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

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  • Jong-Shi Pang

    ()

  • Masao Fukushima

    ()

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    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

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    File URL: http://hdl.handle.net/10.1007/s10287-004-0010-0
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    Bibliographic Info

    Article provided by Springer in its journal Computational Management Science.

    Volume (Year): 2 (2005)
    Issue (Month): 1 (01)
    Pages: 21-56

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    Handle: RePEc:spr:comgts:v:2:y:2005:i:1:p:21-56

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    Web page: http://www.springerlink.com/link.asp?id=111894

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    Related research

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

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