Optimal Nonlinear Solutions for Reverse Stackelberg Games with Incomplete Information

The reverse Stackelberg game provides a suitable decision-making framework for hierarchical control problems like network pricing and toll design. We propose a novel numerical solution approach for systematic computation of optimal nonlinear leader functions, also known as incentives, for reverse Stackelberg games with incomplete information and general, nonconcave utility functions. In particular, we apply basis function approximation to the class of nonlinear leader functions, and treat the incentive design problem as a standard semi-infinite programming problem. A worked example is provided to illustrate the proposed solution approach and to demonstrate its efficiency.