Solving multi-leader-common-follower games

Multi-leader-common-follower games arise when modelling two or more competitive firms, the leaders, that commit to their decisions prior to another group of competitive firms, the followers, that react to the decisions made by the leaders. These problems lead in a natural way to equilibrium problems...

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Bibliographic Details
Published in:Optimization methods & software Vol. 25; no. 4; pp. 601 - 623
Main Authors: Leyffer, Sven, Munson, Todd
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 01.08.2010
Taylor & Francis Ltd
Subjects:
equilibrium problems with equilibrium constraints
Leadership
Mathematical programming
mathematical programming with equilibrium constraints
Nash games
nonlinear complementarity problems
Nonlinear programming
Stackelberg games
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:Multi-leader-common-follower games arise when modelling two or more competitive firms, the leaders, that commit to their decisions prior to another group of competitive firms, the followers, that react to the decisions made by the leaders. These problems lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We develop a characterization of the solution sets for these problems and examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We demonstrate the practical viability of our approach by solving a range of medium-sized test problems.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556780903448052