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On the Generic Structure and Stability of Stackelberg Equilibria

  • Alberto BressanEmail author
  • Yilun Jiang
Article
  • 2 Downloads

Abstract

We consider a noncooperative Stackelberg game, where the two players choose their strategies within domains \(X\subseteq {{\mathbb {R}}}^m\) and \(Y\subseteq {{\mathbb {R}}}^n\). Assuming that the cost functions FG for the two players are sufficiently smooth, we study the structure of the best reply map for the follower and the optimal strategy for the leader. Two main cases are considered: either \(X=Y=[0,1]\), or \(X={{\mathbb {R}}}, Y={{\mathbb {R}}}^n\) with \(n\ge 1\). Using techniques from differential geometry, including a multi-jet version of Thom’s transversality theorem, we prove that, for an open dense set of cost functions \(F\in {{\mathcal {C}}}^2\) and \(G\in {{\mathcal {C}}}^3\), the Stackelberg equilibrium is unique and is stable w.r.t. small perturbations of the two cost functions.

Keywords

Noncooperative game Stackelberg equilibrium Stability Generic properties 

Mathematics Subject Classification

91A10 91B50 58K25 37C20 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA

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