On the (in)efficiency of MFG equilibria

TL;DR

This paper investigates the efficiency of Nash equilibria in mean field games, identifying conditions for efficiency and quantifying inefficiencies when these conditions are not met.

Contribution

It introduces a structure condition determining when MFG equilibria are efficient and provides a quantitative analysis of inefficiencies otherwise.

Findings

Existence of a structure condition for efficient MFG equilibria

Quantification of inefficiency in non-fulfillment cases

Comparison of social costs between MFG equilibria and global planner solutions

Abstract

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this context, we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the game under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how inefficient MFG equilibria are.