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Non-Linear Strategies in a Linear Quadratic Differential Game

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  • Colin Rowat

Abstract

See Birmingham Discussion Paper 05-05R (January 2006) for current version.

Suggested Citation

  • Colin Rowat, 2005. "Non-Linear Strategies in a Linear Quadratic Differential Game," Discussion Papers 05-05, Department of Economics, University of Birmingham.
  • Handle: RePEc:bir:birmec:05-05
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    References listed on IDEAS

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    1. Tsutsui, Shunichi O., 1996. "Capacity constraints and voluntary output cutback in dynamic Cournot competition," Journal of Economic Dynamics and Control, Elsevier, pages 1683-1708.
    2. Wirl, Franz, 2007. "Do multiple Nash equilibria in Markov strategies mitigate the tragedy of the commons?," Journal of Economic Dynamics and Control, Elsevier, pages 3723-3740.
    3. Rubio, Santiago J. & Casino, Begona, 2002. "A note on cooperative versus non-cooperative strategies in international pollution control," Resource and Energy Economics, Elsevier, pages 251-261.
    4. Lockwood, Ben, 1996. "Uniqueness of Markov-perfect equilibrium in infinite-time affine-quadratic differential games," Journal of Economic Dynamics and Control, Elsevier, pages 751-765.
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    6. Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003. "The Economics of Shallow Lakes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, pages 603-624.
    7. Wirl, Franz & Dockner, Engelbert, 1995. "Leviathan governments and carbon taxes: Costs and potential benefits," European Economic Review, Elsevier, pages 1215-1236.
    8. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, pages 136-161.
    9. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, pages 158-187.
    10. Dutta, Prajit K & Sundaram, Rangarajan K, 1993. "The Tragedy of the Commons?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 413-426.
    11. Feichtinger, Gustav & Wirl, Franz, 1993. "A Dynamic Variant of the Battle of the Sexes," International Journal of Game Theory, Springer;Game Theory Society, pages 359-380.
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    13. Karp, Larry, 1996. "Depreciation erodes the Coase Conjecture," European Economic Review, Elsevier, pages 473-490.
    14. Karp, Larry, 1996. "Depreciation erodes the Coase Conjecture," European Economic Review, Elsevier, pages 473-490.
    15. Colin Rowat, 2005. "Non-Linear Strategies in a Linear Quadratic Differential Game," Discussion Papers 05-05, Department of Economics, University of Birmingham.
    16. Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, pages 209-227.
    17. Colin Rowat, 2005. "Non-linear strategies in a linear quadratic differential game," GE, Growth, Math methods 0502001, EconWPA.
    18. Maria Luisa Gota & Luigi Montrucchio, 1999. "On Lipschitz continuity of policy functions in continuous-time optimal growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 479-488.
    19. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, December.
    20. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, pages 13-29.
    21. Vencatachellum, Desire, 1998. "Endogenous growth with strategic interactions," Journal of Economic Dynamics and Control, Elsevier, pages 233-254.
    22. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, pages 3179-3202.
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    Citations

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    Cited by:

    1. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, pages 568-598.
    2. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 585-625.
    3. Lambertini, Luca & Mantovani, Andrea, 2016. "On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation," Economics Letters, Elsevier, pages 9-12.
    4. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, pages 3179-3202.
    5. Nkuiya, Bruno, 2015. "Transboundary pollution game with potential shift in damages," Journal of Environmental Economics and Management, Elsevier, pages 1-14.
    6. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, pages 217-219.
    7. repec:eee:jeborg:v:140:y:2017:i:c:p:91-119 is not listed on IDEAS
    8. Hans Gersbach & Noemi Hummel & Ralph Winkler, 2017. "Sustainable Climate Treaties," CESifo Working Paper Series 6385, CESifo Group Munich.
    9. L. Lambertini, 2017. "Regulating the tragedy of commons: nonlinear feedback solutions of a differential game with a dual interpretation," Working Papers wp1096, Dipartimento Scienze Economiche, Universita' di Bologna.
    10. Rémy Dullieux & Lionel Ragot & Katheline Schubert, 2011. "Carbon Tax and OPEC’s Rents Under a Ceiling Constraint," Scandinavian Journal of Economics, Wiley Blackwell, pages 798-824.
    11. Rémy Dullieux & Lionel Ragot & Katheline Schubert, 2011. "Carbon Tax and OPEC’s Rents Under a Ceiling Constraint," Scandinavian Journal of Economics, Wiley Blackwell, pages 798-824.
    12. Franz Wirl, 2009. "Non-cooperative investment in partnerships and their termination," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 479-494, December.
    13. L. Lambertini & A. Palestini, 2017. "Voluntary Export Restraints in a Trade Model with Sticky Price: Linear and Nonlinear Feedback Solutions," Working Papers wp1109, Dipartimento Scienze Economiche, Universita' di Bologna.
    14. Dina Tasneem & Jim Engle-Warnick & Hassan Benchekroun, 2014. "An Experimental Study of a Common Property Renewable Resource Game in Continuous Time," CIRANO Working Papers 2014s-09, CIRANO.
    15. Lambertini, Luca & Mantovani, Andrea, 2016. "On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation," Economics Letters, Elsevier, pages 9-12.
    16. Habla, Wolfgang & Winkler, Ralph, 2013. "Political influence on non-cooperative international climate policy," Journal of Environmental Economics and Management, Elsevier, pages 219-234.
    17. Siciliani, Luigi & Rune Straume, Odd & Cellini, Roberto, 2013. "Quality competition with motivated providers and sluggish demand," Journal of Economic Dynamics and Control, Elsevier, pages 2041-2061.
    18. Colin Rowat, 2005. "Non-linear strategies in a linear quadratic differential game," GE, Growth, Math methods 0502001, EconWPA.
    19. Wirl, Franz, 2016. "Indeterminacy and history dependence of strategically interacting players," Economics Letters, Elsevier, pages 19-24.
    20. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    21. Colin Rowat, 2005. "Non-Linear Strategies in a Linear Quadratic Differential Game," Discussion Papers 05-05, Department of Economics, University of Birmingham.
    22. Wang, Hefei, 2012. "Costly information transmission in continuous time with implications for credit rating announcements," Journal of Economic Dynamics and Control, Elsevier, pages 1402-1413.

    More about this item

    Keywords

    Differential game; Non-Linear Strategies; Catching up Optimal; Folk Theorem;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • Q00 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - General

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