Reverse Stackelberg Games, Part II: Results And Open Issues.pdf

This technical report by Delft University of Technology's Delft Center for Systems and Control summarizes key developments in reverse Stackelberg games, a hierarchical control framework.

Key Findings:

The paper categorizes findings based on various aspects of the reverse Stackelberg game:

Static vs Dynamic: While static results are scarce, dynamic cases mirror real-world applications better.
Open-loop vs Closed-loop: Most existing work focuses on open-loop strategies, with fewer exploring closed-loop or feedback control structures akin to traditional Stackelberg games.
Information Structure: Studies often assume full knowledge or deterministic information, but stochastic scenarios and partial, non-nested information are also important areas of research.
Sensitivity Analysis: Analyzing the robustness of leader functions to changes in follower behavior is crucial for practical applications.
Multi-level Games: Research has begun to extend the framework to multi-level games with multiple leaders and followers on each level.

Key Contributions:

The report highlights:

Static Analysis: Early work by [4] and [11] provides foundational insights into static reverse Stackelberg games, focusing on Pareto optimality and affine leader strategies.
Dynamic Open-loop Strategies: [15] derives sufficient conditions for the existence of optimal affine leader functions in dynamic open-loop settings with specific function classes.
Uncertainty and Stochastic Games: While less explored, there is a growing need for results addressing uncertainty and stochasticity inherent in real-world scenarios.

Open Issues:

The authors identify several areas requiring further research:

Closed-loop and Feedback Strategies: Developing closed-loop strategies that account for follower dynamics and feedback loops remains challenging but crucial for practical implementation.
Stochastic and Partial Information: Extending results to handle stochasticity and partial, non-nested information is essential for modeling uncertainty in real-world applications.
Sensitivity and Robustness: Analyzing the sensitivity of leader functions to variations in follower behavior will enhance understanding of robustness and control design.
Multi-level Games with Complex Interactions: Further research is needed to develop effective strategies and analysis methods for multi-level reverse Stackelberg games, where complex interactions between leaders and followers at different levels arise.