the principal’s gain will be: 2 1 u r u and outsourcers’ gain will be: 1 1 u r u ;

(4) For neither principal’s supervision nor outsourcers’ behaviorization of moral hazards, the principal’s gain will be: 2 1u u and outsourcers’ gain will be: 1 1u u .

We can adopt payoff matrix as shown in Table I to indicate the situation above.

TABLE I. INCOME STATEMENT OF THE PRINCIPAL AND THE OUTSOURCERS

outsourcers

Behaviorization of moral hazards

Non-behaviorizat-ion of moral

hazards

The principal

supervision u2-C(p)+pβu1-(1-

p)(βu1+r) , u1+(1-p)(r+βu1)-pβu1

u2-C(p)-βu1 , u1+βu1

Non-supervision

u2-r-βu1 , u1+r+βu1 u2-βu1 , u1+βu1

Assumed that the probability for the principal to monitor outsourcers is mp , the gain involved in outsourcers’ behaviorization of moral hazards is as follows:

1 1 1 1

1 1

[ (1 )( ) ]

(1 )( )

a m

m

E p u p r u p u

p u r u

(3)

The gain not involved in outsourcers’ behaviorization of moral hazards is as follows:

2 1 1 aE u u (4)

When the gain involved in outsourcers’ behaviorization of moral hazards is equivalent to that not involved in outsourcers’ behaviorization of moral hazards, the equilibrium point between behaviorization of moral hazards and non-behaviorization of moral hazards will be reached and this point is also a critical point of outsourcers’ behaviorization of moral hazards.

If 1 2a aE E , then:

1 1 1 1 1

1 1

[ (1 )( ) ] (1 )( )

m mp u p r u p u p u r u

u u

The result is:

12

1

m

m

p p ur

p p

(5)

Seen from Eq. (5), the critical value of behaviorization of moral hazards is in positive correlation with the principal’s incentive (punishment) degree 1u toward outsourcers, therefore, the higher the incentive (punishment) degree is, the more the critical value of moral hazards is, that is to say, the higher the incentive (punishment) degree towards outsourcers is, the more impossible the outsourcers’ behaviorization of moral hazards is.

As shown in

21 1

2

(1 )10

2 (1 )

m m m

m

p u p p p p ur

p p p

The critical value of outsourcers’ behaviorization of moral hazards is also increased with the increase of principal’s information degree, which is just in line with the actual situation. We know that the increase of principal’s information degree means increased probability of outsourcers’ behaviorization of moral hazards, hence, the outsourcers will not easily have the behaviors of moral hazards under such circumstances. Only when the gain is enough, the behaviors of moral hazards may occur.

As shown in

21 1

2

(1 )10

2 (1 )

m m

m m

p u p p p p ur

p p p

The critical value of outsourcers’ behaviorization of moral hazards will be also increased with the increase of principal’s supervision probability, that is to say, increased probability of principal’s supervision will prevent the outsourcers’ behaviors of moral hazards.

III. AN ANALYSIS OF OUTSOURCERS’ BEHAVIORIZATION OF

MORAL HAZARDS IN LONG-TERM COOPERATION

We offer an analysis of outsourcers’ behaviorization of moral hazards in the principal-agent contract of Stage I and draw relevant conclusions. Generally speaking, the cooperation between the principal and the outsourcers is in long term. What’s the situation of outsourcers’ behaviorization of moral hazards and what are relevant factors in long-term cooperation?

Based on the analysis [3] of “Becker and Stiger” model (Becker and Stiger,1974), in the event that the principal cooperates with the outsourcers for n times, the outsourcers’ behaviorization of moral hazards and cooperation time is n i in the cooperation of Stage i and the situation of

outsourcers’ behaviorization of moral hazards is the same in the cooperation of Stage 1. Therefore, this paper reflects whether the outsourcers decide to get involved in the behaviors of moral hazards and the situation that they are not involved in the behaviors of moral hazards.

Given that the outsourcers never get involved in the behaviors of moral hazards and their cooperation duration with the principal is n and the outsourcers’ gain is 1iu in every cooperation; the principal sets up incentive contract

1 1 i i iS u u in every stage; if the outsourcers’ behaviorization of moral hazards exists but unknown, the

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outsourcers’ additional gain will be r ; if the outsourcers’ behaviorization of moral hazards exists but known by the principal who offers a punishment to the outsourcers, the outsourcers’ future gain will be 0u in every stage and 0u means the outsourcers’ retained earnings. Such situation also shows that the principal will cancel the qualification of outsourcers in case of the outsourcers’ behaviorization of moral hazards; when the principal monitors the outsourcers, relevant information degree is still p .

Seen from the aforesaid assumption, the expected utility flow of the outsourcers who never get involved in the behaviorization of moral hazards in cooperation will be as follows:

11111

2 uuEa , 121222 uuEa ,… nn

na uuE 112 ,

Given that discount factor is and 0 1 , the present value of total expected utility will be as follows:

12

1

11 11 12 12

2 113 13 1 1

11 1

1

( )

( ) ... ( )

( )

ni iai

i

nn n

ni

i ii

E E

u u u u

u u u u

u u

Given that the principal’s supervision probability is

mp based on outsourcers’ behaviorization of moral hazards, the expected utility flow in different stages is as follows:

11 11 11 0 11 11[(1 )( ) ] (1 )( ) a m mE p p u u r pu p u u r

,

21 12 12 0 12 12[(1 )( ) ] (1 )( ) a m mE p p u u pu p u u ,

…

1 1 1 0 1 1[(1 )( ) ] (1 )( ) na m n n m n nE p p u u pu p u u

Then the outsourcers’ total expected utility in different stages is as follows:

11 1

1

11 1

1

0

11 1

1

(1 ) ( )

1(1 ) ( ) (1 )

1

(1 ) ( )

ni ia

i

ni

m i ii

n

m m m

ni

m i ii

E E

p p u u

r p p pu p p r

p u u

To simplify calculation, please record

11 1

1

( )

n

ii i

i

T u u

where T indicates the present value of outsourcers’ utility in different stages, then

1

0

(1 ) (1 )

1( ) (1 ) (1 )

1

m m

n

m m m

E p p T r p p

pu p p r p T

When there is no difference between the gain based on outsourcers’ behaviorization of moral hazards and that in case of no outsourcers’ behaviorization of moral hazards, the critical point of outsourcers’ behaviorization of moral hazards is obtained. If 1 2E E , then:

0

(1 ) (1 )

1( ) (1 ) (1 )

1

m m

n

m m m

T p p T r p p

pu p p r p T

The result is:

0

1( )

11

n

m

m

p p T ur

p p

(6)

where r indicates the critical gain of outsourcers’ behaviorization of moral hazards. Only when the gain of outsourcers’ behaviorization of moral hazards ' r r , the outsourcers will have the behaviors of moral hazards, otherwise, the behaviors of moral hazards will not occur.

Seen from Eq. (6): r will increase with increased T , which means that the increase of present value of outsourcers’ total utility in different stages will reduce the behaviors of moral hazards; with the principal’s supervision probability and information degree increasing, the outsourcers’ behaviors of moral hazards will be reduced. Furthermore, r in case of 1mp p so that the outsourcers’ behaviors of moral hazards will not occur herein; the punishment towards the outsourcers for their behaviorization of moral hazards is strengthened, that is to say, the qualification of outsourcers will be cancelled in the event of any behavior of moral hazards, which is favorable to reduce the outsourcers’ behaviors of moral hazards.

IV. MEASURES TO INHIBIT OUTSOURCERS’ BEHAVIORIZATION

OF MORAL HAZARDS

According to analyses stated above, this paper concludes that the measures to inhibit and reduce outsourcers’ behaviorization of moral hazards shall be mainly taken in the following respects:

(1) Establishing and improving competitive mechanism in outsourcing market. The competition may promote the outsourcers to disclose their private information in maximum and reduce the asymmetry of information between the principal and the outsourcers; consequently, outsourcers’ behaviors of moral hazards will be reduced to some extent. Meanwhile, the competition is beneficial for outsourcers to form certain self-motivation to help them resist behaviorization of moral hazards independently.

(2) Establishing and improving motivation and supervision system. The motivation and supervision are two

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key factors to ensure that the principal-agent relationship between the principal and the outsourcers takes effect efficiently. The motivation can be converted into a drive to consciously resist the behaviorization of moral hazards and the supervision acts as external stress for outsourcers to reduce the behaviorization of moral hazards.

Two factors are indispensable and complement each other.

REFERENCES [1] S. Y. Xie, Economic Game Theory, Master Dissertation, Fudan

University, 2002.

[2] W. Y. Zhang, Game Theory and Information Economics, Master Dissertation, SDX Joint Publishing Company, 2002.

[3] L. Y. Huang and X. T. Yang, “Study on motivation system of principal-agent relationship in state-owned enterprises,” Journal of Chongqing University: Social Science Edition, vol. 5, no. 1, pp. 38-41, 2000.

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