Abstract
In this paper, extensions are presented for the open-loop Stackelberg equilibrium solution of n-person discrete-time affine-quadratic dynamic games of prespecified fixed duration to allow for an arbitrary number of followers and the possibility of algorithmic implementation. First we prove a general result about the existence of a Stackelberg equilibrium solution with one leader and arbitrarily many followers in n-person discrete-time deterministic infinite dynamic games of prespecified fixed duration with open-loop information pattern. Then this result is applied to affine-quadratic games. Thereby we get a system of equilibrium equations that can easily be used for an algorithmic solution of the given Stackelberg game.
An earlier version of this paper was presented at the 14th Annual SCE Conference on Computing in Econometrics and Finance in Paris, France, June 26–28, 2008. Financial support by the Jubilaeumsfonds der Oesterreichischen Nationalbank (project no. 12166) and by the EU Commission (project no. MRTN-CT-2006-034270 COMISEF) is gratefully acknowledged.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For all equations belonging to this theorem and its proof, i∈N and k∈{0,…,T−1} unless otherwise indicated.
- 2.
For all equations belonging to this corollary k∈{0,…,T−1} unless otherwise stated.
References
Başar, T., & Olsder, G. J. (1999). Dynamic noncooperative game theory (2nd ed.). Philadelphia: SIAM.
Behrens, D. A., Hager, M., & Neck, R. (2003). OPTGAME 1.0: a numerical algorithm to determine solutions for two-person difference games. In R. Neck (Ed.), Modelling and control of economic systems 2002 (pp. 47–58). Oxford: Pergamon.
Cohen, D., & Michel, P. (1988). How should control theory be used to calculate a time-consistent government policy? Review of Economic Studies, 55, 263–274.
Dockner, E. J., & Neck, R. (2008). Time consistency, subgame perfectness, solution concepts and information patterns in dynamic models of stabilization policies. In R. Neck, C. Richter, P. Mooslechner (Eds.), Advances in computational economics: Vol. 20. Quantitative economic policy (pp. 51–101). Berlin: Springer.
Dockner, E. J., Jorgensen, S., Long, N. V., & Sorger, G. (2000). Differential games in economics and management science. Cambridge: Cambridge University Press.
Holly, S., & Hughes Hallet, A. (1989). Optimal control, expectations and uncertainty. Cambridge: Cambridge University Press.
Hungerländer, P., & Neck, R. (2009). A generalization of the open-loop Stackelberg equilibrium solution for affine-quadratic dynamic games (Research Report). Klagenfurt University.
Kydland, F. (1975). Noncooperative and dominant player solutions in discrete dynamic games. International Economic Review 16, 321–335.
Kydland, F. E., & Prescott, E. C. (1977). Rules rather than discretion: the inconsistency of optimal plans. Journal of Political Economy 85, 473–523.
Petit, M. L. (1990). Control theory and dynamic games in economic policy analysis. Cambridge: Cambridge University Press.
Simaan, M., & Cruz, J. B. (1973a). On the Stackelberg strategy in nonzero sum games. Journal of Optimization Theory and Applications, 11, 533–555.
Simaan, M., & Cruz, J. B. (1973b). Additional aspects of the Stackelberg strategy in nonzero sum games. Journal of Optimization Theory and Applications, 11, 613–626.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hungerländer, P., Neck, R. (2011). An Algorithmic Equilibrium Solution for n-Person Dynamic Stackelberg Difference Games with Open-Loop Information Pattern. In: Dawid, H., Semmler, W. (eds) Computational Methods in Economic Dynamics. Dynamic Modeling and Econometrics in Economics and Finance, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16943-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-16943-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16942-7
Online ISBN: 978-3-642-16943-4
eBook Packages: Business and EconomicsEconomics and Finance (R0)