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Expectation-Stock Dynamics in Multi-Agent Fisheries

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  • Gian-Italo Bischi
  • Michael Kopel
  • Ferenc Szidarovszky

Abstract

In this paper we consider a game-theoretic dynamic model describing the exploitation of a renewable resource. Our model is based on a Cournot oligopoly game where n profit-maximizing players harvest fish and sell their catch on m markets. We assume that the players do not know the law governing the reproduction of the resource. Instead they use an adaptive updating scheme to forecast the future fish stock. We analyze the resulting dynamical system which describes how the fish population and the forecasts (expectations) of the players evolve over time. We provide results on the existence and local stability of steady states. We consider the set of initial conditions which give non-negative trajectories converging to an equilibrium and illustrate how this set can be characterized. We show how such sets may change as some structural parameters of our model are varied and how these changes can be explained. This paper extends existing results in the literature by showing that they also hold in our two-dimensional framework. Moreover, by using analytical and numerical methods, we provide some new results on global dynamics which show that such sets of initial conditions can have complicated topological structures, a situation which may be particularly troublesome for policymakers. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Gian-Italo Bischi & Michael Kopel & Ferenc Szidarovszky, 2005. "Expectation-Stock Dynamics in Multi-Agent Fisheries," Annals of Operations Research, Springer, vol. 137(1), pages 299-329, July.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:299-329:10.1007/s10479-005-2262-7
    DOI: 10.1007/s10479-005-2262-7
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    References listed on IDEAS

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    1. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    2. Marc Nerlove, 1958. "Adaptive Expectations and Cobweb Phenomena," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 72(2), pages 227-240.
    3. Bischi, G. -I. & Dawid, H. & Kopel, M., 2003. "Spillover effects and the evolution of firm clusters," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 47-75, January.
    4. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
    5. Clark, Colin W. & Kirkwood, Geoffrey P., 1986. "On uncertain renewable resource stocks: Optimal harvest policies and the value of stock surveys," Journal of Environmental Economics and Management, Elsevier, vol. 13(3), pages 235-244, September.
    6. Bischi, G.-I. & Dawid, H. & Kopel, M., 2003. "Gaining the competitive edge using internal and external spillovers: a dynamic analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2171-2193.
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    Cited by:

    1. N. Quérou & M. Tidball, 2014. "Consistent conjectures in a dynamic model of non-renewable resource management," Annals of Operations Research, Springer, vol. 220(1), pages 159-180, September.
    2. Bischi, Gian Italo & Kopel, Michael & Szidarovszky, Ferenc, 2014. "A note on the paper ‘On dynamical multi-team Cournot game in exploitation of a renewable resource’," Chaos, Solitons & Fractals, Elsevier, vol. 62, pages 34-35.
    3. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    4. Gu, En-Guo, 2009. "Complex dynamics analysis on fish stock harvested by two players with heterogeneous rationality," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 964-974.
    5. Bischi, Gian Italo & Lamantia, Fabio, 2007. "Harvesting dynamics in protected and unprotected areas," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 348-370, March.
    6. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    7. Quérou, N. & Tidball, M., 2010. "Incomplete information, learning, and natural resource management," European Journal of Operational Research, Elsevier, vol. 204(3), pages 630-638, August.
    8. Lamantia, Fabio, 2006. "Variable effort management of renewable natural resources," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 771-782.
    9. Gámez, Manuel & López, Inmaculada & Rodríguez, Carmelo & Varga, Zoltán & Garay, József, 2018. "Game-theoretical model for marketing cooperative in fisheries," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 325-338.
    10. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    11. Marta Elena Biancardi, 2004. "Determinazione di strategie nello sfruttamento di una risorsa rinnovabile," Quaderni DSEMS 09-2004, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    12. Fausto Cavalli & Ahmad Naimzada & Lucia Parisio, 2021. "Learning in a double-phase cobweb model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 579-611, December.

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