Single-leader-multi-follower games

Are Single-Leader-Multi-Follower Problems Particular Cases of Bilevel Optimization?

Categories Bilevel Optimization, Game Theory, Global Optimization Tags , , ,

For more than 20 years, single-leader multi-follower (SLMF) problems have been treated as a more difficult class of problems in comparison to bilevel optimization. In this work we challenge this common belief, studying whether SLMF problems can be reformulated as equivalent bilevel optimization problems. We consider both optimistic and pessimistic formulations. For the optimistic case … Read more

A Tutorial on Solving Single-Leader-Multi-Follower Problems using SOS1 Reformulations

Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Game Theory Tags , , ,

In this tutorial we consider single-leader-multi-follower games in which the models of the lower-level players have polyhedral feasible sets and convex objective functions. This situation allows for classic KKT reformulations of the separate lower-level problems, which lead to challenging single-level reformulations of MPCC type. The main contribution of this tutorial is to present a ready-to-use … Read more