Stackelberg games with the third party

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.