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.
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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.
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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
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