Stackelberg games with the third party
Yiming Jiang, Yawei Wei, Jie Xue

TL;DR
This paper explores the role of a third party in achieving stable Stackelberg equilibria across various game types, addressing time inconsistency and promoting cooperation through supervision and penalties.
Contribution
It introduces a third-party mechanism to ensure equilibrium stability in discrete-time, dynamic, and mean field Stackelberg games with learning followers.
Findings
Third-party supervision effectively prevents defection.
Different discount factors influence equilibrium stability.
Intervention proves practical and adaptable.
Abstract
In this paper, we introduce the third party to achieve the Stackelberg equilibrium with the time inconsistency in three different Stackelberg games, which are the discrete-time games, the dynamic games, and the mean field games. Here all followers are experiencing learning-by-doing. The role of a third party is similar to industry associations, they supervise the leader's implementation and impose penalties for the defection with the discount factor. Then we obtain different forms of discount factors in different models and effective conditions to prevent defection.These results are consistent and the third party intervention is effective and maneuverable in practice.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Holomorphic and Operator Theory · Mathematics and Applications
