论文标题
具有不对称信息和依赖类型的动态游戏的结构化平衡
Structured Equilibria for Dynamic Games with Asymmetric Information and Dependent Types
论文作者
论文摘要
我们考虑了一个动态游戏，其中每个玩家都会观察到世界V的（隐藏）状态的嘈杂版本，从而导致了依赖的私人观察。我们研究结构化的完美贝叶斯平衡，这些平衡在其策略中使用私人信念作为足够的统计数据来总结其观察史。找到适当的结构化策略的适当统计量（状态）的主要困难是由于玩家需要对其他参与者对V的私人信念建立（私人）信念，这反过来又暗示需要建立对信念的无限层次结构，从而使问题无法解决。我们表明并非如此：每个玩家对其他玩家对V的信念的信念的特征是她自己对V和一些适当定义的公众信仰。然后，我们将此设置专门为线性二次高斯（LQG）非零和游戏的情况，我们表征了线性结构化PBE，可以通过类似于标准LQG控制问题的动态编程的向后/正向算法找到。但是，与标准的LQG问题不同，卡尔曼过滤器的某些所需数量依赖于观察，因此无法通过正向递归评估离线。
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.
