Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games (2005 paper)

Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games (2005 paper)

0.00 Avg rating0 Votes
Article ID: iaor200971041
Country: Germany
Volume: 2
Issue: 1
Start Page Number: 21
End Page Number: 56
Publication Date: Jan 2005
Journal: Computational Management Science
Authors: ,
Abstract:

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.

Reviews

Required fields are marked *. Your email address will not be published.