The core of an economy with a common pool resource: A partition function form approach

In this paper we consider a model of an economy with a common pool resource. Under decreasing returns to scale, it is well-known that no Nash equilibrium attains Pareto efficiency. We examine whether it is possible to achieve Pareto efficiency and avoid the tragedy of the commons through cooperation among players. For that purpose, we use the notion of a game in partition function form. Whether or not the core exists depends crucially on the expectations of each coalition regarding the coalition formation of the outsiders. If each coalition has pessimistic expectations, then the core always exists, while if it has optimistic expectations, the core may be empty. Received: January 1998/Final version: November 1998  

Playing with models and optimization to overcome the tragedy of the commons in groundwater

Groundwater is the natural resource most extracted in the world. It supplies 50% of the total potable water requirements, 40% of the industry take, and 20% of agriculture groundwater is a strategic resource for every country. That common‐pool resources are highly susceptible to lead to a tragedy of the commons is a well‐known fact. We claim that a combination of groundwater modeling, optimization, and a game theoretical analysis may in fact avoid the tragedy. A groundwater model in MODFLOW from Zamora aquifer in Mexico was used as input of a basic but instructive, optimization problem: extract the greatest possible volume of water, but at the same time minimizing the drawdown and drawdown velocity. The solutions of the optimization problem were used to construct the payoffs of a hypothetical game among the aquifer users, the resource's administrator, and a resource protector entity. We show that the success of the optimal management program depends heavily on the information that the users have about the resource. Therefore, better decision‐making processes are a consequence of sustainability literacy. Particularly, water literacy could lead to the usage of water considering it as a part of an ecosystem and not only as a natural resource. Additionally, a new non‐classical equation for underground flow was derived, that may be specially important to understand and predict the groundwater flow in highly heterogeneous conditions as in karstic aquifers or fractured media. © 2013 Wiley Periodicals, Inc. Complexity 19: 9–21, 2013  

区域品牌过度使用与投入不足的风险防范及规避

区域品牌作为一种公共物品，同其他公共物品一样具有非竞争性和非排他性的性质，现有理论和研究表明，这种性质决定了区域品牌具有“公共地悲剧”风险，这种风险表现为过度使用.但通过构建博弈模型，对比模型的纳什均衡解和帕累托最优解，可以发现区域品牌化过程中的“公共地悲剧”风险不仅表现为过度使用，也表现为投入不足，即具有双重性.并通过对这种双重性的内在机理进行分析，提出有效防范和规避“公共地悲剧”风险的政策建议.  

Commons dilemma and the “Tragedy of the Commons”

There are a lot of studies on commons dilemma. But few studies succeed to formulate it adequately. Moreover, although there are some situations where the dilemma does not occur, these studies focuses only the case that the dilemma does occur. In the present paper, we formulate the commons dilemma as an N‐person game and examine what situations our formulation represents. We show that there are six regions with respect to the value decrement induced by one additional animal and that commons dilemma does not occur in some of these regions.