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Computation of viability kernels: a case study of by-catch fisheries

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  • Jacek Krawczyk
  • Alastair Pharo
  • Oana Serea
  • Stewart Sinclair

Abstract

Traditional means of studying environmental economics and management problems consist of optimal control and dynamic game models that are solved for optimal or equilibrium strategies. Notwithstanding the possibility of multiple equilibria, the models’ users—managers or planners—will usually be provided with a single optimal or equilibrium strategy no matter how reliable, or unreliable, the underlying models and their parameters are. In this paper we follow an alternative approach to policy making that is based on viability theory. It establishes “satisficing” (in the sense of Simon), or viable, policies that keep the dynamic system in a constraint set and are, generically, multiple and amenable to each manager’s own prioritisation. Moreover, they can depend on fewer parameters than the optimal or equilibrium strategies and hence be more robust. For the determination of these (viable) policies, computation of “viability kernels” is crucial. We introduce a MATLAB application, under the name of VIKAASA, which allows us to compute approximations to viability kernels. We discuss two algorithms implemented in VIKAASA. One approximates the viability kernel by the locus of state space positions for which solutions to an auxiliary cost-minimising optimal control problem can be found. The lack of any solution implies the infinite value function and indicates an evolution which leaves the constraint set in finite time, therefore defining the point from which the evolution originates as belonging to the kernel’s complement. The other algorithm accepts a point as viable if the system’s dynamics can be stabilised from this point. We comment on the pros and cons of each algorithm. We apply viability theory and the VIKAASA software to a problem of by-catch fisheries exploited by one or two fleets and provide rules concerning the proportion of fish biomass and the fishing effort that a sustainable fishery’s exploitation should follow. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Jacek Krawczyk & Alastair Pharo & Oana Serea & Stewart Sinclair, 2013. "Computation of viability kernels: a case study of by-catch fisheries," Computational Management Science, Springer, vol. 10(4), pages 365-396, December.
    • Handle: RePEc:spr:comgts:v:10:y:2013:i:4:p:365-396
    DOI: 10.1007/s10287-013-0189-z
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    Cited by:

    1. Helene Gomes & Luc Doyen & Fabian Blanchard & Adrien Lagarde, 2021. "Viable and ecosystem-based management for tropical small-scale fisheries facing climate change," Bordeaux Economics Working Papers 2021-24, Bordeaux School of Economics (BSE).
    2. Pedro Gajardo & Luc Doyen, 2018. "Viability standards and multi-criteria maximin," Cahiers du GREThA (2007-2019) 2018-04, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    3. Doyen, L. & Armstrong, C. & Baumgärtner, S. & Béné, C. & Blanchard, F. & Cissé, A.A. & Cooper, R. & Dutra, L.X.C. & Eide, A. & Freitas, D. & Gourguet, S. & Gusmao, F. & Hardy, P.-Y. & Jarre, A. & Litt, 2019. "From no whinge scenarios to viability tree," Ecological Economics, Elsevier, vol. 163(C), pages 183-188.
    4. Krawczyk, Jacek B & Townsend, Wilbur, 2015. "Viability of an economy with constrained inequality," Working Paper Series 4689, Victoria University of Wellington, School of Economics and Finance.
    5. Jacek B. Krawczyk & Vladimir P. Petkov, 2022. "A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent," Games, MDPI, vol. 13(5), pages 1-24, August.
    6. Anita King, 2018. "Living Standards Analysis Model: The First Prototype," Treasury Working Paper Series 18/05, New Zealand Treasury.
    7. Schuhbauer, Anna & Sumaila, U. Rashid, 2016. "Economic viability and small-scale fisheries — A review," Ecological Economics, Elsevier, vol. 124(C), pages 69-75.
    8. Krawczyk, Jacek B. & Judd, Kenneth L., 2014. "Which economic states are sustainable under a slightly constrained tax-rate adjustment policy," MPRA Paper 59027, University Library of Munich, Germany.
    9. Luc DOYEN & Claire ARMSTRONG & Stefan BAUMGARTNER & Christophe BÉNÉ & Fabian BLANCHARD & Abdoul Ahad CISSÉ & Rachel COOPER & Léo DUTA & Debora FREITAS & Sophie GOURGUET & Felipe GUSMAO & Astrid JARRE , 2017. "From no whinge policy to viability tree," Cahiers du GREThA (2007-2019) 2017-12, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    10. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "InfsocSol3: An updated MATLAB® package for approximating the solution to a continuous-time infinite horizon stochastic optimal control problem," Working Paper Series 18832, Victoria University of Wellington, School of Economics and Finance.
    11. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "InfsocSol3: An updated MATLAB® package for approximating the solution to a continuous-time infinite horizon stochastic optimal control problem," Working Paper Series 3412, Victoria University of Wellington, School of Economics and Finance.
    12. Krawczyk, Jacek B & Townsend, Wilbur, 2015. "Viability of an economy with constrained inequality," Working Paper Series 19335, Victoria University of Wellington, School of Economics and Finance.
    13. Antoine Brias & Jean-Denis Mathias & Guillaume Deffuant, 2016. "Accelerating viability kernel computation with CUDA architecture: application to bycatch fishery management," Computational Management Science, Springer, vol. 13(3), pages 371-391, July.

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