Achieving Hierarchy-Free Approximation for Bilevel Programs With Equilibrium Constraints

Understand

In this paper, we develop an approximation scheme for solving bilevel programs with equilibrium constraints, which are generally difficult to solve.

• Among other things, calculating the first-order derivative in such a problem requires differentiation across the hierarchy, which is computationally intensive, if not prohibitive.
• To bypass the hierarchy, we propose to bound such bilevel programs, equivalent to multiple-followers Stackelberg games, with two new hierarchy-free problems: a $T$-step Cournot game and a $T$-step monopoly model.
• Since they are standard equilibrium or optimization problems, both can be efficiently solved via first-order methods.