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On the Open-Loop Nash Equilibrium in LQ-Games

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  • Engwerda, J.C.

    (Tilburg University, Faculty of Economics)

Abstract

In this paper we consider open-loop Nash equilibria of the linear-quadratic differential game.As well the finite-planning-horizon, the infinite-planning horizon as convergence properties of the finite-planning-horizon equilibrium if the planning horizon is extended to infinity are studied.Particular attention is paid to computational aspects and the scalar case.
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Suggested Citation

  • Engwerda, J.C., 1996. "On the Open-Loop Nash Equilibrium in LQ-Games," Research Memorandum 726, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:fc3f89f2-441a-4baf-a5a4-c3b659cc8b6e
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    References listed on IDEAS

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    1. de Zeeuw, A J & van der Ploeg, F, 1991. "Difference Games and Policy Evaluation: A Conceptual Framework," Oxford Economic Papers, Oxford University Press, vol. 43(4), pages 612-636, October.
    2. Engwerda, J.C., 1996. "The Infinite Horizon Open-Loop Nash LQ-Game," Research Memorandum 741, Tilburg University, School of Economics and Management.
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    6. Weeren, A.J.T.M. & Schumacher, J.M. & Engwerda, J.C., 1994. "Asymptotic analysis of Nash equilibria in nonzero-sum linear-quadratic differential games : The two player case," Research Memorandum FEW 634, Tilburg University, School of Economics and Management.
    7. Engwerda, J.C., 2012. "Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game," Discussion Paper 2012-052, Tilburg University, Center for Economic Research.
    8. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    10. Levine, Paul & Brociner, Andrew, 1994. "Fiscal policy coordination and EMU : A dynamic game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 699-729.
    11. Veijo Kaitala & Matti Pohjola & Olli Tahvonen, 1992. "Transboundary air pollution and soil acidification: A dynamic analysis of an acid rain game between Finland and the USSR," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 2(2), pages 161-181, March.
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    1. Engwerda, J. C., 1998. "Computational aspects of the open-loop Nash equilibrium in linear quadratic games," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1487-1506, August.
    2. Engwerda, J.C., 1996. "The Infinite Horizon Open-Loop Nash LQ-Game," Other publications TiSEM bb9762e7-faab-4ad2-8dd8-4, Tilburg University, School of Economics and Management.
    3. Engwerda, Jacob & van Aarle, Bas & Plasmans, Joseph & Weeren, Arie, 2013. "Debt stabilization games in the presence of risk premia," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2525-2546.
    4. Engwerda, J.C., 2008. "Uniqueness conditions for the affine open-loop linear quadratic differential games," Other publications TiSEM 53b6b5ec-5e13-4805-8d09-9, Tilburg University, School of Economics and Management.
    5. Engwerda, J.C., 2004. "The open-loop linear quadratic differential game revisited," Other publications TiSEM ff4e8556-547a-4157-a832-a, Tilburg University, School of Economics and Management.
    6. A. Garcia & R. L. Smith, 2000. "Markov Perfect Equilibrium Existence for a Class of Undiscounted Infinite-Horizon Dynamic Games," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 421-429, August.
    7. van den Broek, W.A., 1999. "Moving Horizon Control in Dynamic Games," Discussion Paper 1999-07, Tilburg University, Center for Economic Research.
    8. van den Broek, W. A., 2002. "Moving horizon control in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 937-961, June.
    9. W. A. van den Broek, 1999. "Moving-Horizon Control in Dynamic Games," Computing in Economics and Finance 1999 122, Society for Computational Economics.
    10. Adib Bagh, 2013. "Better Reply Security and Existence of Equilibria in Differential Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 325-340, September.
    11. Fouad El Ouardighi & Gary Erickson & Dieter Grass & Steffen Jørgensen, 2016. "Contracts and Information Structure in a Supply Chain with Operations and Marketing Interaction," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-36, December.
    12. Katrin Erdlenbruch & Raphael Soubeyran & Mabel Tidball & Agnes Tomini, 2012. "(Anti-)Coordination Problems with Scarce Water Resources," Working Papers 12-28, LAMETA, Universtiy of Montpellier, revised Sep 2012.
    13. Engwerda, J.C., 2005. "Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game," Discussion Paper 2005-32, Tilburg University, Center for Economic Research.
    14. Vasile Drăgan & Ivan Ganchev Ivanov & Ioan-Lucian Popa & Ovidiu Bagdasar, 2021. "Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games," Mathematics, MDPI, vol. 9(21), pages 1-15, October.
    15. van den Broek, W.A., 1999. "Moving Horizon Control in Dynamic Games," Other publications TiSEM 493397ad-8362-4236-975a-5, Tilburg University, School of Economics and Management.
    16. Mojtaba Dehghan Banadaki & Hamidreza Navidi, 2020. "Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method," Games, MDPI, vol. 11(3), pages 1-11, July.
    17. Engwerda, J.C., 2000. "Feedback Nash equilibria in the scalar infinite horizon LQ-Game," Other publications TiSEM 58ccf964-4ca1-4d67-9a68-a, Tilburg University, School of Economics and Management.
    18. Tyrone E. Duncan & Hamidou Tembine, 2018. "Linear–Quadratic Mean-Field-Type Games: A Direct Method," Games, MDPI, vol. 9(1), pages 1-18, February.
    19. Helton Saulo & Leandro Rêgo & Jose Divino, 2013. "Fiscal and monetary policy interactions: a game theory approach," Annals of Operations Research, Springer, vol. 206(1), pages 341-366, July.
    20. Nikooeinejad, Z. & Heydari, M. & Loghmani, G.B., 2022. "A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: Economic applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 404-427.

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    Keywords

    game theory; Nash equilibrium;

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