A Class of Mean-field LQG Games with Partial Information

TL;DR

This paper develops a mean-field LQG game framework with partial information, including new filtering models where sensor functions depend on the state-average, providing decentralized strategies and epsilon-Nash equilibria.

Contribution

It introduces a novel partial information structure in mean-field LQG games, incorporating state-average dependent sensors and analyzing the limiting behavior of state filters.

Findings

Partial information models are practically relevant and mathematically tractable.

Filtering equations for individual states are derived with state-average dependence.

Decentralized strategies are obtained via Riccati equations without fixed-point analysis.

Abstract

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of large-population system when studying its dynamic optimizations. Unlike other large-population literature, this current paper possesses the following distinctive features. First, our setting includes the partial information structure of large-population system which is practical from real application standpoint. Specially, two cases of partial information structure are considered here: the partial filtration case (see Section 2, 3) where the available information to agents is the filtration generated by an observable component of underlying Brownian motion; the noisy observation case (Section 4) where the individual agent can access an additive white-noise observation on its own state. Also, it is new in filtering modeling that our sensor function may depend on the state-average. Second, in both cases, the limiting state-averages become random and the filtering equations to individual state should be formalized to get the decentralized strategies. Moreover, it is also new that the limit average of state filters should be analyzed here. This makes our analysis very different to the full information arguments of large-population system. Third, the consistency conditions are equivalent to the wellposedness of some Riccati equations, and do not involve the fixed-point analysis as in other mean-field games. The $\epsilon$-Nash equilibrium properties are also presented.