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The monograph gives a theoretical explanation of observed cooperative behavior in common pool situations. The incentives for cooperative decision making are investigated by means of a cooperative game theoretical framework. In a first step core existence results are worked out. Whereas general core existence results provide us with an answer for mutual cooperation, nothing can be said how strong these incentives and how stable these cooperative agreements are. To clarify these questions the convexity property for common pool TU-games in scrutinized in a second step. It is proved that the convexity property holds for a large subclass of symmetrical as well as asymmetrical cooperative common pool games. Core existence and the convexity results provide us with a theoretical explanation to bridge the gap between the observation in field studies for cooperation and the noncooperative prediction that the common pool resource will be overused and perhaps endangered.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Common Pool Resources

Abstract
This chapter discusses several attributes of a common pool resource and the impact on the resource by the virtue of selfish individual decision making. Especially, we review the usual theoretical prediction that the commons are endangered or perhaps destroyed through overuse. Since this prediction is based on the assumption that individuals involved to jointly manage a common property have not the opportunity to communicate with each other, we confront this prediction with empirical evidence from field studies and experiments that the resource is used more efficiently if allowance was made for communication at moderate costs among the individuals. Nevertheless, we also present an empirical study where individual firms have failed to enhance the efficiency of a common property although the firms had the opportunity to communicate with each other. Although Cooperation is not likely for all common properties with face-to-face communication between egoists, it seems on the basis of empirical studies that Cooperation is an essential feature to exploit a natural exhaustible resource. Since the appearance of the articles of Gordon (1954) and Hardin (1968) an extensive theoretical literature has been published analyzing exhaustible resource under various economic aspects but Cooperation by direct agreements among individuals who exploit a common property was almost completely neglected in the economic literature. It seems to us that according to the traditional noncooperative view it is a commonly held belief among theorists that the exhaustible resource will be destroyed by individuals following their own inter-ests and therefore it was not within the realms of this methodological approach that selfish individuals will cooperate among themselves to extract an exhaustible natural resource.
Holger I. Meinhardt

Chapter 2. A Dynamic Resource Management Problem

Abstract
In this chapter we consider a resource management problem for an incomplete renewable resource like a flshery for the centralized as well as the decentralized case. In the context of the decentralized case we study a closed access fishery to incorporate the impact of Strategie interaction on the stock level of fish. This chapter is devoted to illustrate several aspects of an incomplete renewable common property from which we will abstract in the sequel of our analysis by considering in the chapters 4 to 6 a common property that is completely renewable. Important aspects we cannot treat in the context of a completely renewable resource are the issues whether the pursuing of Nash strategies can destroy the common property or under which conditions the resource will be depleted completely by the appropriators. Another major aspect we cannot treat in our static framework is how a change of the underlying economical strueture affects the stock level of the resource, that is, changes in the market, produetion or cost strueture can change fundamentally the optimal exploitation policy by appropriators in the long run.
Holger I. Meinhardt

Chapter 3. Cooperative Game Theory

Abstract
In preparation for the subsequent chapters we provide the reader in this chapter with some game properties and solution concepts from cooperative game theory with transferable Utility. We conflne ourself in discussing cooperative game theory to the part where the cooperative Output of a coalition can be measured by a numeraire good like money and therefore can be transfered among the players via side-payments. The purpose of this chapter is not to give a comprehensive survey of cooperative game theory. We will just discuss these parts which are valuable to understand the remaining parts of the monograph where we rely to a large extent on cooperative game theory to analyze the incentives for cooperative decision making in common pool situations. In our investigation of a common pool environment we are interested in the feasible gains which are realizable through mutual Cooperation and to the issue whether individuals are better off through Cooperation than acting alone. The formal aspect for Coming up with an answer will be captured through cooperative game theory.
Holger I. Meinhardt

Chapter 4. The Common Pool Game

Abstract
In this chapter, we will construct from a normal form game which describes a common pool Situation with constant marginal costs and Joint production three different types of arguing in the bargaining process. We assume that subjects can communicate with each other and therefore they can reach agreements which can be binding or not binding. For cases in which we assume that subjects involved communicate with each other to coordinate their strategies we must consider which arguments can be presented in the bargaining process. As a consequence, we have to rely on cooperative solution concepts. A cooperative solution concept of considerable interest is the core which gives us knowledge of the incentives for cooperative behavior. Recall that the core describes all allocation vectors that are coalitional rational and Paretoefficient. No coalition can do better by blocking an allocation that belongs to the core. This can also be understood that core allocation can be stabilized by pronouncing threats and counter threats. Moreover, for a nonempty core there exist incentives for cooperative behavior while exhausting the gains that are feasible through mutual Cooperation. Therefore, by working out general core existence results for cooperative common pool TU-games one can give a theoretical explanation for mutual Cooperation in many common pool situations as have been reported by Ostrom et al. (1994) in contrast to the noncooperative prediction reported by Hardin (1968).
Holger I. Meinhardt

Chapter 5. Convexity of Symmetrical TU-CPR Games

Abstract
Having explicitly worked out general α- and β-core existence results in Chapter 4 the purpose of this chapter is devoted to the study of the convexity property in symmetrical TU-CPR games. As we have already mentioned whenever the core is nonempty, we know that there exists an incentive for mutual Cooperation in the grand coalition in order to realize the gains that are feasible through Cooperation. Core existence results can only explain that incentives for Cooperation exist but neither how strong these incentives are nor whether these incentives are also stable against small perturbation in the underlying economic structure. Especially, the last point is important in common pool situations where we observe subjects carrying on with Cooperation after a small exogenous shock. And indeed, Ostrom (1990) has reported Cooperation in more extreme events. For instance, one can observe despite a heavy dryness that Cooperation does not break down by using jointly a ground-water basin for irrigation purpose (cf. (Ostrom, 1990, pp. 69–82)). More formally spoken, can we expect that the core remains nonempty after small perturbations? This is in general true for convex games, since it is well known that the core of convex transferable Utility games is always nonempty and, further, that the core is relatively large with respect to the imputation set (Shapley (1971)). Therefore we can in general expect that the core remains nonempty against small perturbations in the parameter Space. Due to the generically large size of the core it is pertinent to establish convexity in an economical context.
Holger I. Meinhardt

Chapter 6. Convexity of Asymmetrical TU-CPR Games

Abstract
As we have shown by Theorem 5.1 on page 107 in Chapter 5 a symmetrical CPR-game with constant marginal costs and a strictly concave Joint production function is convex. We have mentioned that convexity can be interpreted (a) as an incentive for large-scale Cooperation and (b) that the core for a convex game remains nonempty given small perturbation in the parameter space. Large-scale Cooperation and core stability are indications (a) for strong incentives for Cooperation into the grand coalition and (b) that Cooperation does not break down after an exogenous shock has occurred. But now the crucial question arises whether the convexity property can be extended to the case of asymmetrical endowments, more general concave production functions and more arbitrary cost functions. Otherwise, our interpretation that we can expect for common pool situations strong incentives for Cooperation into the grand coalition and, in addition, stability of Cooperation despite observed shocks, would be too strong. In such a case our interpretation would be only true for a small subclass of TU-CPR games. In other words, convexity of TU-CPR games would be a seldom event; and therefore we could not explain mutual Cooperation and stability of Cooperation for a large dass of common pool problems. Thus, we would have to search for another explanation why the phenomena of Cooperation in contrast to the noncooperative predictions can be observed in so many Situation where appropriators have access to a resource which can be jointly managed. Fortunately, we can extend the convexity result to a large subclass of common pool situations and the Interpretation above is applicable. Moreover, in cases where convexity fails to hold we can derive a weaker convexity result, the so-called average-convexity. For the study of average-convexity in common pool games we refer the reader to Driessen and Meinhardt (2001).
Holger I. Meinhardt

Chapter 7. Concluding Remarks and Outlook on Future Research

Abstract
In this monograph, the aim was to give an account of understanding the incentives for collective decision making in common pool problems where it is allowed for subjects to communicate with each other. We have argued that noncooperative game theory cannot provide us with a convincing explanation for observed cooperative behavior in field studies or experiments, since the branch of noncooperative game theory cannot incorporate in füll extent face-to-face communication among the subjects. Due to this methodological limitation of noncooperative game theory, we have applied a cooperative game theoretical analysis in order to give a theoretical clarification for observed mutual Cooperation in common properties. For doing so, we have studied game properties for different cooperative game theoretical representations of a common pool Situation. First, we have looked for core existence results especially, we have shown core existence for α - and β-common-pool TU games. These core existence results have provided us with a first indication concerning the incentives for collective decision making in common pool situations. In a second step we have derived the convexity result for a large dass of cooperative common pool games. This result can be interpreted as an incentive for mutual Cooperation into the grand coalition. Stability of Cooperation arises due to the fact that the core for convex games is quiet large so that the core still exists after small perturbations into the parameter space, that is, the incentives for mutual Cooperation do not vanish when an exogenous shock occurs. According to these results we can explain cooperation and stability of cooperation in common pooi problems in contrast to noncooperative game theory. These results provide us with a descriptive explanation that rational subjects can extricate by themselves from the common dilemma situation and they use the CPR with care.
Holger I. Meinhardt

Appendix A. An Overview of Bifurcation Theory

Abstract
In this appendix we want to provide a brief introduction and discussion of the concepts of dynamical systems and bifurcation theory which has been used in the preceding sections. We refer the reader interested in a more thorough discussion of the mathematical results of dynamical systems and bifurcation theory to the books of Wiggins (1990) and Kuznetsov (1995). A discussion intended to more economically motivated problems of dynamical systems and chaos can be found in Medio (1992) or Day (1994). It is noteworthy here that chaos is only possible in the nonautonomous case; that is, the dynamical system depends explicity on time; but not for the autonomous case where time does not enter directly in the dynamical system (cf. Wiggins (1990)). Since both models we have considered in the preceding sections are autonomous they cannot reveal any chaos. However, as the reader has seen, the dynamical systems we have derived reveal some bifurcations.
Holger I. Meinhardt

Backmatter

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