The combination of government reserve and enterprise reserve is one of the main models of emergency material storage in Beijing City. In recent years, China was advocating the government and enterprises to establish multi level and multi mode of the storage mode to save cost and improve efficiency. This paper uses mathematical model to establish a cooperative game premise condition, then analyses the emergency material storage cooperative game between the government and the enterprise and establishes binding cost apportionment and punishment measures to get a stable cooperation, so that both sides obtain the biggest benefit. Finally, based on the game of government and enterprise cooperation establish cost lowest Beijing emergency materials storage and transportation mode.
Social emergencies always do occur frequently, whether in public safety or in natural disaster and they usually cause social disorder and great economic losses. According to statistics, emergencies such as natural disasters, accident disasters and public safety events caused millions of casualties and economic losses up to ¥650 billion, about 6% of our national GDP, every year in our country [
Game theory study that how to maximize the utility of decision-maker with given information and how to balance decisions between different decision makers. In economics, equilibrium means making correlative variables at their stable values. Nash equilibrium is defined as a combination of strategic decisions consisting of all participants’ optimal decision, and even if, with others given decisions, no one has enough reason to break the balance.
Basic elements in a game are participants, which are a decision-makers and whose objective is to maximize its utility through making its optimal action (or strategy). It may be a person or a group such as enterprise, country and so on. Action or strategy is the participant’s decision variable. Pay function, is the certain utility level a participant obtained in specific strategies.
Cooperative game is defined as a game which has a binding cooperative agreement. Therefore, the essential difference between cooperative game and non-cooperative game depend on if there has a binding agreement [
Besides satisfying emergency needs, another essential factor is cost when government makes the decision how to store emergency goods. When making the decision, government must consider the different between economic profit and storing cost during cooperation. For this reason there has a specific condition during the cooperative game on storing supplies between government and enterprise, that is building a cost model to determine whether the supplies should be stored using cooperative storing pattern on the basis of the goods’ feature (main factors are storing cost and shelf-life in this case).
Assuming that
Because there has not only the storing cost, may also has other cost and profit during storing process. For instance, the expired cost of government and the profit that enterprise obtained from selling the goods. So here we distinguish storing cost and paying cost.
Supposing that that kind of goods is stored by enterprise, owing to it has liquidity, we can sell them timely before expiry, so here we do not consider the expiration. Same as description before, during shelf-life of the good, emergency event also has two status, occurred or not occurred. If occurred, enterprise can obtain the selling profit besides storing cost. Assuming
Owing to
There are three cases as follow:
(1) If
(2) If
(3) If
To sum up, provided government’s storing cost is more than enterprise’s, that is
Cooperative game depend on if enterprise and government both have profit, that is
(1) Building gaming model
Participant: government and enterprise; Strategy set: (cooperation, betrayal),
In (betray, betray), emergency goods are stored by government, the cost is storing cost
In (betray, cooperate), government and enterprise both store goods, government cost is
In (cooperate, cooperate), goods are stored by enterprise, enterprise cost is
The pay cost has the following relations.
①
On the condition of the government self storage,
②
Enterprise paying cost
(2) Analysis of game model
① If government betrays, enterprise cannot obtain profit from selling goods. If enterprise still cooperates, it will pay the storing cost
Enterprise | |||
---|---|---|---|
Betray | Cooperate | ||
Government | Betray | ||
Cooperate |
Similarly, when enterprise betrays, government cost
② In another case, with government’s cooperation,
At this point, there are two Nash equilibrium (betray, betray) and (cooperate, cooperate). If
It can be seen that, without rational cost sharing, they will not cooperate with each other, also without punitive measure, the agreement is unbinding. Due to these two points, it is instability that government and enterprise cooperate with each other on storing emergency goods. In order to establish a stable cooperation, there need some punitive measures to restrict the betrayal of each other, and an acceptable cost sharing as well.
Under rational conditions both of them wish to cooperate with each other to reduce their cost. Thus a binding cooperative agreement which has cost sharing and penalties must establish to ensure the stability of cooperation.
Suppose that Extra Payment that government pays to enterprise on cost sharing is
If one participant offer no co-operation, they will get punishment
If government betrays,
Same as before, if enterprise choose betrayal,
On Storing Emergency Supplies, establishing cost sharing and penalties will make the cooperation binding and stability between government and enterprise. In the cooperation, government will reduce cost
Taking earthquakes of Beijing as an example, earthquake emergency supplies can be divided into five categories: Life rescue tools, life-saving class of materials [
Enterprise | |||
---|---|---|---|
Betray | Cooperate | ||
Government | Betray | ||
Cooperate |
Parameters set
According to market research results to see the average price of 550 ml mineral water is ¥1.5. Retailers Cost is ¥1.1. Taking into account the government’s bulk purchasing, Government purchase price is ¥1.1. At this point the retailer’s profit margin
Profit margin =
Profit margin =
cost price of every mineral water is about ¥0.8, u = 0.8. The bottle can be recycled, the market price is about ¥0.1, u0 = 0.1. Shelf life is 1 year, t = 1. Mineral storage does not require technical expertise, so enterprise storage costs is the same as government storage costs.
The earthquakes that fewer than five ranges do not belong to the strong shock earthquake. It will not cause a lot of damage, so only consider earthquakes above 5. Beijing earthquakes above 5 are 13 times from AD 294 to 2013. Earthquake occurrence probability of Beijing is
The unit paying cost that government pays when storing that goods per unit time is: (UCT means a unit’s paying cost per unit time)
The unit paying cost that government pays when storing that goods per unit time is: (UCT means a unit’s paying cost per unit time)
The pay of government is more than the pay of enterprises in the storage of mineral water, so the government wants to establish partnerships with enterprises to reduce costs.
The government hopes to reduce costs through cooperation, so the government’s strategy is cooperation. But the corporate dominant strategy of enterprise is always betrayed. At this time, the government cost of cooperation is greater than the cost of betray, so the government chose not to cooperation. The final strategies (cooperate, cooperate) is Nash equilibrium.
But for the whole, the (betray, betray) cost is 1.032; the (cooperate, betray) cost is C; the (betray, cooperate) cost is 1.032 + 0.04 = 1.072; the (cooperate, cooperate) cost is 0.038. The minimum cost is (cooperate, cooperate), so the government hopes to establish cooperative relations.
In order to establish a stable partnerships, there need some punitive measures to restrict the betrayal of each other, and an acceptable cost sharing as well. The government pays to enterprise on cost sharing is
If one participant offers no co-operation, they will get punishment
Enterprise | |||
---|---|---|---|
Betray | Cooperate | ||
Government | Betray | (1.032, 0) | (1.032, 0.04) |
Cooperate | (0, 0.038) |
Enterprise | |||
---|---|---|---|
Betray | Cooperate | ||
Government | Betray | (1.032, 0) | |
Cooperate |
① If government betrays,
Same as before, if enterprises choose betrayal
Finally have a lower overall storage cost 0.038. The cost savings of per bottle of mineral water is 1.032 − 0.038 = 0.994 per year. In the cooperation, government will reduce cost
This work was supported by funding project for Research on emergency material reserve under the integration of Beijing-Tianjin-Hebei. University Under the grant number (15JGB071), and the project for Research on emergency material reserve under the integration of Beijing, Tianjin and Hebei (GJB20161004), the grants from High level scientific research project of Beijing Wuzi University.
Xiangguo Ma,Huihui Su,Liming Sui, (2016) The Cooperative Game Research of Emergency Material Reserve in Beijing City. Open Journal of Social Sciences,04,40-45. doi: 10.4236/jss.2016.47006