Hierarchical Structures and Leadership Design in Mean-Field-Type Games with Polynomial Cost
Abstract
This article presents a class of hierarchical mean-field-type games with multiple layers and non-quadratic polynomial costs. The decision-makers act in sequential order with informational differences. We first examine the single-layer case where each decision-maker does not have the information about the other control strategies. We derive the Nash mean-field-type equilibrium and cost in a linear state-and-mean-field feedback form by using a partial integro-differential system. Then, we examine the Stackelberg two-layer problem with multiple leaders and multiple followers. Numerical illustrations show that, in the symmetric case, having only one leader is not necessarily optimal for the total sum cost. Having too many leaders may also be suboptimal for the total sum cost. The methodology is extended to multi-level hierarchical systems. It is shown that the order of the play plays a key role in the total performance of the system. We also identify a specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play. In the heterogeneous case, it is shown that the total cost is significantly affected by the design of the hierarchical structure of the problem.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 06, 2020
- Source ID
- 10.3390/g11030030
Entities
People
- Hamidou Tembine
- Julián Barreiro-Gomez
- Salah Eddine Choutri
- Zahrate El Oula Frihi
Organizations
- United States Air Force