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