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Markov-Perfect Nash Equilibria in Models With a Single Capital Stock

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Author Info
Dockner, E.J. (University of Vienna)
Wagener, F.O.O. () (Universiteit van Amsterdam)

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Abstract

Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary conditions that allow us to characterize Markov perfect Nash equalibria (MPNE) for these games. These conditions result in an auxilary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of MPNE. The techniques are used to derive detailed properties of MPNE for several games including the exploitation of a finite resource, the voluntary investment in a public capital stock, and the inter-temporal consumption of a reproductive asset.

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Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 06-07.

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Date of creation: 2006
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Handle: RePEc:ams:ndfwpp:06-07

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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.:
  1. Benhabib, Jess & Radner, Roy, 1992. "The Joint Exploitation of a Productive Asset: A Game-Theoretic Approach," Economic Theory, Springer, vol. 2(2), pages 155-90, April.
  2. Dutta Prajit K. & Sundaram Rangarajan K., 1993. "How Different Can Strategic Models Be?," Journal of Economic Theory, Elsevier, vol. 60(1), pages 42-61, June. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Benchekroun, Hassan, 2003. "Unilateral production restrictions in a dynamic duopoly," Journal of Economic Theory, Elsevier, vol. 111(2), pages 214-239, August. [Downloadable!] (restricted)
  6. Marx, Leslie M & Matthews, Steven A, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Blackwell Publishing, vol. 67(2), pages 327-58, April.
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  7. Dockner, Engelbert J. & Van Long, Ngo & Sorger, Gerhard, 1996. "Analysis of Nash equilibria in a class of capital accumulation games," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1209-1235. [Downloadable!] (restricted)
  8. repec:att:wimass:1920026 is not listed on IDEAS
  9. repec:att:wimass:1920324 is not listed on IDEAS
  10. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July. [Downloadable!] (restricted)
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  11. Kossioris, G. & Plexousakis, M. & Xepapadeas, A. & de Zeeuw, A. & Mäler, K.-G., 2008. "Feedback Nash equilibria for non-linear differential games in pollution control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1312-1331, April. [Downloadable!] (restricted)
  12. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July. [Downloadable!] (restricted)
  13. Wirl, Franz, 1996. "Dynamic voluntary provision of public goods: Extension to nonlinear strategies," European Journal of Political Economy, Elsevier, vol. 12(3), pages 555-560, November. [Downloadable!] (restricted)
  14. Eswaran, Mukesh & Lewis, Tracy R, 1984. "Appropriability and the Extraction of a Common Property Resource," Economica, London School of Economics and Political Science, vol. 51(204), pages 393-400, November. [Downloadable!] (restricted)
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  1. Salerno, Gillian & Beard, Rodney & McDonald, Stuart, 2007. "Rent Seeking Behavior and Optimal Taxation of Pollution in Shallow Lakes," MPRA Paper 11225, University Library of Munich, Germany, revised 22 Oct 2008. [Downloadable!]
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