Competition and cooperation in commercial fishing with adaptive expectations

• Autores: G.I. Bischi, M. Kopel, F. Szidarovszky
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese , Francisco Ramón Fernández García , 2002, ISBN 84-472-0733-1, pág. 22
• Idioma: inglés
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• Resumen

  • 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, stressed the problem known as �the tragedy of the commons� (Hardin, 1968, see also Clark, 1990). This problem can be basically identified with a typical prisoner�s dilemma, as �aggressive harvesting� strategies of all the players lead to severe depletion of the resource and, as a consequence, to lower profits for all the competitors, whereas an agreement on a sustainable exploitation leads to higher profits for all (see e.g. Mesterton- Gibbons, 1993).

    Cournot oligopoly games are now a common tool in the description of fishery management, see e.g. Levhari and Mirman, 1982, Okuguchi, 1998, Szidarovszki and Okuguchi, 1998. In these games, the harvesting decisions of profit maximizing agents are characterized by strategic interactions related not only to the influence of total supply on the market prices, but also to cost externalities due to the dependence of harvesting cost on available fish stock, whose evolution is governed by biological laws as well as harvesting activity.

    Following Szidarovszky and Okuguchi (1998, 2000) we propose an oligopoly model where n players (that may represent n different countries fishing in the same sea) sell the harvested fish in n markets, i.e. each player sells in his home market and in (n - 1) foreign markets. Moreover, we assume that agents do not have perfect knowledge of the fish stock. This differs from the current approach in resource economics literature, where it is usually assumed that fishermen, when they decide their optimal harvesting, have precise knowledge of the environment. Instead, we guess that in the real world this will hardly be the case and, more realistically, these economic agents have access to a collection of past data about the harvested amounts of fish and some other indicators of the size of the fish population, from which they try to derive an estimate of the future fish stock. With every new piece of information, their estimate will be updated and used to determine the future harvesting activities.

    In our model we assume a simple learning rule called adaptive expectations : at the end of each period, using past observations about harvests and fish stock, fishermen are able to derive the exact stock of the resource, and then they make a prediction about the future fish stock by forming a weighted average between the current fish stock and their previous prediction (see Bischi and Kopel, 2002).

    We consider two different models: in the first one we assume that each player maximizes his own expected profit, as in a typical non cooperative oligopolistic competition; in the second one we assume that the players form a cooperative venture, where each player determines its harvesting activity such that the joint profit of all players is maximized. We compare the Nash equilibria obtained in these two cases, and we examine their stability properties under the assumption that the game is played repeatedly by boundedly rational players (due to the limited knowledge of the fish stock and the related adaptive learning process).

    In both the models we consider the effect of a new player which enters the game.

    The results obtained confirm that cooperation does not only lead to higher conservation, but the larger stock eventually leads also to a higher total harvest (due to increased growth of the resource) like in the above mentioned prisoner�s dilemma. However, unexpected results are obtained about the global dynamic properties. In fact, from the point of view of the mathematical structure of the dynamic model, when we replace the assumption of fishermen with perfect foresight about the next period fish stock by the weaker assumption of adaptive expectations, a one-dimensional dynamical system is replaced by a two-dimensional one, and this implies that remarkable differences may arise concerning the role of the initial conditions, due to more complex structures of the basins of attraction and to the occurrence of global bifurcations which change their topological properties. The results obtained are characterized by complex dynamic patterns and bifurcation phenomena, because the interactions of human economic decision making with ecological dynamics are highly non linear (on this point see also Rosser, 2001). Moreover, in our model the complexity of the basins of attraction is related to the fact that the dynamic evolution of the game is obtained through the repeated application of a twodimensional noninvertible map (see Mira et al, 1996, Puu, 2000, Agliari et al., 2002).

    The main problems addressed in our work are:

    (i) the influence of the market structure and the role of strategic effects on the oligopoly evolution, both in the non cooperative and in the cooperative case;

    (ii) the role of harvesting costs in the problem of extinction or conservation of the resource;

    (iii) the influence of errors in predicting the fish stock when determining the harvesting activities.