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

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Author Info
Engelbert J. Dockner () (University of Vienna, Austria)
Florian O.O. Wagener () (CeNDEF, 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 equilibria (MPNE) for these games. These conditions result in an auxiliary 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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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-055/1.

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Date of creation: 22 Jun 2006
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Handle: RePEc:dgr:uvatin:20060055

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Web page: http://www.tinbergen.nl/

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Keywords: Capital accumulation games Markov equilibria Resource games Differential games

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Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
D92 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Firm Choice and Growth, Investment, or Financing
Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery

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  4. 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)
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  9. 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)
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  13. 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)
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