Advanced Search
MyIDEAS: Login to save this paper or follow this series

Non-linear strategies in a linear quadratic differential game

Contents:

Author Info

  • Colin Rowat

    (University of Birmingham)

Abstract

We study non-linear Markov perfect equilibria in a two agent linear quadratic differential game. In contrast to the literature owing to Tsutsui and Mino (1990), we do not associate endogenous subsets of the state space with candidate solutions. Instead, we address the problem of unbounded-below value functions over infinite horizons by use of the `catching up optimality' criterion. We present sufficiency conditions for existence based on results in Dockner, Jorgenson, Long and Sorger (2000). Applying these to our model yields the familiar linear solution as well as a condition under which a continuum of non-linear solutions exist. As this condition is relaxed when agents are more patient, and allows more efficient steady states, it resembles a Folk Theorem for differential games. The model presented here is one of atmospheric pollution; the results apply to differential games more generally.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://128.118.178.162/eps/ge/papers/0502/0502001.pdf
Download Restriction: no

Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0502001.

as in new window
Length: 31 pages
Date of creation: 01 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpge:0502001

Note: Type of Document - pdf; pages: 31. University of Birmingham Department of Economics Discussion Paper 05-05
Contact details of provider:
Web page: http://128.118.178.162

Related research

Keywords: differential game; non-linear strategies; catching up optimal; Folk Theorem;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
  2. Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003. "The Economics of Shallow Lakes," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 26(4), pages 603-624, December.
  3. LE VAN, Cuong & MORHAIM, Lisa, 2001. "Optimal growth models with bounded or unbounded returns: a unifying approach," CORE Discussion Papers 2001034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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, April.
  5. Tsutsui, Shunichi O., 1996. "Capacity constraints and voluntary output cutback in dynamic Cournot competition," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1683-1708.
  6. Vencatachellum, Desire, 1998. "Endogenous growth with strategic interactions," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 233-254, September.
  7. Karp, Larry, 1996. "Depreciation erodes the Coase Conjecture," European Economic Review, Elsevier, vol. 40(2), pages 473-490, February.
  8. Seierstad, Atle & Sydsaeter, Knut, 1977. "Sufficient Conditions in Optimal Control Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 367-91, June.
  9. Rubio, Santiago J. & Casino, Begona, 2002. "A note on cooperative versus non-cooperative strategies in international pollution control," Resource and Energy Economics, Elsevier, vol. 24(3), pages 251-261, June.
  10. Dutta, Prajit K & Sundaram, Rangarajan K, 1993. "The Tragedy of the Commons?," Economic Theory, Springer, vol. 3(3), pages 413-26, July.
  11. Wirl, Franz & Dockner, Engelbert, 1995. "Leviathan governments and carbon taxes: Costs and potential benefits," European Economic Review, Elsevier, vol. 39(6), pages 1215-1236, June.
  12. Lockwood, Ben, 1996. "Uniqueness of Markov-perfect equilibrium in infinite-time affine-quadratic differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 20(5), pages 751-765, May.
  13. Wirl, Franz, 2007. "Do multiple Nash equilibria in Markov strategies mitigate the tragedy of the commons?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3723-3740, November.
  14. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
  15. Maria Luisa Gota & Luigi Montrucchio, 1999. "On Lipschitz continuity of policy functions in continuous-time optimal growth models," Economic Theory, Springer, vol. 14(2), pages 479-488.
  16. Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October.
  17. Feichtinger, Gustav & Wirl, Franz, 1993. "A Dynamic Variant of the Battle of the Sexes," International Journal of Game Theory, Springer, vol. 22(4), pages 359-80.
  18. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
  19. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
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 in new window

Cited by:
  1. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
  2. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
  3. Rémy Dullieux & Lionel Ragot & Katheline Schubert, 2011. "Carbon Tax and OPEC’s Rents Under a Ceiling Constraint," Scandinavian Journal of Economics, Wiley Blackwell, vol. 113(4), pages 798-824, December.
  4. Hans Gersbach & Noemi Hummel & Ralph Winkler, 2011. "Sustainable Climate Treaties," Diskussionsschriften dp1105, Universitaet Bern, Departement Volkswirtschaft.
  5. 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.
  6. Wang, Hefei, 2012. "Costly information transmission in continuous time with implications for credit rating announcements," Journal of Economic Dynamics and Control, Elsevier, vol. 36(9), pages 1402-1413.
  7. Luigi Siciliani & Odd Rune Straume & Roberto Cellini, 2011. "Quality competition with motivated providers and sluggish demand," NIPE Working Papers 14/2011, NIPE - Universidade do Minho.
  8. Franz Wirl, 2009. "Non-cooperative investment in partnerships and their termination," Central European Journal of Operations Research, Springer, vol. 17(4), pages 479-494, December.
  9. Dockner, E.J. & Wagener, F.O.O., 2013. "Markov–Perfect Nash Equilibria in Models With a Single Capital Stock (Revised version, March 2013)," CeNDEF Working Papers 13-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpge:0502001. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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