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Research and Applications in Economics Volume 2, 2014
Game Analysis of Interregional Virtual Water Trade in China Feng Li1, Chunyue Wang*2 Bussiness School of Hohai University, Nanjing, Jiangsu, 211100, China
1
Bussiness School of Hohai University, Nanjing, Jiangsu, 211100, China
2
m13705182916@163.com; *2wcyhhu@163.com
1
Abstract Due to the diversity and complexity of our regional economy and water resources situation within our country, there are huge water resource differences among the regions. According to the idea of virtual water trade, regional trade and exchanges will accompany the flow of water. Therefore, this paper uses the game theory of the prisoner's dilemma model and divides the China's geographic area into two game parts, based on the condition of water resources and economic development situations. Then it integrates the water resources with the regional trade and builds the game model of virtual water trade. The game analysis shows that the idea of virtual water trade between regional trade and exchanges will help break the prisoner's dilemma and realize the purpose of coordinating the economic development and water resources flow reasonably, so as to maximize the overall efficiency of our country. Keywords Water Resource; Regional Trade; Virtual Water Trade
Introduction There are many water problems in China, serious shortage of per capita water resources and the serious imbalances in space distribution have brought negative influences on China's economic and social development. The concept of virtual water put forward by professor Allan England London University in 1993 provides a new perspective to better solve the water problems, especially in solving the imbalances in space distribution. The concept was firstly introduced by Cheng Guodong in 2003 and he pointed out that the virtual water is a new thinking towards China's water security. In addition, in March 2003, the BBS of the third world water BBS, which was held in Japan, expanded the concept of virtual water trade and pointed out that virtual water trade can be conducted between countries or between regions. It lays a foundation for studying our regional virtual water trade.
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Water Resources Situation and Game Division Uneven spatial and temporal distribution of water resources in our country are particularly serious and there also exists a serious imbalance between its water supply and demand. There are humid monsoon and monsoon region as well as humid regions and dry regions. Generally speaking, in the east of the dividing line, its rainfall is relatively more and the suitable climatic conditions are beneficial for the economic development. While in the west of the dividing line, it is dry and the climate there has some negative effects on its economic development. Therefore, our country has formed a situation of poor water resources in northwest while relative abundance of water in southeast. In addition, according to the economic development situation of our country, from the view point of development degree, the eastern region is more developed while the western region is relatively backward. Between the eastern region and western region, there are big differences in water resources and economy status .In the long run, the two regions will compete in obtaining as well as utilizing water resource under the premise of the regional economic development. However, the games of water resource between regions will have a two-way impact on our overall water security situation. Therefore, exploring the possibility of cooperation between the two parts and using the idea of virtual water trade to coordinate the imbalance in space distribution will have positive significances in promoting the sustainable development of the economy between east and west and ensuring the water resources better. The Correlation Functions Analysis of the Water Resources and Regional Economy According to characteristics of the water resources distribution and economic development of our country, we assume that there are only two parts in the game of
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water resource and economy development, the main bodies are eastern region and western region. When the two parts achieve the equilibrium of the game, the total social benefit sets as Z, E stands for the benefit of the eastern region; W stands for the benefit of the western region, h stands for the water resources factor, T stands for the economic and trade relations factor. Therefore, we can construct the following formulas to indicate their revenue function: Z=f(E,W)
(1);
E=φ(h,t)
(2);
W=ψ(h,t)
(3);
When the two bodies achieve the equilibrium both in water resource and economy, the total social benefit Z will be Z=f[;E=φ(h,t),W=ψ(h,t)]
(4);
Now we take the derivation towards the above formula Z, then we can get the following formulas: δZ/δh=δZ/δE·δE/δh+δZ/δW·δW/δh δZ/δt=δZ/δE·δE/δt+δZ/δW·δW/δt
(5); (6);
When the two regions achieve the optimal in the water game and economy development game, the social total benefit of Z will reach the largest, that is the above formulas derivation results of both (5)and (6) are 0.When the results are 0 of the two above formulas, we can get δZ/δh=δZ/δE·δE/δh+δZ/δW·δW/δh=0 δZ/δt=δZ/δE·δE/δt+δZ/δW·δW/δt=0
(7); (8);
Make a transposition towards (7) and (8) respectively, we finally get the following lists: δZ/δE·δE/δh= —δZ/δW·δW/δh δZ/δE·δE/δt= —δZ/δW·δW/δt
(9); (10);
Analyzing the (9) and (10),we can have the findings: Considering the water resource factor only, if we want to achieve the maximization of social overall benefit Z, the benefit that the two parts can get from water factor is a reverse relationship. When the eastern and western regions have economic and trade exchanges with each other, the western region will pay more attention to the maintenance of the regional water resources security under the premise of exchange due to its lack of water. The western region will do more on its water resources protection and water pollution governance. To some extent, these measures will make water environment improved in the whole society in our country, water environment improved and the eastern region will also get some benefits without too much efforts. Therefore, the benefit of eastern region is relatively positive while the western region gets a negative benefit due to its
investment. By analyzing the formula of (10), only considering the benefits that get from the trade exchanges between the two regions, the benefits that they can get are different. When they develop trade relations with each other, the west region will pay more attention to making use of the trade relation to promote its development due to its backward in economy status or some other economic factors. The western region will ignore the protection of water resources in order to put more investment in trade maintenance. Due to the lack of the protective measures in water resources, the gains from trade interaction is greater than its benefit lost in worse water condition. However, the eastern region will be adversely affected due to the deterioration of the water environment. Therefore, from a separate analysis of formula (9) and (10), in the aspect of water resources factor, the east and the west have an irreconcilable contradiction. The western region is relatively scarce in water resources, while its advantage industry concentrates in the first and second industries with large water consumption. Besides, the technology in developing and utilizing water resources is far behind the eastern region. Considering our country as a whole, the total benefit Z is based on the development of both the east and west regions, therefore, we need to have a comprehensive analysis towards (9) and (10).It is the differences in water resources and regional economy status that make the virtual water trade possible to work as "selective incentives to achieve the mutual benefit in the process of trade exchange, accompanying indirect flow of water, therefore, both parts will benefit from the virtual water trade. Through the above analysis of the correlation function, we can find that there are complementary and constrained relationships between the two parts. Therefore, we can construct the game model of virtual water trade as an associated game model, and then discuss how to break the prisoner's dilemma under the given assumptions of payment structure, so as to take effective measures to make better use of water resources, serving the interests of the society as a whole and ensuring the sustainable development of water resources. The Game Model of Virtual Water Trade between Regions According to the idea of virtual water trade, an associated game mode is constructed as follows: In the frame of the game, the capital letters refers to east region’s payment, represented by E, while the
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Research and Applications in Economics Volume 2, 2014
lowercase letters refers to west region’s payment, represented by W. And the former refers to the payment structure of water resources, while the latter refers to the payment structure of regional economic payment. Both of them have two strategies of cooperation and noncooperation. Different strategy combinations will form the following virtual water trade model, as shown in Table 1. TABLE 1 GAME OF VIRTUAL WATER TRADE Strategies E
cooperation noncooperation
cooperation (A+E, a+e) (C+G, c+g)
W noncooperation (B+F, b+f) ( D+H, d+h)
In the field of water resources, the eastern region is easy to ignore the protection of water resources due to its relative abundance in water resources, therefore, it is likely to take the noncooperation in water game. While the western region is likely to pay more attention to water resources cooperation in order to protect and rationally develop and utilize the limited water resources due to the relative lack of water resources. So in the water game, the payment structure is: E: C > A > D > B, W: A > B > D > C. According to the line drawing comparison method, the water game falls into the "prisoner's dilemma". In regional trade game, although in recent years the market barriers and local protectionism have been reduced, the conditions of this decreasing trend can bring benefits for both sides. However, in reality, due to the influence of opportunism, there are still many hidden and increasingly diverse market barriers and local protectionism. Thus, when one area chooses an open policy while the other chooses a protectionism policy, the latter one will benefit more due to its protectionism policy for the time being. So when one chooses cooperation, it will open markets to the counter and allow the resources flow freely, then the counter will choose non-cooperative strategies to protect their own market to get more benefits. As for E, due to its relatively abundance in water, it will focus more on trade exchanges between them, creating a good economic development conditions and market environment, so it will take the cooperation strategy in order to ensure its market advantage. So the payment structure is: E：E> G >H >F，W：f> e >h> g. The trade exchanges game falls into the "prisoner's dilemma". By accumulating the above two payment structures and comparing the payment in the virtual water trade game, the virtual water trade game payment result is B + F < < D + H, c+g< d +h, and A + E &c + g, A + E & B + F
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are uncertain. So under the payment structure, virtual water trade game can form two results: one is certain, without the contrast the A +E &C+G，a+e &b+f ,using the marking method and get the “non-cooperation – non-cooperation” result. The other result is uncertain. It is the existence of uncertainty that makes the virtual water trade a possibility to get out of the prisoner's dilemma by some improvements. Now we can move to the two inequalities as E-G C-A,a-b f-e, through such arrangement we can conclude that one way of breaking the prisoner's dilemma is to take the benefits gained in trade game as a kind of incentive measures to perfect the water situation in water game. While, according to the law of the existence of Nash equilibrium, there is an odd number of Nash equilibrium, which is a mixed strategy Nash equilibrium. Each party will choose their own strategy at a certain probability. Suppose the possibility of taking cooperation strategy in international trade for E is α and the possibility of taking cooperation strategy in water resources game is β. Assuming that E chooses cooperation strategy firstly and the other one gets the same benefits between choosing cooperation strategy and noncooperation strategy. Then we get the equations: (a+e)α+(c+g)(1-α)=(b+f)α+(d+h)(1-α), that is α=d-c+h-g/d-c+h-g+a-b+d-f. On the contrary, W chooses cooperation strategy, then we get (A+E)β+(B+F)(1-β)= (C+G)β+(D+H)(1-β), that is β=D-B+H-F/D-B+H-F+A-C+ E-G. While the values of α and β depend on the payment structure and the size of the benefits they get in the game. The key to achieving the cooperation between the two sides is that the benefit gained from trade exchanges can become a kind of incentive to promote the benefit that can be gained from the water cooperation. When the two regions choose cooperation strategy in trade exchanges, then the benefits brought by the trade cooperation game will affect the strategy in water game. That is to say, on the one hand, the product can be regarded as exchange carrier to realize the flow of water indirectly in order to reduce the costs and risks of scheduling the entity water resources; on the other hand, both parts can get economic gains from their development of trade relations, so they can put more investment to raise the technology of water resources development and utilization, improving the water situations. If the two parts choose noncooperation strategy in the water game, not only will it result in the deterioration of regional water resources, but also lead to the deterioration of the overall water environment
Research and Applications in Economics Volume 2, 2014
as a whole. This situation needs to pay a certain cost to take measures to protect the water, which will affect the payment proportion of its total revenue for the two parts. Therefore, it will increase some cost for water resources while less emphasis on trade relations due to its relatively fixed overall benefits. In addition, this kind of less emphasis will increase the possibility of taking noncooperation strategy, harmful to reach the pareto optimality. Conclusions From the above analysis, we can find that the virtual water trade game is equivalent to making a promise or a threat towards the counter. If one takes non-cooperative strategy in one field, it will incur punishment in the field of another. Therefore, when one chooses cooperation strategy at the very beginning, because of its interaction effect between the two fields, no one will deviate from the equilibrium so that it can make it possible to get out of the prisoner's dilemma. According to the distribution of water resources and economic development situation in our country, the western region is relatively lacking water resources and its economic development status is relatively backward. The eastern region is just the opposite. According to the connotation of the virtual water trade, on the one hand, the western region can buy the products from those places with rich water resource in order to make up for the deficiency of scheduling entity water and its difficulty, in addition, it won't produce too much negative ecological impact; on the other hand, the western region should try to minimize planting the crops with high water consumption, instead, it should plant crops with relatively less water consumption. However, we must pay attention to that if we cannot plant the low water consumption crops to replace the high water consumption crops, just apply the application of the concept of virtual water trade mechanically, it will have a negative impact on
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agricultural structure as well as its economy structure. Therefore, the idea of virtual water trade will lose its practical significance to improve the water situation and economy. Considering this, the regional virtual water trade not only requires the east region to increase the exchanging of goods and to promote the flow of water resources indirectly, but also to promote the development of western region economy with developing the mutual-trade relations by providing more supports with technology, social resources. Therefore, the western regionâ&#x20AC;&#x2122;s technology and situation will be improved in water development and its utilization, therefore benefit the whole society. REFERENCES
ALLAN J A. Fortunately there are substitutes for water otherwise our hydro- political futures will be impossible [C]//.ODA. Priorities for Water Resources Allocation and Management, London:ODA, 1993:13-26. Chunyue Wang, Feng Li.[J]Journal of economic water resources, 31(2013):23-26. Gaoming Wu, Gaosheng Wu, Jifeng Xiong etc.. Commercial times 11(2011):49. Jiao Zhou .A Research on the Regional Virtual Water Trade and Its Influencing Factors in China [J] ECONOMIC RESEARCH GUIDE.36 (2010):72-74. Jinming Wang, Xin Hu. Journal of finance and economics studies, 12(2005):93. Shiyu Xie. Game Theory. [M]. 3. Shanghai: Fudan university press, 2006. Feng Li (1970 - ), male (Han Nationality), LianYungang City, Jiangsu Province. Associate professor, Ph.D., engaged in international trade research. Chunyue Wang (1989 - ), female, (Han Nationality), Tang Shan City, Hebei Province. Master graduate student, majoring in international trade.
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