Computational Management Science

, Volume 2, Issue 1, pp 21–56

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


DOI: 10.1007/s10287-004-0010-0

Cite this article as:
Pang, JS. & Fukushima, M. Computational Management Science (2005) 2: 21. doi:10.1007/s10287-004-0010-0


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 

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

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