Lucia Sbragia

Competition and Cooperation in Natural Resources Exploitation: An Evolutionary Game Approach

Since the pioneering work of Gordon (1954), many bioeconomic models for the description of the commercial exploitation of common property renewable resources, such as fisheries, have stressed the problem known as ‘the tragedy of the commons’ (Hardin, 1968; see also Clark, 1990). This problem can be basically identified with a prisoner’s dilemma (see for example, Mesterton-Gibbons, 1993) because the presence of firms playing their dominant strategy which maximizes their own profit (disregarding competitors’ profits) leads to severe depletion of the resource, and consequently to low profits for all. On the other hand if firms cooperate to maximize total profits, then sustainable exploitation is more likely to obtain, which implies higher profits for all in the long run. However, unilateral defection, that is, the decision of an agent to harvest intensively while the other players harvest moderately in order to preserve resources, may lead to very high profits for the defector, and consequently to severe profit loss for the cooperators. This is the essence of the tragedy of the commons, often advanced in order to support the introduction of sanctions against defectors and/or restrictions to open access to common property resources. Dynamic models based on Cournot oligopoly games have been proposed by Levhari and Mirman (1982) and, more recently, by Szidarovszky and Okuguchi (1998, 2000), to describe commercial fishing. In these models, strategic interaction among players is related not only to the selling price, determined by the total harvesting quantity through a given demand function, but also to a cost externality, since resource stock reductions, as a consequence of players’ harvesting, lead to higher unitary fishing costs (see also Bischi and Kopel, 2002). In Szidarovszky and Okuguchi (1998) every player is assumed to decide his/her harvesting activity by solving a profit

Learning the demand function in a repeated Cournot oligopoly game

In this article, single product Cournot oligopolies are considered, where the demand and cost functions are linear. While cost functions are completely known by all firms, they only partially know the demand function, as they misspecify the slope. At any stage of the repeated oligopoly game firms update the slope of their subjective demand functions on the basis of the discrepancy they observe between the expected price, computed according to believed demand, and the price they actually observe. This adjustment process has a unique steady state, where any subjective demand function coincides with the true demand function. If such steady state is stable, then the true slope of the demand function can be learned by all oligopolists, even if they start from misspecified initial guesses. Sufficient conditions for the stability of the steady state are given for n-firms oligopolies. In the particular case of a duopoly, an exact delimitation of the stability region in the parameters’ space is given, and with the help of numerical simulations, the size and the shape of the basins of attraction is analysed, as well as the kinds of attracting sets that characterise the long-run dynamics of the learning process when the steady state is unstable.

Stability of international environmental agreements: an illustration with asymmetrical countries

In this paper we use a dynamic model to analyze the composition and stability of international environmental agreements (IEAs) in an asymmetrical framework. Signatory countries are assumed to optimize the total welfare of the international agreements members, while non-signatory countries optimize their own individual welfare, taking into account the dynamics of the pollution stock. Our model is calibrated using data from the MERGE climate policy assessment model. We briefly review two contrasting approaches to define stability of IEAs, and provide a numerical illustration in each case.

Dynamic Modeling in Renewable Resource Exploitation

This chapter reviews some fundamental models related to the exploitation of a renewable resource, an important topic when dealing with regional economics. The chapter starts by considering the growth models of an unexploited population and then introduces commercial harvesting. Still maintaining a dynamic perspective, an analysis of equilibrium situations is proposed for a natural resource under various market structures (monopoly, oligopoly and open access). The essential dynamic properties of these models are explained, as well as their main economic insights. Moreover, some key assumptions and tools of intertemporal optimal harvesting are recalled, thus providing an interesting application of the theory of optimal growth.