Hypergraphon mean field games

Area of Science:

• Complex Systems
• Game Theory
• Network Science

Background:

• Traditional mean field games often focus on pairwise interactions.
• Modeling large-scale systems with higher-order interactions is computationally challenging.
• Hypergraphs offer a framework to represent complex relationships beyond pairs.

Purpose of the Study:

• To develop a novel framework for mean field games on hypergraphs.
• To extend the theory to multi-layer systems and analyze large-scale dynamical agents.
• To establish theoretical guarantees and computational methods for hypergraphon mean field games.

Main Methods:

• Utilizing the theory of mean field games.
• Employing hypergraphons as limits of large hypergraphs.
• Extending existing numerical and learning algorithms for equilibrium computation.

Main Results:

• Established the first mean field games on hypergraphs.
• Proved the well-foundedness, existence, and approximate Nash properties of hypergraphon mean field games.
• Developed and verified computational algorithms for hypergraphon mean field equilibria.

Conclusions:

• The proposed approach effectively models large-scale multi-agent systems with complex interactions.
• Hypergraphon mean field games provide a robust theoretical and computational tool.
• The framework is applicable to real-world problems like social dynamics and epidemic control.