IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/fc3f89f2-441a-4baf-a5a4-c3b659cc8b6e.html
   My bibliography  Save this paper

On the Open-Loop Nash Equilibrium in LQ-Games

Author

Listed:
  • Engwerda, J.C.

    (Tilburg University, School of Economics and Management)

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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Engwerda, J.C., 1996. "On the Open-Loop Nash Equilibrium in LQ-Games," Other publications TiSEM fc3f89f2-441a-4baf-a5a4-c, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:fc3f89f2-441a-4baf-a5a4-c3b659cc8b6e
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/523997/726.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    3. Douven, R. C. & Engwerda, J. C., 1995. "Is there room for convergence in the E.C.?," European Journal of Political Economy, Elsevier, vol. 11(1), pages 113-130, March.
    4. Tabellini, Guido, 1986. "Money, debt and deficits in a dynamic game," Journal of Economic Dynamics and Control, Elsevier, vol. 10(4), pages 427-442, December.
    5. van Aarle, B. & Bovenberg, A.L. & Raith, M., 1995. "Monetary and fiscal policy interaction and government debt stabilization," Discussion Paper 1995-1, Tilburg University, Center for Economic Research.
    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).
    9. Weeren, A.J.T.M., 1995. "Coordination in hierarchical control," Other publications TiSEM c24c0d84-75c9-4e80-a9cd-0, Tilburg University, School of Economics and Management.
    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.
    12. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    13. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    14. Petit, Maria Luisa, 1989. "Fiscal and Monetary Policy Co-ordination: A Differential Game Approac h," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(2), pages 161-179, April-Jun.
    15. Bas Aarle & Lans Bovenberg & Matthias Raith, 1995. "Monetary and fiscal policy interaction and government debt stabilization," Journal of Economics, Springer, vol. 62(2), pages 111-140, June.
    16. Reinhard Neck & Engelbert Dockner, 1995. "Commitment and coordination in a dynamic game model of international economic policy-making," Open Economies Review, Springer, vol. 6(1), pages 5-28, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Engwerda, J.C., 1998. "On the Scalar Feedback Nash Equilibria in the Infinite Horizon LQ-Game," Other publications TiSEM 3142d140-f18c-4699-be28-9, Tilburg University, School of Economics and Management.
    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, J.C., 1999. "On the solution set of scalar algebraic Riccati equations," Other publications TiSEM 11c4c9d5-d01b-4372-a18b-1, Tilburg University, School of Economics and Management.
    4. 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.
    5. J.C. Engwerda & B. Aarle & J.E.J. Plasmans, 1999. "The (in)finite horizon open‐loop Nash LQ game:An application to EMU," Annals of Operations Research, Springer, vol. 88(0), pages 251-273, January.
    6. Willi Semmler & Alexander Haider, 2018. "Cooperative Monetary and Fiscal Policies in the Euro Area," Southern Economic Journal, John Wiley & Sons, vol. 85(1), pages 217-234, July.
    7. W. A. van den Broek, 1999. "Moving-Horizon Control in Dynamic Games," Computing in Economics and Finance 1999 122, Society for Computational Economics.
    8. Valeria De Bonis & Pompeo Della Posta, 2005. "Strategic interactions between monetary and fiscal authorities in a monetary union," Working Papers de Economia (Economics Working Papers) 26, Departamento de Economia, Gestão e Engenharia Industrial, Universidade de Aveiro.
    9. Bas Van Aarle & Jacob Engwerda & Joseph Plasmans & Arie Weeren, 2001. "Macroeconomic Policy Interaction under EMU: A Dynamic Game Approach," Open Economies Review, Springer, vol. 12(1), pages 29-60, January.
    10. van den Broek, W.A., 1999. "Moving Horizon Control in Dynamic Games," Discussion Paper 1999-07, Tilburg University, Center for Economic Research.
    11. 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.
    12. 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.
    13. Jacob Engwerda & Davoud Mahmoudinia & Rahim Dalali Isfahani, 2016. "Government and Central Bank Interaction under Uncertainty: A Differential Games Approach," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 20(2), pages 225-259, Spring.
    14. Jacob C. Engwerda, "undated". "Computational Aspects of the (In)finite Planning Horizon Open-loop Nash Equilibrium in LQ-Games," Computing in Economics and Finance 1996 _018, Society for Computational Economics.
    15. Enrico Saltari & Willi Semmler & Giovanni Di Bartolomeo, 2022. "A Nash Equilibrium for Differential Games with Moving-Horizon Strategies," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 1041-1054, October.
    16. Giovanni Di Bartolomeo & Debora Di Gioacchino, 2008. "Fiscal-monetary policy coordination and debt management: a two-stage analysis," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 35(4), pages 433-448, September.
    17. Giovanni Di Bartolomeo & Marco Di Pietro & Enrico Saltari & Willi Semmler, 2018. "Public debt stabilization: the relevance of policymakers’ time horizons," Public Choice, Springer, vol. 177(3), pages 287-299, December.
    18. Bas Aarle & Lans Bovenberg & Matthias Raith, 1995. "Monetary and fiscal policy interaction and government debt stabilization," Journal of Economics, Springer, vol. 62(2), pages 111-140, June.
    19. Z. Nikooeinejad & M. Heydari & M. Saffarzadeh & G. B. Loghmani & J. Engwerda, 2022. "Numerical Simulation of Non-cooperative and Cooperative Equilibrium Solutions for a Stochastic Government Debt Stabilization Game," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 775-801, February.
    20. Christos Mavrodimitrakis, 2022. "Debt stabilization and financial stability in a monetary union: Market versus authority‐based preventive solutions," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 2582-2599, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiutis:fc3f89f2-441a-4baf-a5a4-c3b659cc8b6e. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.