In order to prevent and control risk factors which harm the quality and safety of the food supply chain effectively and reduce the probability of food safety incidents, this paper investigated on some problems of the upstream and downstream enterprises of the food supply chain under the three different forms of cooperation based on the neoclassic economics and game theory method. These problems include the effectiveness of the quality and safety efforts, the profits, the effect of the losses that the food safety incidents caused on the quality efforts’ efficacy, and the social welfare comparison. Meanwhile, we constructed evolutionary game model to analyze the macro and micro factors that influenced the cooperation strategy and demonstrated the effect of diversity of decision-making parameters on evolution results based on numerical simulation. By the theoretical and simulation analysis, we found that (1) the quality efforts’ efficacy, the profits, the sensitivity coefficient of the quality efforts efficiency to the losses, and the social welfare without thinking about the externality all met their maximum under the full cooperation situation; (2) strengthening supervision over the source of the food supply chain can reduce the probability of food safety incidents; (3) macro and micro environment will be the important basis for companies’ decision-making on cooperation strategy in the food supply chain.
Food safety is related to the life and health of the whole nation, the healthy development of the economy, social harmony and stability, and the image of state and government. However, the food safety incidents that many factors caused have happened frequently in recent years. These factors included the food markets failures due to the food markets’ externality and “lemon market effect” that information asymmetry in food markets caused [
Risk factors of food safety throughout each link of the whole supply chain are from the source’s supply of raw materials, the cultivation and breeding of agricultural products, the production and processing, and logistics distribution to retail terminal. Risk factors existing in each link (e.g., abuse of pesticides in the planting and breeding links and use of food additives excessively in the production and processing links) would pass on the food supply chain, and then it produced the agglomeration and amplification effects and led to the occurrence of food safety incidents eventually [
Many factors, for example, information asymmetry [
It is exactly based on the above consideration that this paper tries from the aspect of food supply chain to realize close cooperation between all of the links (the node enterprises) in the food supply chain through establishing the cooperation, incentive, and supervision mechanism and to reach the goals for preventing and controlling risk factors which harm the quality and safety of the food supply chain effectively and reducing the probability of food safety incidents. This paper is structured as follows. Section
This paper analyzes the problems about quality and safety cooperation between the upstream enterprise
Both enterprises
The effectiveness of the quality efforts, the profits, and the social welfare of both enterprises
There is no comparison between the extents of the different food commodities’ quality efforts. However, the quality effort efficiency (the probability of food safety incidents) can be compared in the different food commodities.
Products of enterprises
The unit food quality effort (the amount of per unit food quality and safety events that can be reduced) is constant under certain conditions. And the total quality efforts of both enterprises
The quality effort cost is a monotone increasing function of the quality effort efficiency, and the marginal cost of quality effort increases with the increasing of the quality effort efficiency. The inputs on quality efforts have no impact on the food production cost.
The average number of quality and safety events of per unit food of both enterprises
We can construct the profit function of enterprise
In the same way, the profit function of enterprise
The game between enterprises
The game process of three forms.
Let us solve the above problems based on the backward induction.
The downstream enterprise’s quality efforts efficiency is lower than the upstream enterprise when
Bring
With (
Therefore,
There exists local maximum in the overall profits of the food supply chain under the situation of semicooperation, and the downstream enterprise’s quality efforts efficiency is equal to the upstream enterprise when
Thus that
Therefore,
There exists local maximum in the overall profits of the food supply chain under the situation of cooperation, and the downstream enterprise’s quality effort efficiency is equal to the upstream enterprise when
Let
Bring
Therefore, there exists local maximum in the overall profits of the food supply chain due to
Therefore
The extent of quality efforts for food safety must be greater than a certain value, namely,
The equation
If one wants to reduce the probability of food safety incidents when the average number of quality and safety events of per unit food of the upstream and downstream enterprises in one year is the same, one should pay attention to strengthening regulation over the source of the food supply chain. The same number of quality efforts investments can achieve more quality efforts effectiveness in the upstream enterprise.
The quality efforts behavior of the upstream or downstream enterprises can encourage the downstream or upstream enterprises to carry out quality efforts.
The extent of quality efforts is directly proportional to the average number of quality and safety events of per unit food of an enterprise in one year and is inversely proportional to the average number of quality and safety events of per unit food of another enterprise in one year. Namely, for food companies, the more the average number of quality and safety events of the unit food in one year, the greater the resistance of that enterprise to carry out quality efforts.
After the enterprises
The average number of quality and safety events of per unit food of the whole food supply chain in one year will decrease with the increase of the extent of cooperation.
The quality efforts efficiency of enterprises in the state of cooperation is higher than that in the state of noncooperation. Therefore, only with strengthening the quality efforts cooperation between upstream and downstream enterprises can the higher effectiveness on guaranteeing food safety be achieved in the process of strengthening the food safety guarantee.
Assume that
The quality efforts efficiency of the whole supply chain is the highest under the situation that enterprise
The quality efforts efficiency is directly proportional to the loss S that the average quality and safety events of per unit food caused each time under the different cooperation modalities. If the enterprise
There are no intersection points between the curve The curve
Relations between
The proving process which is under the situation of noncooperation is the same as that under the situation of semicooperation and cooperation. Only the curve gradient and the intersection point range of the abscissa are different under the three kinds of cooperation modalities, as shown in Figure
Relations between
Plug the above calculational results into the profit functions, and the profit functions of enterprises under the different cooperation situations can be obtained, as follows.
Noncooperation:
Semicooperation:
Cooperation:
The higher the extent of cooperation in the quality and safety between the upstream and downstream enterprises, the higher the profits of the whole food supply chain that can be achieved. Therefore, one should strengthen cooperation between the upstream and downstream enterprises in the process of carrying out quality efforts.
Regardless of the externality, (the sum of the producer surplus and consumer surplus is social welfare regardless of the externality) the social welfare is that
Bring the simplified demand functions into (
Social welfare will increase with the increase of the extent of cooperation on the quality and safety between the upstream and downstream enterprises without considering the externality influence caused by food safety incidents.
The close cooperation between all of the links (the node enterprises) in the food supply chain can be realized through establishing the cooperation, incentive, and supervision mechanism. However, the macro environment (including the related governmental policies and laws that continue to move forward in a timely fashion and the general public (the consumers’ consumption habit, the consumption concept, consumption evaluation, consumption quality migration, news media exposure, etc.)) and the micro environment (company’s earnings in future, etc.) will also be the important basis for companies’ decision-making in the process of cooperation between the upstream and downstream enterprises. The above model hypothesis does not take into account the macro environment and the micro environment variables.
Therefore, analyzing the enterprises’ behavioral characteristics in the process of cooperation and the factors which influence enterprises’ collaboration strategy for the quality efforts is new expansion of researches on the enterprises’ collaboration strategy for the quality and safety in the conventional sense through applying evolutionary economics approach and introducing the macro and micro environment variables to construct evolutionary game model.
The benefits that the unit quality efforts can bring for the enterprises
The government will grant subsidies which are
This paper constructs the strategic payoff matrix of the game between enterprise
The strategic payoff matrix of the game.
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If the adaptability of adopting a strategy is higher than the average adaptability of the group, then the probability of adopting the strategy will increase gradually as time
Let
Considering the complexity of the computation on the game equilibrium results, this paper analyzes the mechanism that the change of macro-environmental variables influences the evolution of the cooperation strategy behavior with the help of
The influence of the government’s positive stimulus on the cooperation strategy.
The influence of the government’s supervision efficiency on the cooperation strategy.
The influence of the punishing dynamics of government on the cooperation strategy.
The influence of the consumers’ positive guidance on the cooperation strategy.
The influence of the news media’s disclosure mechanism on the cooperation strategy.
The replication dynamic evolutionary phase diagram of the strategy interaction between enterprises.
It can be seen from the numerical simulation results that the government’s positive stimulus, efficient regulation, and appropriate punishment, the consumers’ positive guidance, and the news media’s efficient disclosure mechanism can encourage the enterprises to increase investment in quality efforts and strengthen the enterprises’ cooperation strategy for the quality efforts.
Through comparing Figure
Take the derivative of the inequality’s left side with respect to
It indicates that the income difference that companies adhere to carry out quality efforts changes in the opposite direction with the change of
Suppose the opportunity income’s loss that is caused due to the reason that the enterprises
We can draw the evolutionary phase diagram of the game (Figure
Therefore, increasing the discount value of the enterprise future earnings can encourage the enterprises to cooperate in quality and safety. It indicates that enterprises
This paper mainly discusses two problems: firstly, the cooperation strategy for the quality and safety between the upstream and downstream enterprises of the food supply chain and, secondly, the macro and micro factors that influence the collaboration strategy for the quality and safety. The research results as follows: The food supply chain form that cooperates in both the quality and safety and pricing can achieve the high-quality efforts efficiency and obtain high profits simultaneously in the conditions of three kinds of cooperation modalities, which are noncooperation, semicooperation, and cooperation. The interaction between the loss that the average quality and safety events of per unit food caused each time and the quality efforts marginal cost can influence the upstream and downstream enterprises’ quality efforts effectiveness. The loss that the food quality and safety events caused has a vital impact on the enterprises’ quality efforts efficiency. There is a negative correlation between the quality efforts efficiency and the loss when the degree of quality efforts is higher, and instead there is a positive correlation between them. The direct consequence of enterprises in pursuit of maximum profit is that they will reduce the total investment in quality efforts. But increasing the discount value of the enterprise future earnings can encourage the enterprises to cooperate on quality and safety and enhance mutual trust, establish long-term strategic cooperation partnership, and work hard for creating excellent cooperation environment for the quality and safety in the food supply chain.
Meanwhile, the macro environment will be the important basis for the enterprises’ decision-making on collaboration strategy. The government should establish incentive and supervision mechanism, and they also should increase the compensation intensity for companies that carry out the quality and safety efforts. The supervisory departments should strengthen supervision on enterprises that do not carry out the quality and safety efforts, improve the supervision efficiency, and appropriately punish them. The news media should disclose timely the enterprises’ behavior of not doing more to carry out quality efforts and hurt their chances of hitchhiking. However, excessive punishment can easily lead to the supervisory departments slacking off more and choosing the strategy that does not supervise enterprises. Therefore, the government should simultaneously strengthen supervision and increase the punishing dynamics for the supervisory departments’ behavior, including the laziness behavior, the inaction behavior, and the power rent-seeking behavior.
The signal transmission which is about the quality and safety of the food supply chain can realize the food quality and safety information in two-way communication between enterprises and consumers, and it is beneficial to transform the food quality and safety’s credence goods features into search goods features. Consumers can accurately distinguish the level of food quality and safety and realize the separation between high-quality food production enterprises and low-quality food production enterprises; it also can encourage enterprises that do not carry out the quality and safety efforts to increase investment in quality efforts and ultimately achieve the goal of improving the level of food quality and safety progressively due to the reason that low-quality food production enterprises cannot imitate the strong signal sent from high-quality food production enterprises. Consumers are willing to pay the price discrimination for the food whose level of quality and safety is high. The companies’ profits will increase due to the increased consumer demands, thus further promoting enterprises to increase investment in quality efforts. However, to explore how to improve the signal transmission mechanism and the path that can ensure the efficient transfer of the signal to consumers is worth further analysis.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors wish to express their gratitude to the referees for their invaluable comments. This work was supported by the Major Program of National Social Science Foundation of China (no. 12&ZD204) and the National Natural Science Foundation of China (no. 71173103).