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

Jong-Shi Pang () and Masao Fukushima ()

Computational Management Science, 2005, vol. 2, issue 1, 56 pages

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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Keywords: Quasi-variational inequalities; leader-follower games; Nash equilibrium; electric power market modeling; oligopolistic competition; mathematical program with equilibrium constraints (search for similar items in EconPapers)
Date: 2005
References: Add references at CitEc
Citations: View citations in EconPapers (111)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10287-004-0010-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:comgts:v:2:y:2005:i:1:p:21-56

Ordering information: This journal article can be ordered from
http://www.springer. ... ch/journal/10287/PS2

DOI: 10.1007/s10287-004-0010-0

Access Statistics for this article

Computational Management Science is currently edited by Ruediger Schultz

More articles in Computational Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().