Continuous Aggregative LQG Games with Delayed Discrete Observations

TL;DR

This paper analyzes mean field game equilibria where agents observe population information with delays, providing conditions for Nash equilibrium existence and evaluating the impact of observation delays.

Contribution

It introduces a framework for continuous aggregative LQG games with delayed discrete observations and characterizes agent responses under this structure.

Findings

Conditions for Nash equilibrium existence are established.

The cost increase due to observation delay is quantified.

The impact of delayed observations on equilibrium strategies is analyzed.

Abstract

Mean field game equilibria are predicated on the assumption of immediate pairwise interactions within a population of homogeneous agents with asymptotically vanishing influence as population size increases. However, in many real-world cases, agents receive population-level information with a delay. In this paper, we characterize agent best responses under an information exchange structure whereby agents observe the empirical mean state only at discrete time instants with some delay. Sufficient conditions are presented for the existence of a Nash equilibrium within a finite population of agents, and the cost increase due to delayed discrete empirical mean observations relative to zero-latency discrete observations and continuous global-state observations is also evaluated.