Abstract
In a two-player, continuous time model of dynamic common-property resource of the replenishable type, we illustrate by examples the dual indeterminacy property of the Markovian-Nash equilibrium. Specifically, we have established: (1) The indeterminacy of the inverse equilibrium problem: there exists a continuum of distinct model structures corresponding to one observable equilibrium path; (2) The indeterminacy of the equilibrium problem: there exists a continuum of distinct, observable equilibrium plays corresponding to a single model structure. The method of analysis is to construct candidate equilibrium paths by means of both the Euler-Lagrange and the transversality conditions and then verify that the candidate equilibrium is an equilibrium by the Mangasarian criterion. These results may well have implications to other areas where the dynamic games formulation is relevant, for exdample, the concept of rational expectations and the procedure of calibration in macro-economic analysis.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amit, I. and Halperin, A. (1989), Sharing a common product, Mimeo, Hebrew University, Jerusalem.
Basar, T. (1989), Time consistency and robustness of equilibria in non-cooperative dynamic games, In: van der Ploeg, F. de Zeeuw, A.J. (eds.) Dynamic Policy Games in Economics, North-Holland, New York.
Benhabib, J. and Radner, R. (1992), The joint exploitation of a productive asset: a game-theoretic approach, Economic Theory, 2.
Clark, C.W. (1980), Restricted access to common-property fishery resources: a game theoretic analysis In: Liu, P.T. (ed.) Dynamic Optimization and Mathematical Economics, Plenum, New York.
Clemhout, S. and Wan, H.Y., Jr. (1985), Dynamic common property resources and environmental problems, J. Opt. Th. and Appl. 46, 471–481.
Clemhout, S. and Wan, H.Y., Jr. (1991), Environmental problem as a common-property resource game In: Ehtamo, H. and R.P. Hamalainen (eds.) Dynamic Games in Economic Analysis, Springer-Verlag, New York.
Clemhout, S. and Wan, H.Y., Jr. (1989), On games of cake eating In: van der Ploeg, F, De Zeeuw, A.J. (eds.) Dynamic Policy Games in Economics, North-Holland, New York.
Dockner, E.J. and Long, N.V. (forthcoming), Intertemporal pollution control: cooperative versus non-cooperative strategies, J. of Environmental Econ. and Mgmt.
Dockner, E.J., Hartwick, J.M., and Sorger, G. (1992), The Great Fish War Revisited, mimeo.
Dutta, P.K. and Sundaram, R.K. (1989), The tragedy of the commons? A characterization of stationary perfect equilibrium in dynamic games, University of Rochester, Working paper, No. 172.
Dutta, P.K. and Sundaram, R.K. (1990) How different can strategic models be? Non-existence, chaos and under consumption in Markov-perfect equilibria, Columbia University Discussion Paper, No. 498.
Dutta, P.K. and Sundaram, R.K. (1992) Markovian equilibrium in a class of stochastic games: existence theorems for discounted and undis-counted models, Econ. Theory 2, 197–214.
Kaitala, V. (1986) Game theory models of fishery management -a survey. In: Baser, T. (ed.) Dynamic Games and Applications in Economics, Springer, New York.
Kydland, F.E. and Prescott, E.C. (1982), Time to build and aggregate fluctuations, Econometrica 50, 1345–1370.
Levhari, D. and Mirman, L.J. (1980), The great fish war: an example using the Cournot-Nash solution, Bell J. Econ. 11, 322–334.
Lucas, R. Jr. (1987), Models of Business Cycles, Blackwell, New York.
Mirman, L.J. (1979), Dynamic models of fishing: a heuristic approach In: Liu, P.T. and Suinen, J.G. (eds.) Control Theory in Mathematical Economics, Marcel Decker, New York.
Sundaram, R.K. (1989), Perfect equilibria in non-randomized strategies in a class of symmetric games, J. Econ. Theory 47, 153–77.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this paper
Cite this paper
Clemhout, S., Wan, H.Y. (1994). The Nonuniqueness of Markovian Strategy Equilibrium: The Case of Continuous Time Models for Nonrenewable Resources. In: Başar, T., Haurie, A. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0245-5_19
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0245-5_19
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6679-2
Online ISBN: 978-1-4612-0245-5
eBook Packages: Springer Book Archive