Nonasymptotic mean-field games

Area of Science:

• Game Theory
• Mathematical Economics
• Computational Economics

Background:

• Traditional mean-field game theory assumes a very large number of players, approximating systems with a continuum of decision-makers.
• This continuum approximation is often impractical and meaningless for real-world networks with fewer entities.
• Existing models are limited in their applicability to smaller-scale or sparsely populated systems.

Purpose of the Study:

• To develop a generalized mean-field framework suitable for systems of any size, from large to small.
• To overcome the limitations of traditional mean-field approaches that rely on a continuum of players.
• To provide a more versatile tool for analyzing strategic interactions in diverse network structures.

Main Methods:

• Development of a novel mean-field framework accommodating a finite number of entities.
• Application of the framework to analyze dynamic auction models with asymmetric valuations.
• Extension of the framework to incorporate scenarios with spiteful bidders.

Main Results:

• The proposed mean-field framework demonstrates applicability to systems with a small number of entities, unlike traditional models.
• The framework successfully models complex scenarios such as dynamic auctions with heterogeneous participants.
• Illustrative examples confirm the framework's utility in analyzing non-standard game-theoretic situations.

Conclusions:

• The generalized mean-field framework offers a significant advancement over traditional models by including small-scale systems.
• This approach enhances the practical applicability of mean-field game theory in economics and other fields.
• The framework provides a robust foundation for future research on strategic interactions in networks of varying sizes.