Journal
COMPUTATIONAL MANAGEMENT SCIENCE
Volume 2, Issue 1, Pages 21-56Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10287-004-0010-0
Keywords
Quasi-variational inequalities; leader-follower games; Nash equilibrium; electric power market modeling; oligopolistic competition; mathematical program with equilibrium constraints
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Funding
- National Science Foundation [CCR-0098013, ECS-0080577]
- Office of Naval Research [N00014-02-1-0286]
- Ministry of Education, Science, Culture and Sports of Japan
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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.
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