Establishing the existence of Nash equilibria for partially observed
stochastic dynamic games is known to be quite challenging, with the
difficulties stemming from the noisy nature of the measurements available to
individual players (agents) and the decentralized nature of this information.
When the number of players is sufficiently large and the interactions among
agents is of the mean-field type, one way to overcome this challenge is to
investigate the infinite-population limit of the problem, which leads to a
mean-field game. In this paper, we consider discrete-time partially observed
mean-field games with infinite-horizon discounted cost criteria. Using the
technique of converting the original partially observed stochastic control
problem to a fully observed one on the belief space and the dynamic programming
principle, we establish the existence of Nash equilibria for these game models
under very mild technical conditions. Then, we show that the mean-field
equilibrium policy, when adopted by each agent, forms an approximate Nash
equilibrium for games with sufficiently many agents.

本文研究含有无穷个代理人的部分可观测的均场动态博弈，使用故意使原本的部分可观测随机控制问题变成一个置信度空间上的完全可观测问题的技术，建立了此类游戏模型的纳什均衡存在性，并证明了当代理人足够多时，采用均场均衡策略会形成近似纳什均衡。

带有均场交互的部分可观测随机博弈中的近似纳什均衡

Approximate Nash Equilibria in Partially Observed Stochastic Games with  Mean-Field Interactions

In this paper we study stochastic dynamic games with many players; these are
a fundamental model for a wide range of economic applications. The standard
solution concept for such games is Markov perfect equilibrium (MPE), but it is
well known that MPE computation becomes intractable as the number of players
increases. We instead consider the notion of stationary equilibrium (SE), where
players optimize assuming the empirical distribution of others' states remains
constant at its long run average. We make two main contributions. First, we
provide a rigorous justification for using SE. In particular, we provide a
parsimonious collection of exogenous conditions over model primitives that
guarantee existence of SE, and ensure that an appropriate approximation
property to MPE holds, in a general model with possibly unbounded state spaces.
Second, we draw a significant connection between the validity of SE, and market
structure: under the same conditions that imply SE exist and approximates MPE
well, the market becomes fragmented in the limit of many firms. To illustrate
this connection, we study in detail a series of dynamic oligopoly examples.
These examples show that our conditions enforce a form of "decreasing returns
to larger states"; this yields fragmented industries in the limit. By contrast,
violation of these conditions suggests "increasing returns to larger states"
and potential market concentration. In that sense, our work uses a fully
dynamic framework to also contribute to a longstanding issue in industrial
organization: understanding the determinants of market structure in different
industries.

研究多人随机动态游戏的稳态均衡和市场构造之间的关系，提出了解决 Markov 完美均衡计算不可行的问题的稳定均衡的概念，探讨了市场结构与稳态均衡之间的关系，以及该模型对不同产业市场构造的影响。