Abstract
We present a method for the derivation of feedback Nash equi- libria in discrete-time finite-horizon nonstationary dynamic games. A partic- ular motivation for such games stems from environmental economics, where problems of seasonal competition for water levels occur frequently among heterogeneous economic agents. These agents are coupled through a state variable, which is the water level. Actions are strategically chosen to max- imize the agents individual season-dependent utility functions. We observe that, although a feedback Nash equilibrium exists, it does not satisfy the (exogenous) environmental watchdog expectations. We devise an incentive scheme to help meeting those expectations and calculate a feedback Nash equilibrium for the new game that uses the scheme. This solution is more environmentally friendly than the previous one. The water allocation game solutions help us to draw some conclusions regarding the agents behavior and also about the existence of feedback Nash equilibria in dynamic games.
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References
KRAWCZYK, J. B., and TIDBALL, M., Economic Coordination in an Environmental Dynamic Game, Proceedings of the 2002 International Symposium on Dynamic Games, St Petersburg, Russia, 2002.
KRAWCZYK, J. B., and TIDBALL, M., Intertemporal Competition for Water Levels, Paper Presented at the 2003 Conference of the Society for Computational Economics, Seattle, Washington, 2003.
MATHEVET, R., LIFRAN, R., MAUCHAMP, A., LEFEBVRE, G., and POULIN, B., ReedSim: Simulating Ecological and Economical Dynamics of Mediterranean Reedbeds, Paper presented at the 2003 MODSIM Conference, Townsville, Australia, 2003.
RUBIO, S. J., and CASINO, B., Competitive versus Efficient Extraction of a Common Property Resource: The Groundwater Case, Journal of Economic Dynamics and Control, Vol. 25, pp. 1117–1137, 2001.
CARLSON, D. A., and HAURIE, A., Infinite-Horizon Dynamic Games with Coupled State Constraints, Annals of the International Society of Dynamic Games, Vol. 5, pp. 195–212, 2000.
KRAWCZYK, J. B., and ZACCOUR, G., Management of Pollution from Decentralized Agents by Local Government, International Journal of Environment and Pollution, Vol. 12, pp. 343–357, 1999.
HAURIE, A., and POURTALLIER, O., Diagonal Strict Convexity in Dynamic Programming Equations for Feedback Nash Equilibria, Proceedings of the 2000 Symposium of the International Society on Dynamic Games, Adelaide, South Australia, 2000.
ROSEN, J. B., Existence and Uniqueness of Equilibrium Points for Concave n-Person Games, Econometrica, Vol. 33, pp. 520–534, 1965.
FUDENBERG, D., and TIROLE, J., Game Theory, MIT Press, Cambridge, Massachusetts, 1991.
HAURIE, A., and KRAWCZYK, J. B., An Introduction to Dynamic Games, Internet textbook, 2002; see http://ecolu-info.unige.ch/~haurie/fame/textbook.pdf.
BAŞAR, T., and OLSDER, G. K., Dynamic Noncooperative Game Theory, Academic Press, New York, NY, 1982.
KRAWCZYK, J. B., Controlling a Dam to Environmentally Acceptable Standards Through the Use of a Decision Support Tool, Environmental and Resource Economics, Vol. 5, pp. 287–304, 1995.
KRAWCZYK, J. B., LIFRAN, L., and TIDBALL, M., Use of Coupled Incentives to Improve Adoption of Environmentally Friendly Technologies, Journal of Environmental Economics and Management, Vol. 49, pp. 311–329, 2004.
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The paper draws from Refs.1–2. Its earlier version was presented at the Victoria International Conference 2004, Victoria University of Wellington, Wellington, New Zealand, February 9–13, 2004.
We thank the anonymous referee and Christophe Deissenberg for insightful comments, which have helped us to clarify its message. We also thank our colleagues Sophie Thoyer, Robert Lifran, Odile Pourtalier, and Vladimir Petkov for helpful discussions on the model and techniques used in this Paper.
Gratitude is expressed to the Kyoto Institute for Economic Research, Kyoto University, for this author's support in the final stages of the paper preparation
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Krawczyk, J.B., Tidball, M. A Discrete-Time Dynamic Game of Seasonal Water Allocation. J Optim Theory Appl 128, 411–429 (2006). https://doi.org/10.1007/s10957-006-9020-0
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DOI: https://doi.org/10.1007/s10957-006-9020-0