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

Author

Listed:
  • Dockner, E.J.

    (University of Vienna)

  • Wagener, F.O.O.

    () (Universiteit van Amsterdam)

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.

Suggested Citation

  • Dockner, E.J. & Wagener, F.O.O., 2006. "Markov-Perfect Nash Equilibria in Models With a Single Capital Stock," CeNDEF Working Papers 06-07, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:06-07
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    References listed on IDEAS

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    1. Robert Becker & Ram Dubey & Tapan Mitra, 2014. "On Ramsey equilibrium: capital ownership pattern and inefficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 565-600, April.
    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. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
    4. Kossioris, G. & Plexousakis, M. & Xepapadeas, A. & de Zeeuw, A., 2011. "On the optimal taxation of common-pool resources," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1868-1879.
    5. Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
    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, vol. 26(4), pages 603-624, December.
    7. Ken-Ichi Akao, 2008. "Tax schemes in a class of differential games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 155-174, April.
    8. 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.
    9. 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, October.
    10. 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.
    11. Prajit Dutta & Roy Radner, 2012. "Capital growth in a global warming model: will China and India sign a climate treaty?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 411-443, February.
    12. 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.
    13. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
    14. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    15. Benhabib, Jess & Radner, Roy, 1992. "The Joint Exploitation of a Productive Asset: A Game-Theoretic Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 155-190, April.
    16. Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
    17. Gerhard Sorger, 2008. "Strategic saving decisions in the infinite-horizon model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 353-377, September.
    18. 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.
    19. 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.
    20. 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.
    21. Larry Karp & Jiangfeng Zhang, 2012. "Taxes versus quantities for a stock pollutant with endogenous abatement costs and asymmetric information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 371-409, February.
    22. Benchekroun, Hassan, 2003. "Unilateral production restrictions in a dynamic duopoly," Journal of Economic Theory, Elsevier, vol. 111(2), pages 214-239, August.
    23. 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.
    24. 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.
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    Cited by:

    1. Colombo, Luca & Labrecciosa, Paola, 2015. "On the Markovian efficiency of Bertrand and Cournot equilibria," Journal of Economic Theory, Elsevier, vol. 155(C), pages 332-358.
    2. Florian Wagener, 2013. "Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict," Computational Management Science, Springer, vol. 10(4), pages 423-450, December.
    3. 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.
    4. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    5. repec:eee:jeborg:v:140:y:2017:i:c:p:91-119 is not listed on IDEAS
    6. Tasneem, Dina & Engle-Warnick, Jim & Benchekroun, Hassan, 2017. "An experimental study of a common property renewable resource game in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 91-119.
    7. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    8. repec:spr:grdene:v:27:y:2018:i:2:d:10.1007_s10726-017-9545-7 is not listed on IDEAS
    9. 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.
    10. 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.
    11. repec:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0213-3 is not listed on IDEAS
    12. Grega Smrkolj & Florian Wagener, 2014. "Research among Copycats: R&D, Spillovers, and Feedback Strategies," Tinbergen Institute Discussion Papers 14-112/II, Tinbergen Institute, revised 22 Jun 2017.
    13. Herbert Dawid & Michel Y. Keoula & Peter M. Kort, 2017. "Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms," Dynamic Games and Applications, Springer, vol. 7(4), pages 555-577, December.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery

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