非对称信息依赖型动态对策的结构均衡
Structured Equilibria for Dynamic Games with Asymmetric Information and Dependent Types
摘要：
我们考虑一个动态博弈与不对称信息，每个球员私下观察一个嘈杂的版本（隐藏）的世界V的状态，导致依赖私人的意见。我们研究了结构化的完美贝叶斯均衡，在他们的策略中使用私人信仰作为总结他们的观察历史的足够的统计数据。为结构化策略找到适当的充分统计量（状态）的主要困难来自这样一个事实，即参与者需要在其他参与者对V的私人信念上构建（私人）信念，这反过来又意味着需要构建一个无限的信念层次，从而使问题无法解决。我们发现，这是不是这样的：每个球员的信念对其他球员的信念V可以由她自己的信念V和一些适当定义的公共信念的特点。然后，我们专门这个设置的情况下，线性二次高斯（LQG）非零和游戏，我们的特征线性结构PBE，可以通过一个向后/向前算法类似于动态规划的标准LQG控制问题。然而，与标准LQG问题不同的是，卡尔曼滤波器所需的一些量是依赖于观测的，因此不能通过前向递归离线评估。
英文摘要：
We consider a dynamic game with asymmetric information where each player observes privately a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study structured perfect Bayesian equilibria that use private beliefs in their strategies as sufficient statistics for summarizing their observation history. The main difficulty in finding the appropriate sufficient statistic (state) for the structured strategies arises from the fact that players need to construct (private) beliefs on other players' private beliefs on V, which in turn would imply that an infinite hierarchy of beliefs on beliefs needs to be constructed, rendering the problem unsolvable. We show that this is not the case: each player's belief on other players' beliefs on V can be characterized by her own belief on V and some appropriately defined public belief. We then specialize this setting to the case of a Linear Quadratic Gaussian (LQG) non-zero-sum game and we characterize linear structured PBE that can be found through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, some of the required quantities for the Kalman filter are observation-dependent and thus cannot be evaluated off-line through a forward recursion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
