Abstract
This paper addresses the problem whether a cooperative agreement, made at the start of a game, can be sustained over time. The players can reopen negotiations or reconsider their strategies at any instant of time during the play of the game. Research in differential games has addressed the question of individual rationality over time under headings such as time consistency, dynamic stability, agreeability, or acceptability, and often in an applied context. The question is whether a bargained solution, satisfying individual rationality at the start of the game, will remain individually rational as the state vector evolves over time. The paper collects various research works on intertemporal individual rationality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Başar, T. and G.J. Olsder, Dynamic Noncooperative Game Theory. Academic Press. New York, 1995.
Chiarella, C., M.C. Kemp, N.V. Long, and K. Okuguchi, “On the Economics of International Fisheries”, International Economic Review 25, 1984, 85–92.
Dockner, E., S. Jørgensen, N. Van Long, and G. Sorger, Differential Games in Economics and Management Science. Cambridge University Press, Cambridge, U.K., 2000.
Dockner, E., G. Feichtinger, and S. Jørgensen, “Tractable Classes of Non Zero-Sum Open-Loop Nash Differential Games”, Journal of Optimization Theory and Applications 45, 1985, 179–198.
Dutta, P.K., “A Folk Theorem for Stochastic Games”. Journal of Economic Theory 66, 1995, 1–32.
Friedman, J.W., Game Theory with Applications to Economics. Oxford University Press, Oxford, U.K., 1986.
Gao, L., A. Jakubowski, M.B. Klompstra, and G.J. Olsder, “Time-Dependent Cooperation in Games”, in: T.S. Başar and P. Bernhard (eds.), Differential Games and Applications. Springer-Verlag, Berlin, 1989.
Haurie, A., “A Note on Nonzero-sum Differential Games with Bargaining Solution”. Journal of Optimization Theory and Applications 18, 1976, 31–39.
Haurie, A. and G. Zaccour, “A Differential Game Model of Power Exchange between Interconnected Utilities”. Proceedings of the 25th IEEE Conference on Decision and Control, Athens, Greece, December 1986, 262–266.
Haurie, A. and G. Zaccour, “A Game Programming Approach to Efficient Management of Interconnected Power Networks”, in: R.P. Hämäläinen and H. Ehtamo (eds.), Differential Games — Developments in Modelling and Computation. Springer-Verlag, Berlin, 1991.
Jørgensen, S. and G. Zaccour, ‘Time Consistent Side Payments in a Dynamic Game of Downstream Pollution”. To appear in Journal of Economic Dynamics and Control, 2001.
Kaitala, V. and M. Pohjola, “Optimal Recovery of a Shared Resource Stock: A Differential Game Model with Efficient Memory Equilibria”. Natural Resource Modeling 3, 1988, 91–118.
Kaitala, V. and M. Pohjola, “Economic Development and Agreeable Redistribution in Capitalism: Efficient Game Equilibria in a Two-class Neoclassical Growth Model”. International Economic Review 31, 1990,421–437.
Kaitala, V. and M. Pohjola, “Sustainable International Agreements on Greenhouse Warming: A Game Theory Study”, in: Control and Game-Theoretic Models of the Environment, C. Carraro and J. A. Filar (eds.). Annals of the International Society of Dynamic Games Vol. 2, 1995, 67–87.
Kydland, F.E. and E.C. Prescott, “Rules Rather Than Discretion: The Inconsistency of Optimal Plans”. Journal of Political Economy 85, 1977, 473–493.
Liu, P.T., “Non-Zero Sum Differential Games with Bargaining Solution”, Journal of Optimization Theory and Applications 11, 3, 1973, 284–292.
Miller, M. and M. Salmon, “Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies”. The Economic Journal. Supplement. Vol. 95, 1985, 124–17.
Petrosjan, L.A. and N.A. Zenkevich, Game Theory. World Scientific, Singapore, 1996.
Petrosjan, L.A., “Agreeable Solutions in Differential Games”. International Journal of Mathematics, Game Theory and Algebra 7, 2/3, 1997, 165–177.
Petrosjan, L.A. and G. Zaccour, “Time-Consistent Shapley Value Allocation of Pollution Cost Reduction”, mimeo, 2000.
Rincon-Zapatero, J.P., G. Martfn-Herran, and J. Martinez, “Identification of Efficient Subgame-perfect Nash Equilibria in a Class of Differential Games”. Journal of Optimization Theory and Applications 104, 2000, 235–242.
Tolwinski, B., A. Haurie and G. Leitmann, “Cooperative Equilibria in Differential Games”. Journal of Mathematical Analysis and Applications 119, 1986, 182–202.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Jørgensen, S., Zaccour, G. (2002). Time Consistency in Cooperative Differential Games. In: Zaccour, G. (eds) Decision & Control in Management Science. Advances in Computational Management Science, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3561-1_19
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3561-1_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4995-0
Online ISBN: 978-1-4757-3561-1
eBook Packages: Springer Book Archive