Solving Multi-Follower Games

We consider bilevel programs where a single leader interacts with multiple followers who are coupled by a Nash equilibrium problem at the lower level. We generalize the value function reformulation to include multiple followers. This allows us to propose a convergent method based on the sequential convex approximation paradigm, and study the (exact or inexact) … Read more

A branch-and-bound algorithm for non-convex Nash equilibrium problems

This paper introduces a spatial branch-and-bound method for the approximate computation of the set of all epsilon-Nash equilibria of continuous box-constrained non-convex Nash equilibrium problems. We explain appropriate discarding and fathoming techniques, provide a termination proof for a prescribed approximation tolerance, and report our computational experience. Article Download View A branch-and-bound algorithm for non-convex Nash … Read more

A branch-and-prune algorithm for discrete Nash equilibrium problems

We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. … Read more