Abstract
AbstractGovindan and Klumpp [7] provided a characterization of perfect equilibria using Lexicographic Probability Systems (LPSs). Their characterization was essentially finite in that they showed that there exists a finite bound on the number of levels in the LPS, but they did not compute it explicitly. In this note, we draw on two recent developments in Real Algebraic Geometry to obtain a formula for this bound.
Funder
Rheinische Friedrich-Wilhelms-Universität Bonn
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Software
Reference15 articles.
1. Basu, F., and Roy, M.-F.: Quantitative Curve Selection Lemma, arXiv Preprint (2018)
2. Blume, L.E., Brandenburger, A., Dekel, E.: Lexicographic probabilities and equilibrium refinements. Econometrica 59, 81–98 (1991)
3. Blume, L.E., Zame, W.R.: The algebraic geometry of perfect and sequential equilibria. Econometrica 62, 783–94 (1994)
4. Bochnak, J., Coste, M., Roy, M.-F.: Real algebraic geometry. Springer-Verlag, Berlin (1998)
5. Chen, Y., Dang, C.: A differentiable homotopy method to compute perfect equilibria. Springer, Mathematical Programming (2019)