NATURAL RESOURCE EXPLOITATION UNDER COMMON PROPERTY RIGHTS

ABSTRACT. Renewable natural resources such as ground‐water, pastures and fisheries are often governed bycommon propertyrights in which members of a group jointlyown the exclusive use of the resource. We develop a formal model of a common propertycontract based on differential game theory and then use the model to examine (i) the incentives of individual users of the common resource; (ii) the resulting harvest and stock time paths; (iii) the local stabilityof the steady state; and (iv) the steadystate comparative statics. Moreover, we compare the qualitative properties of the common propertyregime to those generated under perfectlydefined private rights and open access. We show how common prop‐ertyownership of natural resources can generate rent and be a second‐best solution when private propertyrights are costly to establish.     

COEXISTENCE OR EXCLUSION IN A COMPETITIVE COMMON-POOL FISHERY: A REVISIONIST VIEW

ABSTRACT. One of the earliest applications of game theory to renewable resource modeling was Colin Clark's analysis, in 1980, of the competitive exploitation of a common-pool resource. His model described the dynamics of a single Gordon-Schaeffer fish stock, being harvested non-cooperatively by two or more independently managed fleets. He showed that aggressive harvesting by all fleets (a Nash equilibrium) would lead to stock drawdown to a level which would successively eliminate all of the less efficient harvesters. Furthermore, when the fleets were closely matched, the survivor(s) of this aggressive competition would be forced, by the threat of competitors' reentry, to hold the stock in its severely degraded state, and hence to harvest at only marginal profitability. This outcome has often been compared to the open access “tragedy of the commons.” and to the outcome of the well-known “prisoners' dilemma” game. In this article I will argue that, for closely matched fleets, a more likely outcome is that the fleets will tacitly agree, without overt communication, to focus simultaneously on a specific set of coordinated policies which will permit their continuing coexistence and profitable operation. This policy profile also forms a Nash equilibrium, one which is secured by the mutual ability of the fleets to quickly recognize and credibly punish any unilateral deviations from the anticipated actions. Thus the dynamic harvesting game more nearly resembles the repeated prisoners' dilemma than it does the classical single stage version.     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

Cost/risk balanced management of scarce resources using stochastic programming

We consider the situation when a scarce renewable resource should be periodically distributed between different users by a Resource Management Authority (RMA). The replenishment of this resource as well as users demand is subject to considerable uncertainty. We develop cost optimization and risk management models that can assist the RMA in its decision about striking the balance between the level of target delivery to the users and the level of risk that this delivery will not be met. These models are based on utilization and further development of the general methodology of stochastic programming for scenario optimization, taking into account appropriate risk management approaches. By a scenario optimization model we obtain a target barycentric value with respect to selected decision variables. A successive reoptimization of deterministic model for the worst case scenarios allows the reduction of the risk of negative consequences derived from unmet resources demand. Our reference case study is the distribution of scarce water resources. We show results of some numerical experiments in real physical systems.     

Groundwater management: Waiting for a drought*

In this article we present a stylized model for optimal management of an unconfined groundwater resource when the threat of drought exists. The drought is modeled as a stochastic event that hits at an uncertain date and two benchmark management policies are investigated: (a) A policy of optimal dynamic management ignoring the threat of drought; and (b) an economically optimal policy that accounts for the threat of a drought. We show that the optimal predrought steady‐state equilibrium stock size of groundwater under policy b is larger than that under policy (a) Furthermore, we show that an increase in the probability of a drought gives rise to two counteracting effects: One in the direction of a larger predrought steady‐state equilibrium stock size (a recovery effect) and one in the direction of a lower predrought steady‐state equilibrium stock (an extinction effect). We find that the recovery effect dominates the extinction effect. Recommendations for Resource Managers: We analyze two groundwater extraction policies that can be used when a threat of drought exists: (a) Dynamic optimal management ignoring the threat of drought; and (b) dynamic optimal management taking the threat of drought into account. We show that the predrought steady‐state equilibrium stock size of water should be larger under the policy (b) than under policy (a). This conclusion has three implications for resource managers:

• Current groundwater management should take future extraction possibilities into account.

• A resource manager ought to take the threat of drought into account in groundwater management.

• A buffer stock of water should be built‐up before the drought to be drawn upon during the event.

     

THE ECONOMICS OF DEFICIT IRRIGATION

Abstract Natural resource economists have paid great attention to irrigation water allocations among competing users. However, the intrauser allocation problem is greatly understudied. As irrigation becomes increasingly capital‐intensive, inefficient within‐field allocation and ill‐designed water‐conservation policy can bring considerable value loss to the water resource. We offer a comprehensive treatment of the economic problem of the intrauser allocation of a limited amount of irrigation water. A framework is provided for determining optimal irrigation intensity and extensity in both static and dynamic settings. An empirical application in West Texas cotton production demonstrates model implementation and offers new insights into the water‐saving potential of government‐sponsored cost‐share programs for promoting high‐efficiency irrigation adoption.     

Modeling of uplink power control for cognitive radio networks: Cooperative and noncooperative

In this paper, the uplink power control problem is modeled by considering both cooperative and noncooperative methods respectively to protect licensed users in cognitive radio networks. The cooperative power control optimization problem is modeled as a concave minimization problem. According to the properties of the power control optimization problem, an improved branch and bound algorithm is proposed. On the other hand, for the noncooperative power control case, a game theoretic model with the exponential pricing function is adopted to restrict the interference to the licensed users. Further, Nash equilibrium for the power control game is discussed. Finally, the performance of the proposed models is evaluated by computer simulation.     

Large scale nonlinear deterministic and stochastic optimization: Formulations involving simulation of subsurface contamination

Once subsurface water supplies become contaminated, designing cost-effective and reliable remediation schemes becomes a difficult task. The combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water. Both deterministic and stochastic programming problems have been formulated and solved. These tend to be large scale problems, owing to the simulation component which serves as a portion of the constraint set. The overall problem of combined groundwater process simulation and nonlinear optimization is discussed along with example problems. Because the contaminant transport simulation models give highly uncertain results, quantifying their uncertainty and incorporating reliability into the remediation design results in a class of large stochastic nonlinear problems. The reliability problem is beginning to be addressed, and some strategies and formulations involving chance constraints and Monte Carlo methods are presented.     

EFFICIENT MANAGEMENT OF GROUNDWATER QUALITY

This work develops a theoretical framework that considers the pollution transport in groundwater in an optimization of social benefits from a groundwater resource, and provides a spatial and temporal allocation of the use of contaminating inputs. A space dependent social cost function is constructed, taking into account factors such as the wells' locations and emitting firms' locations, in addition to profits from polluting activities. The social optimization is formulated using the pollution concentrations as state variables and the pollution transport as state dynamics. This optimization yields a spatially differentiated shadow price which leads to optimal policy which is nonuniform in general, and uniform only for special cases.     

ROBUST MATHEMATICAL PROGRAMMING FOR NATURAL RESOURCE MODELING UNDER PARAMETRIC UNCERTAINTY

Abstract Inaccurate specification of model coefficients can lead to false or distorted findings in modeling investigations of natural resource management. Hence, this paper outlines a decision framework for optimization problems in which only the bounded set of outcomes for uncertain parameters is known. These models can be solved with standard mathematical programming software and are no larger than their deterministic equivalent. The robust approach is contrasted against deterministic analysis and is demonstrated for two applications regarding the management of natural resources. Deterministic plans are infeasible in at least 40% of cases when parameters vary from their point estimates. Inclusion of robust constraints immunizes against this infeasibility, thereby removing errors arising from false certainty. Additionally, incorporation of bounded parameters in the objective function yields interval‐valued sets containing potential outcomes. However, this increase in the general relevance of model output introduces some degree of suboptimality as deterministic plans are buffered to proactively account for potential variability. The cost of robustness increases with the simulated spread of uncertain coefficients but may be reduced through accounting for the uncertainty aversion of decision makers.