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A class of linear quadratic dynamic optimization problems with state dependent constraints

Author

Listed:
  • Rajani Singh

    (University of Warsaw)

  • Agnieszka Wiszniewska-Matyszkiel

    (University of Warsaw)

Abstract

In this paper, we analyse a wide class of discrete time one-dimensional dynamic optimization problems—with strictly concave current payoffs and linear state dependent constraints on the control parameter as well as non-negativity constraint on the state variable and control. This model suits well economic problems like extraction of a renewable resource (e.g. a fishery or forest harvesting). The class of sub-problems considered encompasses a linear quadratic optimal control problem as well as models with maximal carrying capacity of the environment (saturation). This problem is also interesting from theoretical point of view—although it seems simple in its linear quadratic form, calculation of the optimal control is nontrivial because of constraints and the solutions has a complicated form. We consider both the infinite time horizon problem and its finite horizon truncations.

Suggested Citation

  • Rajani Singh & Agnieszka Wiszniewska-Matyszkiel, 2020. "A class of linear quadratic dynamic optimization problems with state dependent constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 325-355, April.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:2:d:10.1007_s00186-019-00688-4
    DOI: 10.1007/s00186-019-00688-4
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    1. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    2. J. B. Krawczyk & M. Tidball, 2006. "A Discrete-Time Dynamic Game of Seasonal Water Allocation," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 411-429, February.
    3. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    4. L. Doyen & A. A. Cissé & N. Sanz & F. Blanchard & J.-C. Pereau, 2018. "The Tragedy of Open Ecosystems," Dynamic Games and Applications, Springer, vol. 8(1), pages 117-140, March.
    5. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
    6. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    7. Fischer, Ronald D. & Mirman, Leonard J., 1992. "Strategic dynamic interaction : Fish wars," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 267-287, April.
    8. Michèle Breton & Lucia Sbragia & Georges Zaccour, 2010. "A Dynamic Model for International Environmental Agreements," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 45(1), pages 25-48, January.
    9. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    10. Vladimir V. Mazalov & Anna N. Rettieva, 2010. "Fish Wars With Many Players," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 385-405.
    11. Rubio, Santiago J. & Ulph, Alistair, 2007. "An infinite-horizon model of dynamic membership of international environmental agreements," Journal of Environmental Economics and Management, Elsevier, vol. 54(3), pages 296-310, November.
    12. Ehtamo, Harri & Hamalainen, Raimo P., 1993. "A cooperative incentive equilibrium for a resource management problem," Journal of Economic Dynamics and Control, Elsevier, vol. 17(4), pages 659-678, July.
    13. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    14. Breton, Michèle & Keoula, Michel Yevenunye, 2014. "A great fish war model with asymmetric players," Ecological Economics, Elsevier, vol. 97(C), pages 209-223.
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    Cited by:

    1. Agnieszka Wiszniewska-Matyszkiel & Rajani Singh, 2020. "When Inaccuracies in Value Functions Do Not Propagate on Optima and Equilibria," Mathematics, MDPI, vol. 8(7), pages 1-25, July.
    2. Katarzyna Kańska & Agnieszka Wiszniewska-Matyszkiel, 2022. "Dynamic Stackelberg duopoly with sticky prices and a myopic follower," Operational Research, Springer, vol. 22(4), pages 4221-4252, September.

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