Quality Control in Food Supply Chain Incorporating Government ...

incentives in order to promote their productions. Then enterprises like this don’t have to fear the
consequences of their poor quality.
Besides, more other literatures have talked about the effect of government supervision of
products. Since the government's safety supervision system reform of developed countries in 1990,
China has undergone a series of food safety issues in recent years, causing customers in the market
paying more and more attention to food quality. Zhan and Kong (2004), Yu and Zhou (2005) and
Wang (2011) [9] , from the perspective of game theory, point out that the quality of the products in
the food industry is the result of coordination jointly by the enterprise and government.
2. Dynamic game model of Government and Enterprise
2.1 Basic assumptions and models
In order to facilitate the analysis, this paper makes the following basic assumptions under the
premise of no affecting the results: 1) In a oligopoly market of the food industry,customers choose
products considering the price of the products p e
and the quality of all products i . 2) The
participants have the same information about the behavioral characteristics,strategies and revenue
functions of other actors. The game has only two participants: government and food production
enterprises. They make decisions respectively on the degree of probability and quality efforts. 3)
Food sales is D . The cost of government supervision using administrative means is θ Dm
. The
probability of government detection isθ . Government inspection cost for each product is m . If the
government finds out the quality of the product is lower than the requirements, penalty on producer
is d . 4) Orders of government’s and enterprises’ behaviors are not consistent. Both sides decide
their actions based on self-interest maximization .
The Demand Curve
Market demand producers face is uncertain, so the article sets the demand function on the basis
of the one Lu (2008) putted forward:
The demand function is De () = l+ αe
(1)
i
Inside: α represents the entire needs of customers in the whole market, which reflects the
development level of the product in the market as a whole (Banker R D, 1998).
2.2 Government decides first. The enterprise undertakes strategic analysis.
This article establishes a two-stage game model according to the relationship between government
and the leading enterprises in the supply chain. The first stage is government decision making on
detection, and the second stage is enterprise’s choice of quality efforts strategy under the estimation
of the probability of governmental detection.
kG
First, government's utility function is U ( θ ) = ln
G 1- θ
, ( ) '
0, ( )
'
U θ > U θ < 0
G
G , and kG
is the
government utility parameters , θ ∈(0,1) .
So the government's benefits is
⎧ k
G
⎪ln -θDm + γ ( ei-e L)
+ d , e
ieH
⎩ 1-θ
After the government determines his own strategy, producing company will determine the
quality strategy based on the strategy of the government. Company’s demand function is (1). The
government will give each industry the corresponding quality requirements in the beginning of the
industry production. Assuming the quality requirements are set from e L
to e H ,
and producer’s cost
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