Stabilizing management of fluctuating resources

We consider a resource management problem in which the management objective is to minimize fluctuations in resource stocks. Stabilizing management policies constitute the designing of memoryless state feedback control strategies for a discrete time resource model which contains unknown but bounded fluctuations. We also show that the problem of maximizing sustainable yield in an uncertain fishery can be considered as the problem of stabilizing of the stock level.The paper corresponds to an invited talk at the 14th Symposium on Operations Research, Ulm, September 6–8, 1989.The support by Yrjö Jahnsson Foundation is gratefully acknowledged.This work was supported by NSF and AFOSR under grant ECS 8602524.     

OPTIMAL RECOVERY OF A SHARED RESOURCE STOCK: A DIFFERENTIAL GAME MODEL WITH EFFICIENT MEMORY EQUILIBRIA

We consider an optimal two-country management of depleted transboundary renewable resources. The management problem is modelled as a differential game, in which memory strategies are used. The countries negotiate an agreement among Pareto efficient harvesting programs. They monitor the evolution of the agreement, and they memorize deviations from the agreement in the past. If the agreement is observed by the countries, they continue cooperation. If one of the countries breaches the contract, then both countries continue in a noncooperative management mode for the rest of the game. This noncooperative option is called a threat policy. The credibility of the threats is guaranteed by their equilibrium property. Transfer or side payments are studied as a particular cooperative management program. Transfer payments allow one country to buy out the other from the fishery for the purpose of eliminating the inefficiency caused by the joint access to the resources. It is shown that efficient equilibria can be reached in a class of resource management games, which allow the use of memory strategies. In particular, continuous time transfer payments (e.g., a share of the harvest) should be used instead of a once-and-for-all transfer payment.     

BOOK REVIEW

An Introduction to Game-Theoretic Modeling, Michael Mesterson-Gibbons, Addison-Wesley, Redwood City, 1992, 237 pp.     

Energy‐dispersive diffraction with synchrotron radiation and a germanium detector

The response of an intrinsic Ge detector in energy‐dispersive diffraction measurements with synchrotron radiation is studied with model calculations and diffraction from perfect Si single‐crystal samples. The high intensity and time‐structure of the synchrotron radiation beam leads to pile‐up of the output pulses, and the energy distribution of the pile‐up pulses is characteristic of the fill pattern of the storage ring. The pile‐up distribution has a single peak and long tail when the interval of the radiation bunches is small, as in the uniform fill pattern, but there are many pile‐up peaks when the bunch distance is a sizable fraction of the length of the shaping amplifier output pulse. A model for the detecting chain response is used to resolve the diffraction spectrum from a perfect Si crystal wafer in the symmetrical Laue case. In the 16‐bunch fill pattern of the ESRF storage ring the spectrum includes a large number of `extra reflections' owing to pile‐up, and the model parameters are refined by a fit to the observed energy spectrum. The model is used to correct for the effects of pile‐up in a measurement with the 1/3 fill pattern of the storage ring. Si reflections (2h,2h,0) are resolved up to h = 7. The pile‐up corrections are very large, but a perfect agreement with the integrated intensities calculated from dynamical diffraction theory is achieved after the corrections. The result also demonstrates the convergence of kinematical and dynamical theories at the limit where the extinction length is much larger than the effective thickness of the perfect crystal. The model is applied to powder diffraction using different fill patterns in simulations of the diffraction pattern, and it is demonstrated that the regularly spaced pile‐up peaks might be misinterpreted to arise from superlattices or phase transitions. The use of energy‐dispersive diffraction in strain mapping in polycrystalline materials is discussed, and it is shown that low count rates but still good statistical accuracy are needed for reliable results.     

The management of high seas fisheries

The intergovernmental United Nations Conference on Highly Migratory and Straddling Stocks, initiated in 1993 and finished in 1995, addressed the conservation and management of fishery resources located both within the coastal state 200 mile Exclusive Economic Zone (EEZ) and the adjacent high seas. These types of marine resources continue to be a source for international conflicts and debates. The original United Nations Law of the Sea of 1982 failed to address transboundary fisheries in a proper way. In particular, the agreement did not recognize the emergence of the complicated straddling stock issue. In the new United Nations Law of the Sea agreement of 1995, a consensus was reached that the management of the straddling and highly migratory fish stocks should be carried out through regional fisheries management organizations. We present a review of the straddling stock issues in the international agreement emerging from the negotiations within the United Nations. The review is contrasted with and clarified by game theoretic analyses. We also discuss one international fishery exemplifying the case, the Norwegian springspawning herring. The main conclusion is that the local problems, faced during the stage of setting up regional fisheries organizations for the management of straddling and highly migratory fish stocks, are expected to be much more complicated and difficult to solve as compared to the cases of shared fish stocks. In the current paper, we present two reasons for this increased complexity. The first is the larger number of players as compared to the case of shared fish stocks and the second is the possibility of new members entering the regional fisheries organizations.     

SHARING THE BENEFITS OF COOPERATION IN HIGH SEAS FISHERIES: A CHARACTERISTIC FUNCTION GAME APPROACH

In the current paper we examine a game-theoretic setting in which three countries have established a regional organization for the conservation and management of straddling and highly migratory fish stocks. A characteristic function game approach is applied to describe the sharing of the surplus benefits from cooperation. We demonstrate that the nucleolus and the Shapley value give more of the benefits to the coalition with substantial bargaining power than does the Nash bargaining scheme. We also compare the results that are obtained by using the nucleolus and the Shapley value as solution concepts. The outcomes from these solution concepts depend on the relative efficiency of the most efficient coalition. Furthermore, the question of fair sharing of the benefits is considered in the context of straddling stocks.     

Stabilizing employment in a fluctuating resource economy

We consider a resource management problem in which the management objective is to minimize fluctuations in resource economics. Stabilizing management policies consist of memoryless state feedback control strategies for a class of discrete-time resource models which contain unknown but bounded fluctuations. The underlying theory is based on conditions developed for Lyapunov-type stability of sets. The design of the stabilizing policies is illustrated by a simulation example from resource economics. Specifically, employment of fishermen is stabilized by using a subsidizing and taxing policy in an open-access common-property fishery in which the value of the resource and the resource level fluctuate, and where entry and exit dynamics are determined by fluctuating revenues obtained from the fishery.This work was supported by NSF and AFOSR under Grant No. ECS-86-02524.The support by the Yrjö Jahnsson Foundation is greatly acknowledged.     

Water and ice in contact with octadecyl-trichlorosilane functionalized surfaces: a high resolution x-ray reflectivity study

We present a high energy x-ray reflectivity study of the density profiles of water and ice at hydrophobic and hydrophilic substrates. At the hydrophobic water/octadecyl-trichlorosilane (water-OTS) interface, we find clear evidence for a thin density depletion layer with an integrated density deficit corresponding to approximately 40% of a monolayer of water molecules. We discuss the experimental results in terms of a simple model of hydrophobic/hydrophilic solid-liquid interfaces. Our results also exclude the presence of nanobubbles. A detailed study of possible radiation damage induced by the intense x-ray beam at the dry OTS surface and at the ice-OTS, as well as at water-OTS interfaces, discloses that noticeable damage is only induced at the water-OTS interface, and thus points to the dominant role of highly mobile radicals formed in bulk water close to the interface.