Solving Multi-Leader-Follower Games

Sven Leyffer (leyffermcs.anl.gov)
Todd Munson (tmunsonmcs.anl.gov)

Abstract: Multi-leader-follower games arise when modeling competition between two or more dominant firms and lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We 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.

Keywords: Nash games, Stackelberg games, nonlinear programming, nonlinear complementarity, NCP, MPEC, equilibrium problems with equilibrium constraints

Category 1: Complementarity and Variational Inequalities

Category 2: Applications -- OR and Management Sciences

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Preprint ANL/MCS-P1243-0405, Mathematics and Computer Science Division Argonne National Laboratory, Argonne, IL 60439, USA April 2005

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Entry Submitted: 04/26/2005
Entry Accepted: 05/03/2005
Entry Last Modified: 04/26/2005

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