The incentive controllability and ε-incentive controllability in an inverse Stackelberg game

The inverse Stackelberg game is as common and significant as Nash games and has found its applications in many fields such as economics and mechanism design. However, it is admittedly difficult to solve equilibrium of general inverse Stackelberg game or to analyse it. One way to study the game is to find the team solution first, or equally to study the incentive design problem. This paper explores the incentive controllability and ε-incentive controllability of the inverse Stackelberg game with single leader and single follower for a specific emission reduction game. Then it is proved that if the player's action is assumed to be nonnegative, the game is neither incentive controllable nor ε-incentive controllable; however, if the range of player' action is expanded to ℝ, the game is not incentive controllable yet but is ε-incentive controllable and the ε-strategy for the leader can be obtained by trembling a quadratic function. Numerical illustration and theoretical discussion are provided to show the complexity inside the problem, which may be inspiring for the future work.