Computational Management Science

, Volume 2, Issue 1, pp 21–56 | Cite as

Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games

  • Jong-Shi Pang
  • Masao Fukushima


The noncooperative multi-leader-follower game can be formulated as a generalized Nash equilibrium problem where each player solves a nonconvex mathematical program with equilibrium constraints. Two major deficiencies exist with such a formulation: One is that the resulting Nash equilibrium may not exist, due to the nonconvexity in each player’s problem; the other is that such a nonconvex Nash game is computationally intractable. In order to obtain a viable formulation that is amenable to practical solution, we introduce a class of remedial models for the multi-leader-follower game that can be formulated as generalized Nash games with convexified strategy sets. In turn, a game of the latter kind can be formulated as a quasi-variational inequality for whose solution we develop an iterative penalty method. We establish the convergence of the method, which involves solving a sequence of penalized variational inequalities, under a set of modest assumptions. We also discuss some oligopolistic competition models in electric power markets that lead to multi-leader-follower games.


Quasi-variational inequalities leader-follower games Nash equilibrium electric power market modeling oligopolistic competition mathematical program with equilibrium constraints 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroy, New YorkUSA
  2. 2.Department of Applied Mathematics and PhysicsGraduate School of Informatics, Kyoto UniversityKyotoJapan

Personalised recommendations