Optimal Affine Leader Functions in Reverse Stackelberg Games

A generalizing analysis is made in order to ease the solvability of the generally complex single-leader-single-follower reverse Stackelberg game. This game is of a hierarchical nature and can therefore be implemented as a structure for multi-level decision-making problems, like in road pricing. In particular, a leader function of the affine type is analyzed in order to procure a systematic approach to solving the game to optimality. To this end, necessary and sufficient existence conditions for this optimal affine leader function are developed. Compared to earlier results reported in the literature, differentiability of the follower objective functional is relaxed, and locally strict convexity of the sublevel set at the desired reverse Stackelberg equilibrium is replaced with the more general property of an exposed point. Moreover, a full characterization of the set of optimal affine leader functions that is derived, which use in the case of secondary optimization objectives as well as for a constrained decision space, is illustrated.